Doctor Thesis-Eirik Falck Da Silva

Computational Chemistry Study

of Solvents for Carbon Dioxide

Absorption

Eirik Falck da Silva

Doctoral Thesis

Norwegian University of

Science and Technology

Fakultet for Naturvitenskap og Teknologi

Institutt for Kjemisk Prosessteknologi

Trondheim, August 2005

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Contents List of Papers................................................................................................................5 Abstract.........................................................................................................................7 Acknowledgements ......................................................................................................9 1 Introduction........................................................................................................11

1.1 Purpose.................................................................................................... 11 1.2 Global Warming...................................................................................... 12 1.3 Mitigation................................................................................................ 13

1.3.1 Background ..................................................................................... 13 1.3.2 CO2 Capture and Storage ................................................................ 13

2 CO2 Absorption..................................................................................................17 2.1 Introduction............................................................................................. 17 2.2 Solvents................................................................................................... 19 2.3 Challenges............................................................................................... 20 2.4 Current Understanding of the CO2 Absorption Process.......................... 21

3 Computational Chemistry.................................................................................25 3.1 Introduction............................................................................................. 25 3.2 Quantum Mechanics ............................................................................... 26

3.2.1 Introduction..................................................................................... 26 3.2.2 The Born-Oppenheimer Approximation......................................... 28 3.2.3 Hartree-Fock Self-Consistent Field Method................................... 28 3.2.4 Post-HF Methods ............................................................................ 28 3.2.5 Density Functional Theory.............................................................. 29 3.2.6 Basis Sets ........................................................................................ 30 3.2.7 Basis Set Superposition Error ......................................................... 31 3.2.8 Temperature .................................................................................... 32 3.2.9 Performance .................................................................................... 32

3.3 Molecular Mechanics.............................................................................. 33 3.3.1 Introduction..................................................................................... 33 3.3.2 Force Field Parameterization .......................................................... 35 3.3.3 Atomic Charges............................................................................... 36 3.3.4 Polarizable Force Fields.................................................................. 38

3.4 Simulations ............................................................................................. 39 3.4.1 Introduction..................................................................................... 39 3.4.2 Free Energy Perturbations............................................................... 41

3.5 QM/MM.................................................................................................. 43 3.6 Computational Chemistry and Experiment............................................. 43 3.7 Review of Computational Chemistry Work on CO2 Absorption............ 45

4 Modeling of Solvation Energy...........................................................................47 4.1 Introduction............................................................................................. 47 4.2 The liquid state........................................................................................ 48

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4.3 Statistical Mechanics .............................................................................. 49 4.4 Models to Calculate the Free Energy of Solution ................................... 52

4.4.1 Introduction..................................................................................... 52 4.4.2 Equation of State and Lattice Models ............................................. 53 4.4.3 Continuum Models.......................................................................... 56 4.4.4 Molecular Simulation...................................................................... 62 4.4.5 RISM and RISM-SCF..................................................................... 63 4.4.6 Supermolecule Approach................................................................ 64 4.4.7 Hybrids of Computational Chemistry approaches .......................... 65 4.4.8 Descriptor Models........................................................................... 66 4.4.9 Other Models................................................................................... 67 4.4.10 Hybridization of Gibbs Energy Models and Computational Chemistry Based Models ................................................................................ 68

4.5 Comparison of Methods to Calculate the Free Energy of Solution ........ 69 4.5.1 Methods........................................................................................... 69 4.5.2 The Basicity .................................................................................... 71 4.5.3 Amines ............................................................................................ 72 4.5.4 Results............................................................................................. 73 4.5.5 Conclusion ...................................................................................... 79

5 Reaction Mechanisms and Equilibrium...........................................................81 5.1 Introduction............................................................................................. 81 5.2 Reaction Mechanisms ............................................................................. 81

5.2.1 Introduction..................................................................................... 81 5.2.2 Bicarbonate Formation.................................................................... 82 5.2.3 Carbamate formation....................................................................... 84 5.2.4 Bases ............................................................................................... 87 5.2.5 Alcohol-Group Bonding to CO2 ..................................................... 87 5.2.6 Carbamate as Reaction Intermediate............................................... 88 5.2.7 Molecules with Multiple Amine Functionalities ............................ 89 5.2.8 Shuttle Mechanism.......................................................................... 91 5.2.9 Summary and Conclusion ............................................................... 92

5.3 Determining Equilibrium ........................................................................ 94 5.3.1 Equilibrium and Kinetics ................................................................ 94 5.3.2 Temperature Dependency of Equilibrium Constants...................... 95 5.3.3 Activity Coefficients ....................................................................... 96 5.3.4 Process Energy Consumption ......................................................... 97 5.3.5 Summary ......................................................................................... 98

6 Other Solvent Properties ...................................................................................99 6.1 Introduction............................................................................................. 99 6.2 Solubility in Water .................................................................................. 99 6.3 Solvent Degradation.............................................................................. 100 6.4 Corrosion............................................................................................... 101

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6.5 Foaming ................................................................................................ 102 6.6 Toxicology ............................................................................................ 103 6.7 Cost ....................................................................................................... 103 6.8 Precipitations......................................................................................... 104

7 Present and Potential Solvents........................................................................105 7.1 Introduction........................................................................................... 105 7.2 Solvents in Use ..................................................................................... 105

7.2.1 Ethanolamine ................................................................................ 105 7.2.2 Tertiary Amines ............................................................................ 106 7.2.3 Sterically Hindered Amines .......................................................... 106 7.2.4 Multiple Amine Functionalities .................................................... 107 7.2.5 Ionic solvents ................................................................................ 107 7.2.6 Patented Solvents .......................................................................... 107

7.3 Ideal Solvent Properties ........................................................................ 108 7.3.1 Equilibrium Constants .................................................................. 108 7.3.2 Other Properties ............................................................................ 110

7.4 Comparison with Ethanolamine............................................................ 111 7.5 Conclusion ............................................................................................ 111

8 Future Work.....................................................................................................113 8.1 Continuation of the Present Research ................................................... 113 8.2 Other Applications of Present Work..................................................... 113 8.3 Beyond Amines..................................................................................... 114

References .................................................................................................................115

5

List of Papers I. da Silva, E. F. and Svendsen, H. F. (2003) Prediction of the pKa Values of

Amines Using ab Initio Methods and Free Energy Perturbations Ind. Eng. Chem. Res. 42, 4414-4421.

II. da Silva, E. F. and Svendsen, H. F. (2004) Ab Initio study of the reaction of

carbamate formation from CO2 and alkanolamines Ind. Eng. Chem. Res. 43, 3413-3418.

III. da Silva, E. F. (2004) Use of Free Energy Simulations to predict Infinite

Dilution Activity Coefficients Fluid Phase Eq. 221, 15-24. IV. da Silva, E. F. (2005) Comparison of Quantum Mechanical and Experimental

Gas Phase Basicities of Amines J. Phys. Chem. A 109, 1603-1607.

V. da Silva, E. F. and Svendsen, H. F. (2005) Study of the Carbamate Stability of Amines Using ab Initio Methods and Free-Energy Perturbations, Accepted in Ind. Eng. Chem. Res.

VI. da Silva, E. F., Kuznetsova, T. and Kvamme, B. (2005) Molecular Dynamics

Study of Ethanolamine as a Pure Liquid and in Aqueous Solution. VII. da Silva, E. F., Yamazaki, T. and Hirata, F. (2005) Comparison of Solvation

Models in the Calculation of Amine Basicity.

7

Abstract Absorption with aqueous amine solvents is at present the most viable technology

for CO2 capture. While this is a proven technology, efforts are ongoing to improve

it in order to make it a more attractive technology for large scale use to reduce CO2

emissions. Finding solvents with better properties is one approach to improving the

technology.

In this thesis methods in computational chemistry are used to improve the

understanding of the chemistry of CO2 absorption in amine-water systems. The

work is also intended to provide models that can be used to predict the performance

of new solvents. Such predictive models are intended to facilitate the screening for

new solvents.

The main focus of the computational chemistry work has been to model solvent

effects. Most of the work has been based on use of quantum mechanical

calculations to determine gas phase properties and different models to determine

the solvation energy. Most of the solvation energy calculations have been based on

molecular simulations and continuum models. In addition solvation energies

calculated with the RISM-SCF model have been studied.

The reaction mechanisms of the process have been studied in detail. Calculations

have been used to attempt to resolve uncertainties regarding mechanisms. The

work is in most cases in agreement with the consensus in the literature, but it is

concluded that carbamate formation is most likely to be a single-step mechanism.

From the study of reaction mechanisms it is concluded that the reactivity of an

amine solvent with CO2 is governed by two equilibrium constants: the base

stability and carbamate stability.

These two equilibrium constants have been modeled with gas phase quantum

mechanical calculations and different solvation models. Comparison with

experimental data suggests that both equilibrium constants can be modeled with a

8

semi-quantitative accuracy. The models are not entirely accurate but do mostly

capture trends observed in experimental data.

In addition to the equilibrium constants there are other properties that may affect

the overall performance and viability of a solvent in large scale industrial use.

These properties are also discussed and the possibility of modeling them is

assessed.

The ideal values for the main equilibrium constants are unknown and the present

work does therefore not reach any specific conclusions on what the ideal solvent is.

This thesis does however offer a fairly detailed plan of how to find optimal

solvents and tools to carry out the screening.

9

Acknowledgements I would like to express my gratitude to all those people that in different ways have

helped me with my work on this doctor thesis.

First of all I would like to thank Professor Hallvard Svendsen for giving me the

opportunity to do this work. I am also grateful to him for continuous support,

interesting discussions and giving me freedom in choosing how to approach

different issues. I would also like to thank people in the Department of Chemical

Engineering, in particular in the reactor technology group, for providing a good

working environment. Special thank goes to Karl Anders Hoff and Jana

Poplsteinova Jakobsen for helping to introduce me to the field of gas processing.

My own work has been based on theory and models not studied in the chemical

engineering department. I have therefore often relied on help from researchers at

other groups and institutions.

At NTNU I would especially thank Professor Per-Olof Åstrand at the Department

of Chemistry for insight and discussions on computational chemistry.

Professor Bjørn Kvamme and Tatyana Kuznetsova at the University of Bergen

have been of great help in understanding, and working with, molecular simulation.

Professor Fumio Hirata and Takeshi Yamazaki at the Institute for Molecular

Science in Okazaki, Japan, have helped me with use and understanding of RISM

models. I am also grateful to Professor Hirata for being a very good host during my

visit to the Institute for Molecular Science.

I should also like to thank Professor Bjørn Hafskjold and Yasuo Oishi for first

introducing me to computational chemistry.

I am also grateful to numerous reviewers that have often provided constructive

criticism of my work.

Finally I would like to express special thanks to Mami, for love and support.

1 Introduction

11

1 Introduction Considering these and many other major and still growing impacts of human

activities on earth and atmosphere, and at all, including global, scales, it seems to

us more than appropriate to emphasize the central role of mankind in geology and

ecology by proposing to use the term 'anthropocene' for the current geological

epoch.

Paul J. Crutzen and Eugene F. Stormer

1.1 Purpose

The main aim of my thesis has been to contribute to the selection of optimal

solvents for CO2 capture from exhaust gases. The main tools of the work have been

various forms of computational chemistry. Selection of solvents for CO2 capture is

not a simple task. There are a number of properties that contribute to determine if a

solvent can be applied economically at an industrial scale. At the same time it is

not a priori given what the ideal properties are. Extensive and time-consuming

experimental work is also required to draw confident conclusions on the viability

of a given solvent. The process of solvent selection or design can perhaps in some

ways be compared to the process of drug design.

Computational chemistry has come to play a significant role in drug design, and

my ambition with this work has been to apply computational chemistry in a similar

fashion in CO2 capture. This work can not resolve all issues regarding solvent

selection, rather it is a part of a larger project where different modeling and

experimental tools are applied together. I have attempted to focus my work on the

central issues where computational chemistry can contribute the most to the

process or solvent selection. Part of the work has gone into making predictions of

properties that can be used to find promising solvent molecules. Another part of the

1 Introduction

12

work has been to contribute to the general understanding of the chemistry of the

systems.

This thesis has three main parts. The first chapters deal with the how-and-why of

this work. First the issue of global warming and mitigation is briefly presented in

the present chapter. An introduction is then given to amine-based CO2 absorption,

the technology which is the topic of the present work. Then computational

chemistry is presented, with special attention given to issue of modeling energies in

solution.

The second part is a set of chapters drawing conclusions from the present work

and looking at remaining issues. At the end is included the papers with the results

of research carried out as a part of this thesis. Most of the actual research findings

are in the papers.

1.2 Global Warming

The United Nations Panel on Climate Change has concluded that if no steps are

taken, human emissions of greenhouse-gases are likely to result in a warming of

1.4 to 5.8 °C over the next 100 years (IPCC 2001a). Human emissions are already

believed to be affecting the climate, and to have been the main cause of observed

warming during the last century. While it is almost certain that our emissions of

greenhouse-gases will result in the planet becoming warmer, the specific

consequences for life on our planet are more difficult to predict. It has been

observed by some that what we are doing amounts to carrying out a laboratory

experiment with our entire planet. Some of the more likely consequences are

stronger heat-waves, changing precipitation patterns, disappearing glaciers, loss of

biodiversity and rising sea levels (IPCC 2001b). More recent work such as the

Arctic Climate Impact Assessment Report (ACIA 2004) strengthens these

conclusions.

1 Introduction

13

1.3 Mitigation

1.3.1 Background

The issue of anthropogenic global warming leads us to the question of what, if

anything, we can do to combat it. The answer is to reduce our emissions of

greenhouse gases. While the answer is simple there is a significant challenge

involved in carrying out such reductions. Consumption of fossil fuels is at present a

necessity in the industrialized world. Use of fossil fuels inevitably leads to carbon

dioxide (CO2) being formed and CO2 is the greenhouse gas responsible for most of

the anthropogenic global warming (IPCC 2001a). As new countries develop, their

consumption of energy and CO2 emissions are expected to increase.

There are three main alternatives to reducing our CO2 emissions without

hampering economic growth (Haug 2004). One is to use energy more efficiently,

thereby reducing the energy consumption. The second option is to change to

consumption of renewable energy sources and the final option is to burn fossil fuels

while capturing and storing the CO2 instead of releasing it unto the atmosphere.

None of these options are by themselves likely to be enough to stabilize our

emissions of CO2 and the viable way forward is therefore likely to be a

combination of these approaches (IPCC 2001c, Herzog et al. 2000 and Kuuskra et.

al 2004). The option of burning fossil fuels while storing the CO2 instead of

releasing it unto the atmosphere is referred to as “CO2 capture and storage”,

“Carbon capture and storage” or “CO2 sequestration”.

1.3.2 CO2 Capture and Storage

Combustion of fossil fuels takes place as a set of reactions between oxygen and

hydrocarbons with CO2 as one of the products. Usually the reaction is carried out,

not with pure oxygen, but with air as a reactant. The exhaust gas that is produced

resembles air but with a higher concentration of CO2. The total amount of exhaust

1 Introduction

14

gas produced is very large and to store all of it is not an option (Thambimuthu and

Davidson 2004). The CO2 must therefore be separated from the other exhaust gas

components. Once the CO2 has been isolated it can be transported and stored. The

main option for storage being explored at present is geological storage, i.e. to pump

the CO2 in to geological formations below the earth’s surface (Hepple and Benson

2005). The most demanding part of this approach is the capture, how to separate

the CO2 from other exhaust gas components. Other aspects such as compression of

the gas and transport do however also contribute to the overall cost.

There are a number of technologies available for capturing CO2. The technologies

vary in complexity, degree of maturity and cost. The technologies can be separated

into different categories (Thambimuthu and Davidson 2004 and Bolland 2004), a

overview is given in Figure 1.1.

Figure 1.1 Technologies for CO2 capture (Bolland 2004).

1 Introduction

15

Technologies based on capturing the CO2 from the exhaust gas are referred to as

post-combustion technologies. Technologies based on using pure oxygen as a fuel

are called oxyfuel processes. Finally there are technologies based on converting

hydrocarbons to hydrogen and CO2. This approach is called pre-combustion.

Another classification of separation technologies is presented in Figure 1.2.

Figure 1.2 Technologies for CO2 capture (Rao and Rubin 2002).

The present thesis deals with chemical absorption of CO2, this technology is today

the most important post-combustion CO2 capture technology. Of all the available

CO2 capture technologies this also represents at present the most efficient

technology for capturing CO2. This in part reflects technological maturity, the

technology having been patented for natural gas sweetening as early as 1930 (Kohl

and Nielsen 1997). It has also been used in small-scale removal of CO2 from

exhaust gas (Reddy et al. 2003 and Yagi et al. 2004). Chemical absorption is also a

technology that can be fairly easily installed. Existing power-plants can be

retrofitted with equipment for chemical absorption (Thambimuthu and Davidson

2004); whereas many other technologies involve new forms of power plant

technology. Research is being carried out to improve the different technologies,

1 Introduction

16

and improvements are likely to change the relative performance of different

technologies. Recent investigations (Kvamsdal et al. 2004 and de Koeijer 2004)

have however suggested that chemical absorption of CO2 is likely to remain a

highly competitive technology for CO2 capture in the future.

2 CO2 Absorption

17

2 CO2 Absorption We've learned from experience that the truth will come out. Other experimenters

will repeat your experiment and find out whether you were wrong or right.

Nature's phenomena will agree or they'll disagree with your theory. And, although

you may gain some temporary fame and excitement, you will not gain a good

reputation as a scientist if you haven't tried to be very careful in this kind of work.

Richard P. Feynman

2.1 Introduction

In the present chapter a general presentation will be made of the CO2 capture

technology and the nature of available experimental data for the process will be

summerized. Where nothing else is indicated the material is drawn from the

textbook “Gas Purification” (Kohl and Nielsen 1997). Figure 2.1 illustrates the

apparatus commonly used for CO2 capure.

Figure 2.1 CO2 Absorber columns.

2 CO2 Absorption

18

A cooled exhaust gas is led into the bottom of the absorber column. The gas rises

through the column meeting a counter-current liquid stream. The CO2 absorbs and

reacts with components in the liquid, and the gas stream gradually loses its CO2

while moving up the column.

At the top the gas with low CO2 content is released into the atmosphere. The CO2

content of the liquid increases as the liquid moves down the column. The liquid

stream is typically at 90-95% of equilibrium with incoming exhaust gas at the

column bottom. At the bottom the liquid is taken out and is pumped to the top of a

second column, the stripper (also called desorber). In the stripper the temperature

and/or pressure are set so that the chemical equilibrium in the liquid are reversed

and the CO2 is released into the gas phase. Pressure release is very common in

natural gas applications whereas changing the temperature is the most common

approach for exhaust gas treatment. Change in temperature is usually achieved by

adding heat as steam in the reboiler below the stripper column. A gas phase

consisting only of CO2 and steam is taken out at the top of the column. The steam

is separated from CO2 in the overhead condenser and the CO2 can be compressed

and sent to storage. The liquid at the bottom of the stripper column will have a low

concentration of CO2; and is again ready to be used for CO2 absorption. It is sent

back to the top of the absorber column. The liquid keeps circulating between

absorber and stripping column, transporting the CO2 between the columns. In an

industrial process the absorber will often be operated at temperatures around 40-

55 °C while the stripper will be operating at around 120°C.

Exhaust gas pressure is usually much lower than encountered in natural gas

processing. The Sleipner natural gas sweetening process is for example operated at

a 100 bar (de Koeijer and Solbraa 2004) while exhaust gas is usually at

atmospheric pressure. This means that while the technology for CO2 removal from

natural gas removal can be applied for exhaust gas treatment, optimal operating

conditions and solvents are quite different.

2 CO2 Absorption

19

The concentration of CO2 in the exhaust gases will vary with the nature of the

fossil fuel used. Typically a coal fired power station will have an exhaust

containing 10-12 volume percent CO2 (Rao and Rubin 2001), whereas a natural gas

fired power station can produce an exhaust gas with a CO2 concentration as low as

3 volume percent (Reddy et al. 2003). This means that even for different exhaust

gases optimal process settings may vary.

2.2 Solvents

There are a number of different solvents that are, and have been, applied in CO2

absorption. Most solvents are mixtures of water and base molecules. The bases can

either be organic or inorganic compounds. Almost all organic bases are amine

molecules, and such amine solvents are the topic of the present thesis.

The standard amine solvent for exhaust gases is ethanolamine; this molecule is

shown in the Figure 2.2. Most of the other common solvents are also

alkanolamines, i.e. molecules with both amino and hydroxyl functional groups.

Different amines vary significantly in how they react with CO2. Ethanolamine is a

particularly important solvent because it is the most widely used at present, and it

represents the benchmark that new solvents will be compared with. Amines can be

classified into different groups depending on the number of carbon atoms directly

bonding to the nitrogen atom; there are primary, secondary and tertiary amines.

Tertiary amines differ from the others in how they can react with CO2. I will return

to the various amines and reaction mechanisms in later chapters.

2 CO2 Absorption

20

Figure 2.2 Ethanolamine.

In addition to solvents that react chemically with CO2 there are other solvents that

have a capacity to absorb CO2 without reacting, these are called physical solvents.

There is to my knowledge no physical solvent that is being considered for the

treatment of exhaust gases and chemical absorption is believed to be the viable

option. Solvents with some degree of both chemical and physical absorption might

however be an interesting option. An example of a physical solvent that can be

applied in such a way is Sulfolane (Jenab et al. 2005).

2.3 Challenges

The CO2 absorption process is an established and proven technology, the overall

challenge is to bring the costs down to the point where it becomes an attractive

option in mitigation of global warming. The cost of the process stems from several

components. There is the cost of building the plant and purchasing the solvents.

There are also the operational costs, in particular the energy required to run the

process. Thermal energy is required to heat the solvent entering the stripper, to

generate the heat required to release the CO2 and to generate steam for dilution in

the stripper (Erga, Juliussen and Lidal 1995). In addition electric energy is required

for blowing the exhaust gas through the absorber and for solvent pumping.

One approach to making the process more efficient is to find solvents with more

favorable characteristics than the ones presently in use. This is the topic of the

2 CO2 Absorption

21

present thesis. The performance of the process can also be improved in other ways;

a better design can be proposed or the conditions under which the process is run

may be optimized.

There are other solvent properties besides the reactivity towards CO2 that are of

importance for the overall economy of the process. The solvent may be corrosive,

and the effect on the equipment must be considered. The solvent can also degrade

over time as a consequence of undesired reactions taking place. If the solvent has a

high vapor-pressure it will also evaporate in the absorber and in the stripper. Water

washes are for this reason mounted on the absorber and stripper to recover the

solvent. A recent study has suggested that the water wash operation significantly

affects the overall system performance (Tobiesen, Svendsen and Hoff 2005). The

cost of producing the solvent is also a factor to be considered, particularly if the

solvent has a high degradation rate and must be replaced often. It is also of great

importance that a solvent to be utilized in large quantities in an industrial process is

not toxic. I will return to the various solvent characteristics in a later chapter.

2.4 Current Understanding of the CO2 Absorption Process

The foundation for my work lies in the current level of understanding of the CO2

absorption process. The nature, quality and quantity of experimental data available

is therefore of importance. I have already noted that the CO2 absorption technology

is quite mature, it does however not necessarily follow that the process is well

understood. A lot of experimental work has been published on various aspects of

the absorption process. Here I will briefly go through the nature of published data.

A number of studies deal with the gas-liquid equilibrium of CO2-amine-water

systems. In such equilibrium experiments the system pressure and temperature is

set. The CO2 partial pressure and CO2 concentration in the liquid is then

2 CO2 Absorption

22

determined. Results from such experiments can be used to generate plots as the one

shown in Figure 2.3.

Figure 2.3 Plot from Ma’mun, Nilsen and Svendsen (2005).

Another important form of experiment is study of the kinetics. The experimental

setup for kinetics studies varies significantly but the general approach is to measure

the rate of CO2 uptake in the liquid at a given set of conditions. The conditions set

are usually temperature, pressure and liquid composition. Versteeg et al. (1996)

provide a fairly comprehensive review of kinetic data. The CO2 uptake does not

necessarily reflect a single rate of reaction and some analysis work is usually

required to extract reaction kinetics data from the experimental results.

Calorimetric experiments can be used to obtain information on the enthalpy of

CO2 absorption. An example is the work by Oscarson et al. (1989). They report

enthalpy data based on such calorimetric measurements for the CO2–aqueous

diethanolamine system. The same kind of measurements can also be used to

determine heat capacities.

1

10

100

1000

10000

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

CO2 loading / (mol of CO2/mol of MDEA)

pC

O2 /

kPa

2 CO2 Absorption

23

Physical properties such as density, boiling point and viscosity have also been

measured for many pure amines and amine-water systems. The extent of such data

is however more limited than for common organic molecules.

The types of experiment described so far do not give much direct insight into the

composition of the liquid phase. In recent years some effort has however gone into

experimental work that can provide such information about the nature and

composition of the liquid. Most important is the use of NMR-measurements

(Bishnoi 2000 and Poplsteinova 2004). NMR-data can provide information on the

presence and concentration of various species. From such measurements more

robust and quantitative conclusions can be drawn on the liquid composition. Such

experiments do however also have their limitations. There can be difficulties in

precisely measuring concentrations, protonation equilibriums are difficult to study

and measurement at higher temperatures is difficult.

A lot of the experimental work is done as part of the development of modelling

tools. Models are constructed to predict the overall performance of the CO2

absorption process. The work of Hoff (2004) is an example of such model

development. Such models are based on fitting parameters to experimental data for

a given system and their applicability for conditions beyond those at which they

were fitted can be uncertain.

The main aspects of the absorption process are at present fairly well understood.

The species formed are known and the reactions taking place are fairly well

understood. Equilibrium and kinetic constants are however not that well

established. The liquid consists of a significant number of components in

equilibrium. Determining the relative concentrations of species in the liquid only

from knowledge of amine concentration and CO2 uptake is clearly not an easy task.

The equilibriums and thermodynamics of these systems are for this reason to some

extent uncertain.

2 CO2 Absorption

24

Most of the experimental work reported in the open literature has been carried out

in the context of direct application to process-development and process-modelling.

There is much less published work dedicated to studying the systems in terms of

chemistry and physical chemistry. Data on liquid structure and molecular structure

is for example very sparse. This means that there is little experimental data that can

be used directly in the validation or parameterization of molecular level models

such as the ones used in the present work.

3 Computational Chemistry

25

3 Computational Chemistry The underlying physical laws necessary for the mathematical theory of a large part

of physics and the whole of chemistry are thus completely known, and the difficulty

is only that exact application of these laws leads to equations much too

complicated to be soluble.

Paul A. M. Dirac (1929)

3.1 Introduction

The present chapter will be devoted to introducing computational chemistry and

it’s various branches. Computational chemistry can perhaps be loosely defined as

chemistry modeling based on a molecular or atomic level description. The term

covers a fairly broad range of theories and methods.

The various methods of computational chemistry can be thought of as offering a

toolbox. For different problems studied choices must be made as to what methods

are best suited. In the present work several different issues related to CO2

absorption are studied. In studying these problems an eclectic approach has been

chosen; namely to attempt to find the method best suited to each problem.

As a result a fairly large number of methods have been employed. And these

methods again draw on different fields of theory. No attempt will be made to cover

the underlying theory in any detail here. The present chapter will rather focus on

introducing the various branches of computational chemistry in general terms. The

introduction is intended to give general insight into the various methods, in

particular their strengths, weaknesses and limitations. In addition the terminology

to be used in the following chapters and papers will be introduced.

The chapter will be divided into two parts, first a brief presentation of the main

elements of computational chemistry will be made. This presentation will follow

the outline used by Grant and Richards (1995) in their textbook “Computational


26

Chemistry”. In the second part a discussion will be made on the general issue of the

application of computational chemistry. The issue of modeling of chemistry in

solution will be discussed in the next chapter. Where nothing else is indicated the

material in this chapter is drawn from Grant and Richards (1995) and the textbook

“Essentials of Computational Chemistry” by Cramer (2002).

3.2 Quantum Mechanics

3.2.1 Introduction

The claim made by Dirac regarding the laws of chemistry and physics (quoted in

the beginning of this chapter) referred mainly to the postulation of the Schrödinger

equation. In its barest, and most innocent, form it can be written as:

H Eψ ψ= (3.1)

H is the shorthand form of the Hamilton operator which takes into account the

contributions to the energy of the system. E is the energy of the system and ψ is

the wave function. The energy has only certain allowed values, with a

corresponding wave function for each allowed energy level.

The Hamiltonian consists of the potential and kinetic energy contributions. In the

absence of external magnetic and electrical fields and ignoring relativistic effects it

takes the following form: 2 22

2 2

2 2k k l

i ki k i k i j k le k ij ij kl

e Z e Z ZeHm m r r r< <

=− ∇ − ∇ − + +∑ ∑ ∑∑ ∑ ∑ (3.2)

where i and j run over electrons, k and l run over nuclei, is the Planck’s constant

divided by 2π , em is the mass of the electron, km is the mass of the nucleus k.

2∇ is the Laplacian operator, e is the charge on the electron, Z is an atomic number

and abr is the distance between particles a and b . From the Hamiltonian it can be

seen that the Schrödinger equation is a set of differential equations.


27

For the wave function itself it is difficult to give a simple definition or direct

physical interpretation. The product of the wave function with its complex

conjugate *ψ ψ does however have a physical interpretation; it gives the

probability density for the system. For an electron *ψ ψ multiplied with a volume

element would give the probability of the electron being in that volume element.

The normalized integral of 2ψ over all space must be unity. The wave function

can therefore be thought of as a kind of road-map to how the electrons are

localized.

There is no way to directly derive the wave function itself, but there are some

conditions it must meet. It must be “well-behaved”, displaying only smooth

changes and going to zero at infinity. The variational principle states that the lower

the ground state energy calculated by a wave function is, the higher is the quality of

the wave function.

Assuming that each electron can be treated separately one can operate with one-

electron wave functions also called orbitals. In a system with more than one atom,

i. e. a molecule, we deal with molecular orbitals.

All electrons are characterized by a spin quantum number, with two possible

eigenvalues. The Pauli principle states that two electrons can not have the same

quantum numbers. One molecular orbital is therefore limited to two electrons with

opposite spin.

The Schrödinger equation is a postulate, believed to be entirely accurate. The

complexity of it is however such that the largest system for which it is analytically

solvable is the hydrogen atom. It was this state of affairs that led Dirac to make his

observation.

Since Dirac made his observation a lot of work has gone into making

approximations that make it possible to make calculations on systems of practical

interest. Some of the main approximations will be briefly outlined here.


28

3.2.2 The Born-Oppenheimer Approximation

The atoms in a system are much heavier and move much more slowly than the

electrons. It is therefore assumed that the movements can be decoupled. The energy

of the electrons is calculated with the atoms in fixed positions. This approximation

is in most cases entirely reasonable and universally applied.

3.2.3 Hartree-Fock Self-Consistent Field Method

Much of the difficulty of solving the Schrödinger equation stems from the need to

simultaneously determine the energy of each electron in the presence all other

electrons. In the Hartree-Fock (HF) method this is avoided by calculating the

energy of each electron in the averaged static field of the others. Initially a guess is

made of the electron energies. The energy of each electron is then calculated in the

field of the initial electron configuration. This procedure is repeated in an iterative

loop until convergence (Self-Consistent referring to this iterative calculation).

The Hartree-Fock method can therefore be thought of as a kind of mean-spherical

approximation at the electron level. The difference between the Hartree-Fock

energy and the energy for the full Schrödinger equation is called the correlation

energy. Hartree-Fock calculations are sufficiently accurate to provide insight into

many problems and they are widely used. As Hartree-Fock calculations have been

applied to different problems it has however become increasingly clear that the

correlation energy is of great significance in determining the properties of a system.

Efforts have therefore been made to improve on the Hartee-Fock energy.

3.2.4 Post-HF Methods

There a number of different methods that go beyond Hartree-Fock calculations, one

of the widely used approaches is perturbation theory. In perturbation theory the

Hartree-Fock solution is treated as the first term in a Taylor series. The


29

perturbation terms added involve the electron repulsion. One of the more common

forms was developed by Møller and Plesset. The second order perturbation form is

referred to as MP2. This form will be utilized in the present work.

It should be noted that the electron-electron repulsion energy is not necessarily a

small perturbation. In cases in which this term is large the application of

perturbation theory can become more difficult.

There are a number of other techniques to include electron correlation that can

potentially provide very accurate results, such calculations can however become

very time consuming and at present they tend to be used for small molecules with

maybe 3-4 heavy (non-hydrogen) atoms. The molecules studied in the present work

are somewhat larger and the decision has been made not to use such time-

consuming methods.

3.2.5 Density Functional Theory

Density Functional Theory (DFT) is based on determining the electron density

rather than the wave function. The electron density unlike the wave function is a

physically observable quantity. It has been proven that given the electron density

the Hamilitonian operator is also determined. A variational principle has also been

established for DFT. Unlike HF theory DFT in itself contains no approximations.

There is however no way to derive an energy contribution in DFT known as the

exchange-correlation energy. The quality of the models is usually determined by

some form of comparison with experimental data. DFT models are therefore in a

sense semi-empirical models and once assumptions about the exchange-correlation

energy are introduced (as they must be) there is no variational principle. This

means that for DFT, unlike HF and post-HF methods, there is no a priori way to

establish how good a given method is and no systematic way to improve upon it.

This state of affairs led many researchers to look at DFT with skepticism. It has


30

however become clear that DFT methods often produce results of comparable

quality to much more expensive post-HF methods. It has also become fairly well

established for what type of molecules and properties DFT methods are reliable.

One of the most common DFT methods is the so-called B3LYP method, which is a

form of hybrid between DFT and HF methods. It is considered to be fairly robust,

perhaps because it balances some of the weaknesses of DFT and HF methods.

B3LYP is the DFT method that will be used in the present work.

3.2.6 Basis Sets

HF and Perturbation Theory have taken us from the Schrödinger equation to a

solvable set of equations (DFT offering an alternative route). In order to carry out

calculations a representation of the wave function is also needed. Each molecular

orbital is constructed from linear combinations of basis functions.

For computational reasons gaussian type orbitals (2re− ) are commonly used.

Gaussian type orbitals do however not have the correct shape required to reproduce

the form of a electron distribution. Orbitals are therefore usually constructed as

combinations of a set of gaussians in order to reproduce the correct shape.

Basis-sets must be sufficiently flexible to allow the description of electron

distribution in various forms of molecules and the quality of the results obtained do

in general improve with increasing size and flexibility of the functions employed.

On the other hand calculations will also become more time consuming with

increasing basis set size. One of the common approaches is to add more basis sets

for the valence electrons compared to inner orbitals.

In the present work the common 3-21G, 6-31G and 6-311G basis sets will be

utilized. 3-21G indicates a single basis set consisting of 3 gaussian functions for

inner electrons and two separate basisfunctions, one consisting of 2 gaussians

functions and the other 1 gaussian function for valence electrons. In 6-31G the


31

number of gaussian functions to represent the basis sets is increased and in 6-311G

the number of separate basis functions for valence electrons is also increased.

It is common to add further sets of basis functions. One approach is to add higher

level orbitals to electrons at a given level, one may for example add d-orbitals to

electons in a p-orbital and p-orbitals to electrons occupying s-orbitals. Such orbitals

are called polarizable orbitals and the inclusion of such d-orbitals will in the

present work be indicated with a (d) and p-orbitals with (p). It is common to

indicate the use of polarizable orbitals with a (x,y) notation, where x is the number

of polarizable orbitals on heavy (non-hydrogen) atoms and y indicates the

polarizable functions on the hydrogen atoms. Another notation that is sometimes

used is to indicate (d) polarization with a “*” and (d,p) polarization with “**”. This

notation is utilized in one of the papers in the present work.

Finally there is in some cases a special need to allow electrons to localize far

from the atom center. Standard basis-sets are in such cases augmented with so-

called diffuse basis sets. In the present work such diffuse basis-sets on heavy (non-

hydrogen) atoms are indicated with a “+”, if they are also included on hydrogen

atoms it is indicated with “++”. One of the circumstances in which such diffuse

basis sets are required is in the accurate modeling of hydrogen bonds.

Some basis-sets are regarded as being better than others in providing quality

results for a given amount of computation time. Some basis sets have therefore

become standard for calculations. In the present work all calculations will be done

with such widely used basis-sets.

3.2.7 Basis Set Superposition Error

When atoms interact the basis sets allocated to each of them will overlap. This

overlapping gives electrons greater freedom to localize and can result in a

reduction of the energy. This reduction in energy would however not have occurred


32

if the basis sets had been infinitely large. This energy reduction is therefore an

artifact of working with limited basis sets. This is called the basis set superposition

error (BSSE).

For atoms on different molecules there are schemes to correct for the BSSE. Most

common is the so-called Counterpoise correction. For interactions within the same

molecule application of such corrections is however more difficult (Reiling et al.

1996 and Lii et al. 1999). This is of importance in the present work because many

alkanolamine molecules display intramolecular hydrogen bonding. The BSSE is

expected to become smaller with increasing basis set and in calculating

intramolecular hydrogen bonds it would therefore seem that larger basis sets are

more reliable. In the present work the general approach will therefore be to use

large basis-sets in order to obtain more accurate results.

3.2.8 Temperature

Standard quantum mechanical calculations are usually carried out on a single or

small number of molecules at 0 K, and without accounting for the zero-point

energy. The intramolecular effects of temperature are usually calculated by using

the harmonic oscillator approximation. This relies on calculating the second

derivative of the energy with respect to the displacement ( r ).

It should be noted that because quantum mechanical calculations are usually

carried out on very small number of molecules in vacuum, pressure effects are not

accounted for.

3.2.9 Performance

The quantum mechanics based methods are often referred to as ab inito methods,

as none of the methods rely on parameterization to experimental data. This is an

important point because it distinguishes quantum mechanical calculations from

many other forms of modeling carried out in science. The development of such


33

calculations has however not taken place without experimental input (this being

particularly true for DFT methods). Comparison with experimental data is used to

validate the calculations. Sometimes comparisons with experiment have shown

methods to be less reliable than expected, while others have proven more reliable.

This partly happens because there can occur various forms of fortuitous

cancellation of errors.

It has already been noted that quantum mechanical calculations can be time-

consuming. Some of the calculations in the present work took 2-4 days of CPU

time.

Quantum mechanical calculations can today be carried out for systems of up to

maybe a 100 atoms. The calculation time can increase quite steeply when

increasing the size of the basis set or using more advanced methods.

In the present work quantum mechanical calculations will mainly be used to

calculate geometries and energies of molecules.

For geometry optimization most quantum mechanical methods are fairly reliable.

High level calculations are of quality comparable to experimental data, HF

calculations with smaller basis sets also tend to be reasonably accurate.

Calculation of energy is in general more difficult. Results can vary quite

significantly with the level of theory. Prediction of absolute energy values are

difficult, but relative trends in energies can usually be calculated with reasonable

accuracy.

3.3 Molecular Mechanics

3.3.1 Introduction

Quantum mechanical calculations are, as have already been mentioned, time-

consuming. Molecular Mechanics (MM) offer a simplified form of molecular

representation that makes it possible to perform significantly faster calculations.


34

A molecular mechanics representation can best be summarized as soft spheres

attached by springs to represent bonds. The potential energy between non-bonded

atoms is usually expressed as the sum of Lennard-Jones and Coulomb potential

functions: 12 6

4 ij ij i jij

i j i jij ij ij

q qU

r r r< <

⎡ ⎤⎛ ⎞ ⎛ ⎞σ σ⎢ ⎥⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜= ε − +⎢ ⎥⎟ ⎟⎜ ⎜⎟ ⎟⎟ ⎟⎜ ⎜⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦∑ ∑ (3.3)

where the sums are over all pairs of interaction sites and ε and σ are the Lennard-

Jones potential parameters, iq is the partial electric charge of interaction site i and

rij is the separation between interaction sites. Interaction sites are usually, but not

always, atomic centers. This form of representation only accounts for two-body

interactions. In a real system many-body effects, such as three-body and four-body

interactions, can also play a part. There is therefore an approximation involved in

the form of such potential functions. To correct for this, parameters can be set to

implicitly account for the many-body effects.

For bond-lengths simple harmonic stretching functions are often used where the

energy increases as the bond-length deviates from some equilibrium bond-length.

For bond angles harmonic functions of the following form are often utilized:

( ) ( )20U kθθ = θ−θ (3.4)

where θ is the bond angle and the subscript 0 denotes the equilibrium value. kθ is

the spring constant. Dihedral angle energies around bonds are given by some form

a fourier series. One of the common forms is the following:

( ) ( )5

1

cos ii

i

U C=

φ = φ∑ (3.5)

where φ is the dihedral angle and the iC are constants.


35

3.3.2 Force Field Parameterization

The quality of the results produced by MM calculations obviously depends on the

parameters chosen for the various interactions and some form of parameterization

must be undertaken. A set of parameters for a single molecule or groups of

molecules are called force fields.

A fairly large number of schemes have been proposed to develop force fields,

partly reflecting the fact that different researchers are looking at different

applications. One of the main applications is biological systems, in which case the

focus is often on reproducing the structural characteristics of molecules of

biological importance. A second application is the modeling of liquids.

In the modeling of liquids, parameters are often chosen to reproduce the

properties of liquids as determined from experimental work. There is however a

number of different properties one can choose to reproduce. Among them are

density, diffusion rates, dielectric constants and radial distribution functions. An

example of such work is the “Optimized Parameters for Liquid Simulations”

(OPLS) force field developed by Jorgensen and coworkers (Jorgensen et al. 1996

and Rizzo and Jorgensen 1999). In addition there is the choice of attempting to

reproduce the properties for a given temperature, or to attempt the more ambitious

task of reproducing properties over a range of temperatures as done by Walser et al.

(2000). For some solvents such as water, a fairly large body of experimental data is

available. In other cases, such as for the amines of interest in the present study,

experimental data is however more sparse.

For a solvent such as water there exist a remarkably large number of force fields

(Guillot 2002). This confronts the practitioner with some difficult choices when

selecting force fields for a specific problem. It would seem that some work remains

on determining which force fields are more reliably for specific tasks, and if any

can be regarded as “better” in a general sense.


36

Quantum mechanical calculations are often used for setting force field

parameters. They can for example be used for determining molecular geometries

and atomic charges.

3.3.3 Atomic Charges

One of the most important and difficult issues in the design of a force field is the

selection of charges. In most common force fields fixed charges are used and they

are often, but not always, located at the atom centers. These atomic charges are

intended to reproduce the net effect of electrons and nuclei for a given atom. As

electrons are not located at a single point operating with charges situated at the

atomic centers does represent an approximation. Operating with fixed charges is

also an approximation, as the location of electrons can be effected by the

environment the molecule finds itself in.

Two main approaches to determining atomic charges can be identified in the

literature. One approach is to fit the charges in simulations intended to reproduce

various experimental properties. Such fitting is usually done for small organic

molecules. For larger molecules experimental data is often more sparse and the

number of charges to fit is much larger. In such cases one will often rely on atomic

charges being transferable parameters. Having determined charges for alcohol-

groups, amine-groups and alkane-groups in small molecules one assumes these to

be the same in larger molecules. The OPLS force field is based on this approach

(Jorgensen et al. 1996). The second approach is to determine the atomic charges

from quantum mechanical calculations, an example of this is the work by Kollman

and coworkers (Cornell et al. 1995). This second approach is very appealing

because it reduces the need for experimental data and gives the modeling a stronger

predictive character (provided it works).


37

Even if a quantum mechanical calculation contains information about position of

nucleus and electrons, the task of determining atomic charges is still a difficult one.

Atomic charges are not uniquely defined and the task of assigning parts of the

electron distribution to atoms in a molecule is ambiguous. The first such scheme

was the Mullikan population, which is based on determining how much each

atomic basis set contribute to the wave function. While Mullikan populations have

been widely used, they have come to be regarded as unreliable (Franckl and

Chirlian 2000). One of the newer schemes is to reproduce the electrostatic potential

around the solute, even for this approach there are however a number of different

implementations (Franckl and Chirlian 2000). Singh and Kollmann (1984)

developed a procedure based on reproducing the electrostatic potential on

gridpoints distributed spherically around each solute atom center, outside the van

der Waals volume of the solute. This type of charges will be utilized in the present

work, these will be referred to by their common acronym “MK”. It has become

clear that the calculated charges are sensitive to the specific procedure chosen to fit

the electrostatic potential (Franckl and Chirlian 2000). Other difficulties are that

such procedures tend to work poorly for atoms buried inside a molecule and that

charges can display a high degree of conformer dependency (Bayly et al. 1993).

There are also schemes that attempt to use the quantum mechanical

representation while at the same time reproducing some experimentally measured

property. One such hybrid scheme is CM2 charges (Li, Zhu, Cramer and Truhlar

1998) that reproduces experimental dipole moments. This type of charges will also

be used in the present work.

While selection of atomic charges is a difficult issue, it should also be noted that

in many contexts different force fields produce quite similar results. In such cases

one does not have to worry too much about the selection of charges. In general

different schemes to calculate atomic charges do also produce charges that are in

reasonable qualitative agreement (da Silva, Yamazaki and Hirata 2005).


38

3.3.4 Polarizable Force Fields

One of the most important approximations in standard simulations with molecular

mechanics representation is the use of fixed charges. Introduction of polarizability

is one way to improve the representation while avoiding the expense of quantum

mechanical calculations. Such models were recently reviewed by Rick and Stuart

(2002). There are some main approaches to adding polarization in simulations.

Among them are shell models based on polarizable point dipoles, were fixed

charges are attached to each other with harmonic springs. Another form of model is

based on charges being allowed to fluctuate between sites in a molecule.

The charges in a molecule do depend on the surrounding environment. It is

therefore to be expected that a model with fixed charges will have problems

representing a molecule in different states such as solids, liquids and gases.

Polarizable models should have the potential to represent a molecule in different

states. Another difficulty with fixed charges is that they can not reflect changes in

charge distribution that may take place as a molecule changes conformer. This is

again something that a polarizable model has the potential to handle. On the other

hand simulations with polarizable models do take longer time than simulation with

fixed charges.

Rick and Stuart (2002) conclude that polarizable models in several respects do

perform better than models with fixed charges. Compared to a model with fixed

charges there is however a greater number of parameters to be set in a polarizable

model and this does offer some added challenges.

While a polarizable model is in form more realistic than a model with fixed

charges, it is not given that it will produce more realistic results. In using a ball-

and-stick representation of molecules there is a number of assumptions involved,

and in it is not given that overall performance will improve by improving on one of

the approximations.


39

In the present work simulations with polarizable molecular representations are

not used. Mainly because I feel that such advanced and time-consuming modeling

should only be utilized when simpler fixed charge models are shown to be

inadequate. Such forms of models should however be considered if fixed charge

models are found wanting in a given context.

3.4 Simulations

3.4.1 Introduction

There are two forms of simulations that are used in computational chemistry:

Molecular Dynamics (MD) and Monte Carlo (MC). These are used for calculations

of ensembles of molecules. Simulation techniques are described in detail in the

textbooks “Computer Simulations of Liquids” (Allen and Tildesley 1987) and

“Understanding molecular simulation” (Frenkel and Smit 2002).

Molecular Dynamics calculations are based on calculating the forces between

molecules and atoms in a system and allowing them to move according to Newtons

laws of motion. From the calculated forces the acceleration and velocity of the

particles in the system are calculated. The particles are moved over a small time-

step, forces and velocities are recalculated and the system is moved forward a new

time-step. For each time-step the properties of the system such as energy and

temperature are monitored. A simulation is carried out for whatever number of

time-steps is deemed necessary to obtain reliable averages.

Monte Carlo simulations are on the other hand based on random alterations of the

coordinates of the system. The energy change for each alteration is calculated, the

probability of the alteration being accepted depending on the associated change in

energy. For changes leading to lower energy the probability is higher. The standard

approach is Metropolis sampling in which the sampling has a Boltzmann-weighted


40

probability. As in MD the simulation is continued for whatever number of steps

deemed necessary for sampling.

Often in simulations the purpose is to simulate the bulk behavior of liquids.

Simply placing a number of molecules in a vacuum would produce a cluster that

might have properties different from bulk liquid. It is therefore customary both in

MD and MC to do calculations with periodic boundary conditions. The cell

containing the ensemble is then surrounded by replicas of itself.

Simulations are usually carried out with a molecular mechanics level

representation. Simulations with such a molecular representation can be carried out

on ensembles of thousands of molecules. This is significantly more than in QM

calculations, but is still an extremely small number compared to the number of

molecules present in even the smallest droplet of water. In the present work most

simulations are done on ensembles of 256 molecules. Such an ensemble is usually

regarded as large enough for reliable calculations, at the same time as such

calculations can be carried out in reasonable amounts of time.

The Lennard-Jones and Coulomb interactions are usually truncated at some

value. This is mainly done to save time in the calculations. The Lennard-Jones

potential decays steeply as a function of distance and its truncation is

unproblematic. Coulomb interactions have a slower decay, but for neutral species

the truncation can still be a reasonable simplification. For ionic species truncation

is however usually not an acceptable option. Although there are schemes to handle

long-range forces, simulations of ionic systems are challenging. The standard way

of handling long-range electrostatics is the use of Ewald sums.

Simulations are often carried out in microcanonical ( NVE ), canonical ( NVT )

and constant number of particles-constant pressure-constant temperature ( NPT )

ensembles. The grand-canonical ensemble with constant free energy, volume and

temperature ( VTµ ) is also used in some types of simulation.


41

When carrying out simulations the statistical sampling is always a concern. The

question of whether the system has sampled sufficiently the full set of

configurations it can take on (the phase space) must be addressed. Verifying this is

difficult, and is not only an issue of doing a long enough simulation. If one can

imagine the potential energy of phase space as a kind of landscape, one can think

of the simulation as risking becoming trapped in a valley. As simulations are based

on statistical averaging of properties, there is always some degree of statistical

uncertainty in the results obtained.

While MD and MC can be used to calculate many of the same properties, they

differ in some important respects. In MC simulations time is not a parameter and

there is no easy way to obtain time-dependent properties such as diffusion-rates.

MD has been developed further in handling of long-range electrostatic interactions.

MC calculations can sometimes provide more efficient sampling of phase space.

3.4.2 Free Energy Perturbations

The free energy of solvation is the energy associated with a molecule going from

the gas phase to solution and is a central concept in understanding chemistry in

solution. Determination of free energies is also one of the main issues in this thesis.

Kollman (1993) provided a review of the main simulation techniques for

determining free energies. The main techniques are free energy perturbations

(FEP), thermodynamic integration and slow growth. FEP sees the widest use and is

also the technique I have adopted in my work. The fundamental equation that free

energy perturbations are based on is the following (Kollman 1993): /ln H RT

B A AG G G RT e−∆− =∆ =− (3.6)

where B AH H H∆ = − and A

refers to an ensemble average over a system

represented with the Hamiltonian AH . If the systems differ in a significant way the


42

equations will however not lead to a meaningful result. This problem can be

overcome by performing multiple simulations over intermediate steps between A

and B. A coupling parameter (λ ) is introduced that allows the smooth conversion

of system A to B. The mutation of any geometry or potential parameter of the

system can then be represented in the following form (Jorgensen and Ravimohan

1985):

( ) ( )0 1 0ξ λ ξ λ ξ ξ= + − (3.7)

The total free-energy change is obtained by adding together the contributions from

each single perturbation. In the present work calculations are performed with the

double-wide sampling scheme (Jorgensen and Ravimohan 1985). In this scheme

the free energy difference for 1i iλ λ +→ and 1i i−→λ λ are evaluated in a single

ensemble.

The mutation will usually be between two different solute molecules. The essence

of the FEP is to mutate one molecule into another and compute the energy

associated with the transformation. FEPs are in general more accurate for

calculating differences between molecules with similar properties. More accurate

results are for example obtained when perturbating between molecules of the same

charge, as opposed to between species with different charges. Calculating the

absolute free energy of solvation is more difficult than simply calculating relative

free energies, the two systems one is calculating the energy between in this case

being very different (differing by the number of molecules). In this work most

calculations are done as relative free energy perturbations.

While the general concept of FEP calculations is easily understood, the technical

issues involved are far from trivial. Kofke and Cummings (1997, 1998) have

concluded that perturbations that involve growth are superior to those involving

shrinking or deletion of molecules. They conclude that shrinking offers loss of

accuracy due to biases in the sampling. More recently Kofke (2005) has however

concluded that the error involved in insertion and deletion approaches may vary


43

from system to system. The development of optimal FEP methods does therefore

appear to be a work in progress.

The selection of methods in this work has been dictated mainly by available

simulation codes, rather than any assessments of the merits of various methods to

determine the free energy.

3.5 QM/MM

QM/MM is a general term for calculations combining quantum mechanical (QM)

and molecular mechanics (MM) representations. Such calculations can be

advantageous when one wishes to model parts of a system with greater accuracy.

For studies of a reaction in solution one might for example represent the reacting

molecules at a QM level, while solvent molecules are represented at MM level. In a

more sophisticated calculation one might also represent the closest solvent

molecules at QM level, while solvent molecules at a greater distance are

represented at a MM level. While QM/MM calculations are less time consuming

than pure QM calculations, they can still be prohibitively expensive.

Gao (1996) has reviewed the various types and levels of QM/MM coupling. In

the present work QM geometries and atomic charges will be used in simulations.

This can be regarded as a very weak form of QM/MM coupling.

3.6 Computational Chemistry and Experiment

Computational chemistry will never be a full replacement for doing experiments,

but can often supplement experimental work. Very often neither experiment nor

computational chemistry can by itself give us the full insight we could desire. In

many cases one must therefore piece together whatever information can be drawn

from either source, to draw whatever conclusions can be drawn. Sometimes

computational chemistry can be used to calculate properties that are not at all

available from experimental work, while some issues can be difficult both in the


44

laboratory and on the computer. When working with results from modeling and the

laboratory one should have a feeling for the quality of the data from different

sources. Computational chemistry has grown as a field rather quickly, and many

researchers are perhaps not fully aware of the potential of its methods. On the other

hand I have the impression that researchers sometimes are more aware of the

limitations of the tools they work with, than that of other methods, and may come

to overestimate the quality of the work in a different field.

In the field of CO2 absorption there is as noted in the last chapter considerable

amount of experimental data. On the other hand it must also be noted that the

systems in the process display considerable complexity. The systems consist of

many components in an aqueous solution. Several of the components are ionic and

many components can have large numbers of potential conformers. In addition the

process runs at temperatures ranging from 50ºC to 130ºC. There are also

degradation products, impurities and surface effects that may change the chemistry,

or affect the process operation in some other way. Given the complexity of the

system, the amount of experimental data available must actually be considered to

be rather sparse. The multi-component nature of the liquid in the system also

present challenges for computational chemistry work. The absence of experimental

data at the molecular level also means that it can be difficult to validate models

being used and conclusions drawn regarding the nature of the system.

The approach in this work has therefore been somewhat pragmatic. The most

effort has been put into areas where computational chemistry was thought to give

the most valuable new insight, where as some aspects have been approached

tentatively.


45

3.7 Review of Computational Chemistry Work on CO2 Absorption

There has been published some computational chemistry work on chemistry

directly related to the CO2 absorption process. Ohno and co-workers (Ohno et al.

1998 and Ohno et al. 1999) have done some very detailed work on 2-(N,N-

Dimethylamino)ethanol and 2-(N-Methylamino)ethanol. These papers combine

quantum mechanical calculations with infrared and Raman spectroscopy. These

papers offers valuable results in terms of the adopted conformers of amines and

CO2 bound amine molecules.

Papers by Chakraborty et al. (1988) and Jamroz et al. (1997) deal with

interactions between CO2 and amine molecules. While interesting these papers

provide no clear conclusions of direct relevance to CO2 absorption. Suda et al.

(1998) attempt to correlate the amount of CO2 absorbed in a liquid with frontier

orbital properties. While this is an interesting approach the correlations obtained

were not very good. In summary may be concluded that very little computational

chemistry work has been done for the specific purpose of understanding the CO2-

absorption process.

There has been done some computational chemistry work on the liquid structure

of ethanolamine (Button et al. 1996, Alejandro et al. 2000 and Gubskaya and

Kusilik 2004a) and ethanolamine in aqueous solution (Gubskaya and Kusilik

2004b). These papers do give some insight into the liquid structure of

ethanolamine, but they do not deal with the more complex multi-component

systems encountered in CO2 absorption. For other amine solvents of interest in CO2

capture I am not aware of any computational chemistry work having been done.

While there has been done very little computational chemistry work on CO2

absorption, there has been done a lot of work on molecules similar to those utilized

in this process. Molecules with amino- and hydroxyl-groups are important in all

forms of living organism, and the modeling of them is subject of substantial work


46

in biochemistry. Most of the models applied in this thesis originated in studies of

systems of importance in biochemistry.

4 Modeling of Solvation Energy

47

4 Modeling of Solvation Energy Realistic relative gas-phase energies of ionization may soon be estimated by

molecular quantum mechanics. If an accurate set of solution energies can be

determined, we can expect that the next generation of calculations may include

solvation energies, and thus complete quantum mechanical calculations for

protonation reactions in solution might become possible.

Jones and Arnett (1974)

4.1 Introduction

This chapter is intended as a review of available approaches to modeling energies

in solution. It will be mainly focused on issues directly relevant to CO2 absorption,

but will also touch upon some general issues. In addition to briefly describing

different solvation models, results will also be presented comparing different

models ability to predict relative base strength.

Liquids do in general probably represent the most difficult phase to model. In the

gas phase intermolecular interactions are limited and it is often sufficient to look at

the characteristics of a single molecule. In such a case quantum mechanical

calculations can be applied successfully, examples of this will be shown later in

this chapter. Solids are more complex, but the modeling of them is in some cases

made easier by their periodic nature.

In a liquid a single molecule interacts with a large number of neighbor molecules

that do not display any orderly structure. The interactions are also shifting

continuously as molecules move around, and the observed properties of liquids

represent averages of these interactions. Rigorous quantum mechanical calculations

of all these interactions are simply not feasible at present or in the foreseeable

future. This leaves scientists with the challenge of finding the best approximations

in simplifying a complex problem.


48

4.2 The liquid state

While liquids do by nature not display any long term periodicity or regular

structure, they do have some structural characteristics. One common way to

describe such structural features is by use of radial distribution functions ( ( )g r ).

The radial distribution describes the probability of encountering two atoms at given

distances ( 12r ). Usually it is given in a normalized form so that the probability

density of 1 is the average density of the system. A radial distribution function will

often look something like the one shown in Figure 4.1.

Figure 4.1 Radial distribution function.

Atoms do not overlap and at very short range the probability of finding a second

atom will be zero. At slightly larger distances there is the ideal distance for direct

interaction between the atoms and this usually results a peak in the function, atoms

at this distance form what is called the first solvation shell. Because other atoms do

not overlap with the ones in the first solvation shell the radial distribution function


49

will usually show a marked drop after the first peak. At longer distances the radial

distribution will average out to the average density of the system, which in other

words means that positions of atoms at long range are not correlated. With radial

distributions for all types of atomic sites in a liquid one can form a picture of the

interactions. In addition to the radial distribution functions there are other

properties that can be used to summarize the characteristics of liquids. An example

of such a property is the angular pair correlation function, this carries information

about how molecules in a liquid orientate relative to each other (Gray and Gubbins

1984). Another example is spatial distribution functions, these provide three

dimensional pictures of interactions in a liquid, the work by Gubskaya and Kusilik

(2004a) is an example of the use of such distribution functions.

4.3 Statistical Mechanics

Statistical mechanics offers tools for analytically describing interactions in liquids.

Here a brief outline will be given based on a compendium by Kjellander (1992).

One central parameter is the pair correlation function:

( )1 2 1 2( , ) , 1h r r g r r= − (4.1)

where g is the radial distribution function for atoms (or other form of site) located

at 1r and 2r . At the heart of much of the statistical mechanics works on liquids is

the Ornstein-Zernike equation. The Ornstein-Zernike equation states that the pair

correlation function can be written in the following form:

( ) ( ) ( ) ( ) ( )1 2 1 2 1 3 3 3 2 3, , , ,h r r c r r c r r n r h r r dr= +∫ (4.2)

Here ( )1 3,c r r is the direct correlation function and ( )3n r is the density at a given

point. What this equation states is that the correlation between two particles in a

liquid ( 1 2( , )h r r ) can be divided into two parts, one direct and one indirect. The

direct part is called the direct correlation function. The indirect part comes from


50

particle 2 again correlating with the other particles in the system, these particles

again correlating directly with particle 1.

The 3 2( , )h r r in the integral can be written in the same form as the Ornstein-

Zernike equation:

( ) ( ) ( ) ( ) ( )3 2 3 2 3 4 4 4 2 4, , , ,h r r c r r c r r n r h r r dr= +∫ (4.3)

Inserting this into the Ornstein-Zernike equation the following equation is

obtained:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )1 2 1 2 1 3 3 3 2 3 3 4 4 4 2 4 3, , , , , ,h r r c r r c r r n r c r r dr c r r n r h r r dr dr= + +∫ ∫ (4.4)

This procedure can be repeated and the result is clearly an infinite sum of integral

equations. The Ornstein-Zernike equation is by itself the definition of the direct

correlation function and it should be noted that no approximations are required in

formulating it. This function is expected to have a simpler form than the pair

correlation function. If one combines the Ornstein-Zernike equation with a closure

equation one can obtain a solvable set of equations. One of the simpler closure

equations is the mean-spherical approximation:

( ) 1h r =− for r σ≤ (4.5)

( ) Uc rkT

=− for r σ>

where U is the interatomic potential energy and σ is the radius of the atom.

A widely used closure is the Percus-Yevick equation:

( ) ( ) ( ) ( )( )/ 1u r kTg r e h r c r−≈ + − (4.6)

A second widely used closure equation is the so-called Hypernetted Chain(HNC)

approximation:

( ) ( ) ( ) ( )/u r kT h r c rg r e− + −≈ (4.7)


51

These closure equations represent approximations and the solutions obtained with

these equations are therefore approximate. For simple idealized liquids such as

hard spheres or soft spheres these equations can be solved and results can be

compared with molecular simulations utilizing the same molecular representation.

Such comparisons have revealed that most of the closure equations produce

satisfactory results in some cases but fail in others. The Percus-Yevick closure is

known to work well in describing interactions between hard spheres, but performs

less well for systems with electrostatic interactions. The HNC closure performs

well for a number of different types of systems, but can fail for some mixtures of

different solvent molecules and can sometimes lead to diverging calculations

(Hirata 2003). Efforts have been made to develop closure equations that produce

results in better general agreement with those obtained from simulations. Hansen

and McDonald (1990) provide a brief review of such efforts. A more recent

example is the KH closure suggested by Hirata and co-workers (Hirata 2003).

The Ornstein-Zernike equation is for independent single-sites (atoms) and the

extension to molecules consisting of several-sites is not trivial. One Ornstein-

Zernike based model that is easily extended to molecules is the reference

interaction site model (RISM). This model was first derived by Chandler and

Anderson (1972). It can be written as:

=h ω*c*ω +ρω*c*h (4.8)

Here “*” represents convolutions and c and h are in this case matrixes of the

various correlation functions for the different sites in molecules. ω is a matrix of

intramolecular correlations. Hansen and McDonald (1990) refer to this theory as

the “RISM approximation” and unlike the Ornstein-Zernike equation itself

approximations have been made in deriving it. Hansen and McDonald (1990)

summarize some of the failures of RISM and look at efforts to come up with more

accurate models. They do observe that while there have appeared models that in a

formal sense would appear more correct than RISM, they have not yielded better


52

results. Work by Lue and Blankschtein (1995) provides an example of more recent

efforts to develop integral equation theories. They present results for water for the

site-site Ornstein-Zernike equation and the Chandler-Silbey-Ladanyi equations. It

should also be noted that efforts have been made to improve or correct the RISM

formulation (Hirata 2003 and Kvamme 2002). Development of such integral

equation theories is clearly a difficult issue, the mathematics of formulating the

equations is in itself demanding and so is the issue of solving these equations for a

given system.

It should be emphasized that these integral equation models do not say anything

about the nature of molecular interactions, rather they can be seen as an alternative

to simulations that when coupled with a molecular representation offers a model of

the liquid state. RISM as a model for solvation will be discussed in section 4.4 5.

4.4 Models to Calculate the Free Energy of Solution

4.4.1 Introduction

The free energy of the solvation ( 0sG∆ ) is the free energy change associated with a

molecule leaving the gas phase and entering a condensed phase. It is the liquid

property that will be of greatest interest in the present work. It may for a given

species A be determined from equilibrium data by the following equation (Cramer

2002):

[ ]

[ ][ ]

0

0( ) lim ln

sol

sols A

gas eq

AG A RT

A→

⎧ ⎫⎪ ⎪⎪ ⎪⎪ ⎪∆ = −⎨ ⎬⎪ ⎪⎪ ⎪⎪ ⎪⎩ ⎭ (4.9)

This formulation draws on work by Ben-Naim (Ben-Naim and Marcus 1984 and

Ben-Naim 1992). While the equation in the form it is stated here is for infinite

dilution, it can also be formulated for other conditions. While the free energy of

solvation is perhaps not a quantity that most people in chemical engineering are


53

familiar with, it does contain information relevant to several aspects of liquids

equilibrium that in chemical engineering is represented in other forms. If the

energy for the reaction in the gas phase and the solvation energy for each

component is known the reaction energy in solution can be calculated. The free

energy of solution also conveys information about the vapor-pressure of a given

species (Winget et al. 2000) and solvation energies can also be converted into

activity coefficient data (da Silva 2004).

The present review is intended to cover all the main approaches to calculating

solvation energies. The form of the present outline draws mainly on reviews by

Bacskay and Reimers (1998) and Orozco and Luque (2000). While I have tried to

make this review fairly broad the main focus will be on models that may be

suitable for modeling CO2 absorption. As noted in Chapter 2 the CO2 capture

processes is usually run with base molecules in water and most attention will also

be given to the modeling of aqueous solution. Water is also, for obvious reasons,

the solvent that has received the greatest attention in the literature.

4.4.2 Equation of State and Lattice Models

The interest of chemists in understanding, modeling and predicting the behavior of

liquids predates computational chemistry and there are models not based on any

form of computational chemistry. The present outline of such models is drawn

from the textbook “Molecular Thermodynamics of Fluid-Phase Equilibria

(Prausnitz, Lichtentaler and Gomes de Azevedo 1999). The authors distinguish

between two main approaches. One is based on approaching a liquid with a gas

model and the second on approaching it with a solid-like lattice model.

The first approach leads us to the equation of state models. From an equation of

state the free energy (Helmholtz or Gibbs) can be determined and from an equation

of state for mixtures the free energy of each component can be derived.


54

The lattice models are based on thinking of molecules in liquids as occupying

spaces in a grid. Mixing of two pure components can be envisioned as molecules

exchanging places in the grid. If interaction parameters are introduced the energy

and entropy change associated with mixing can be calculated.

Considering a liquid as a dense gas or a rigid lattice is a fairly drastic

approximation and the first such models were not all that successful. More

advanced models have however been developed that successfully capture the

behavior of many types of solvents. Such models are however in general not able to

predict properties for systems where no experimental data is available. The

parameters in the equations are fitted to reproduce experimental data, and the

parameters together with the equations can perhaps be thought of as a way to

summarize experimental data for a given system. What such models can do is

predict the behavior for a system over changing concentrations, temperature and

pressure. Examples of such applications on CO2 capture related issues can be found

in the work of Solbraa (2002) and Hoff (2003).

There is however a family of models derived from equation of state and lattice

models to do predictive calculations. These are group contribution models. The

most famous of these is perhaps the UNIFAC model (Fredenslund, Gmehling and

Rasmussen 1977). These are based on breaking up a molecule into units such as

hydroxyl-, alkane- and amino-groups. The properties of the solvent are attributed to

its various groups. Some form of database is constructed of groups and their

parameters, when a new molecule is encountered the groups it is composed of is

identified and from these the properties are predicted. While such models see fairly

wide use they do have clear limitations.

In Figure 4.2 is shown two possible conformers of ethanolamine. In one of the

conformers there is an intramolecular hydrogen bond, if such a bond is formed in

solution then this will reduce the extent of bonding formed with other species. The

interactions with other species will therefore depend on which conformer form is


55

preferred. Yet present group contribution methods do not take account of such

conformer effects and their reliability in cases where such issues arise would seem

questionable, a conclusion also drawn by Wu and Sandler (1991).

Figure 4.2 Conformers of ethanolamine.

Another, and perhaps more fundamental, issue is if the parameters in a model such

as UNIFAC are sufficient to capture effects of all interactions in a liquid. UNIFAC

is in form similar to traditional equations of state models such as UNIQUAC and

NRTL. These are all sets of quite simple equations, energy interactions between

different species are usually represented by a single parameter. It would seem

questionable if such a small number of parameters can accurately capture the

complex interactions in a liquid. In Figure 4.3 three pairs of water molecules are

shown. The interaction energy is obviously different for the different pairs, the

energy depending on distance and orientation of the molecules. A single parameter

can perhaps express the average of all interactions in a given system, but if the

composition of a system changes the average interaction for a given component

might also change.


56

Figure 4.3 Interactions of water molecules.

More advanced models have been proposed in recent years, one notable model

being the Statistical Associated-Fluid Theory (SAFT) (Chapman et al. 1989 and

Chapman et al. 1990). This model has expressions to take account of contributions

from short-range repulsion, long-range dispersion, chemical bonding and

association or hydrogen bonding between different molecules. It is also noteworthy

that the model was tested for consistency with molecular simulation during

development.

While advanced models such as SAFT seem better formulated to capture the

various effects that play a part in solution the number of parameters in the model is

also inevitably greater than for the simpler models such as UNIQUAC. In the

absence of more detailed experimental data the determination of parameters for a

more advanced model can be a difficult task. While such advanced models do

represent progress and may in general be considered to be better than simpler

models, the underlying issues of parameter fitting must always be kept in mind.

4.4.3 Continuum Models

Continuum models are the group of solvation models in computational chemistry

that have seen the greatest use. These models have a long history, some of the early

work was carried out by the Norwegian Lars Onsager (Onsager 1936). Rather then

explicitly representing solvent molecules, the solvent is represented by a


57

continuous electric field that represents a statistical average over all solvent degrees

of freedom. Such models are also known as implicit solvation models. The outline

given here will be based on the textbook “Essentials of Computational Chemistry”

(Cramer 2002). Continuum models have been the subject of numerous reviews in

recent years (Tomasi and Persico 1994, Cramer and Truhlar 1999, Orozco and

Luque 2000) and I will to some extent draw on these too in the present outline.

At the heart of the continuum models is the Poisson equation. This is valid when

a surrounding dielectric responds linearly to embedding charges:

( ) ( )2 4πρφ

ε∇ =−

rr (4.10)

where ρ is the charge density, φ is the electrostatic potential and ε is the dielectric

constant. The Poisson equation is valid under conditions of zero ionic strength, for

charged species the Possion-Boltzmann equation applies:

( ) ( ) ( ) ( ) ( ) ( )2 sinh 4B

B

qk Tq k T

φε φ ε λ κ πρ

⎡ ⎤⎢ ⎥∇ ⋅∇ − =−⎢ ⎥⎣ ⎦

rr r r r r (4.11)

where λ is a function that switches from zero in areas not accessible to the

electrolyte to one in areas that are accessible and q is the magnitude of the charge. 2κ is the Debye-Huckel parameter:

22 8

B

q Ik Tπκε

= (4.12)

where I is the ionic strength. The work needed to create a charge distribution can

be determined from the following equation.

( ) ( )12

G dρ φ=− ∫ r r r (4.13)

In continuum models the solute is placed in a cavity representing the space

occupied by the solute in the solvent. Such a procedure is illustrated in Figure 4.4.


58

Figure 4.4 Creation of Cavity and Insertion of Solute in Solvent.

In the first continuum models cavities were simple spheres, while in most present

models they are usually built as a set of spheres around each atomic centre.

Continuum model calculations can be carried out with either a molecular

mechanical or quantum mechanical representation of the solute, the latter does

however represent a more rigors model. In quantum mechanical continuum

calculations an iterative cycle is often used. First the solute with its gas phase

electron distribution is inserted into the cavity. The solvent electrostatic field that

arises from the solute charges is calculated, this is usually called the reaction field.

The reaction field is then introduced as an external potential in the quantum

mechanical calculation. This is done by solving the following form of the

Schrödinger equation:

12

H V E⎛ ⎞⎟⎜ − =⎟⎜ ⎟⎜⎝ ⎠

ψ ψ (4.14)

where V is the reaction field inside the cavity. The reaction field is then

recalculated based on the new solute charge distribution. This is repeated in an

iterative procedure until the energy of the system converges. The energy change

obtained from such a calculation is usually called the electrostatic energy. There

are however other contributions to the solvation energy.

The free energy of solvation can be thought of as consisting of three main

contributions (Orozco and Luque 2000):


59

s electrostatic cavitation van der WaalsG G G G∆ =∆ +∆ +∆ (4.15)

The electrostatic contribution is the term just described. The cavitation term

represents the energy that is needed to create room for the solute in the solvent.

Finally the van der Waals term is the energy that comes from dispersion and

repulsion interactions between solute and solvent molecules. In addition it should

be noted that if the solute causes rearrangement in the solvent structure that can

also give a contribution to the solvation energy (Cramer and Truhlar 1999). The

continuum models are in essence electrostatic models and estimates for the other

contributions must be sought elsewhere. The cavitation and van der Waals terms

are usually included as semi-empirical terms which size is made proportional to the

size of the solute cavity.

It should be clear from this outline that determining the size and shape of cavities

is a central issue in developing and applying continuum models. Cossi et al. (1996)

describe the selection of cavities as “one of the most delicate steps in defining a

continuum solvation model”. While cavities can be easily understood as the space

occupied by a solute molecule in a solvent this is not an unambiguously defined

property, nor is it experimentally observable. Many definitions have been

proposed, one of the more common is the van der Waals surface, defined as the

cavity formed by van der Waals spheres centered on the atoms (Cossi et al. 1996).

There is also no requirement that the same definition of the cavity be used in the

calculation of electrostatic and other terms, in the PCM model (to which I will

return) different definitions are in fact utilized (Cossi et al. 1996).

As noted some of the energy contributions in continuum models are usually

determined in some form of fitting to experimental data and there is also some

arbitrariness in the selection of cavities. Continuum models are often directly fitted

to free energies of solvation. This fitting process does mean that these models tend


60

to be semi-empirical in nature. One consequence is that the models tend to be

limited to the solvent and conditions for which they were parameterized. It also

means that the validation of different models can be somewhat difficult. The

empirical contributions may mask errors in the electrostatic model, this means that

the underlying quality of the model is not that easily determined from comparisons

with experimental data. This can perhaps create challenges in the further

development of continuum models.

Continuum models are in general reasonably good at reproducing the free

energies of neutral solutes, but less accurate for ions. The nature of the models does

raise some questions about how reliable they can be. One of the issues often

debated is to what extent they can capture effects of interactions in the first

solvation shell such as hydrogen bonding (Cramer and Truhlar 1999 and Kawata et

al. 1996).

In a continuum model a solvent is represented by a fairly small number of

parameters, among them the dielectric constant. With such a form of solvent

representation it is unclear if and how such models can be extended to mixtures of

solvents. Many continuum models do also tend to be dedicated to calculations at

infinite dilution.

A great number of variations of continuum models have been proposed, here I

will briefly review some of the more common models.

PCM The Polar Continuum Models (Miertus, Scrocco and Tomasi 1981, Cossi,

Barone, Cammi and Tomasi 1996 and Cances, Mennucci and Tomasi 1997) are the

continuum models that see the greatest use in the context of quantum mechanical

calculations. One of the main reasons for this is that the models are implemented in

the widely used Gaussian programs (Frisch et al. 1998). These models are also

regarded as being fairly robust and flexible in the sense that they can be easily

applied to different molecules and systems. In the PCM the cavity surface is

divided into surface areas called tessarae.


61

The reaction field of the solvent is represented by charges placed on the cavity

surface. PCM calculations can be carried out on in combination with most forms of

quantum mechanical calculations.

SM The “Solvent Model” are a series of models developed by Cramer, Truhlar

and co-workers (Chambers et al. 1996 Li et al. 1999). The philosophy behind these

models is somewhat different from that behind the PCM models. In the

development of SM models a number of different forms have been tested. The

developers, rather than focusing on developing a single form of rigorous model,

have implemented various models. They have studied how different models, when

properly parameterized, are able to reproduce the experimental free energies. A

particular feature is the use of atomic surface tensions ( kσ ) (Li et al. 1999). The

free energy is in this model the sum of electrostatic and surface tension

contributions. These atomic surface tensions are purely empirical terms intended to

capture cavitation, van der Waals contributions and any other contributions arising

from the first solvation shell.

The SM models are in general based on simpler electrostatic calculations than the

PCM models and offers results of comparable quality from calculations that are

much less time consuming. They do however rely on more extensive use of

empirical data.

COSMO-RS The COSMO model was originally only one type of

implementation of a continuum model (Klamt 1995 and Andzelm, Kölmer and

Klamt 1995). In the COSMO calculations the solvent was considered to be an

electric conductor with an infinite dielectric constant, this having the virtue of

facilitating the calculations. COSMO-RS (“Realistic Solvent”) represents the

development by Klamt and co-workers (Eckart and Klamt 2002 ) of a model

designed to study properties both for pure components and liquid mixtures. The

model can therefore be used for a number of problems of interest in chemical

engineering. While results published with the COSMO-RS model seem


62

encouraging (Eckart and Klamt 2002) it must be noted that this is a proprietary

model and that there might therefore perhaps be less transparency regarding its

strength and weaknesses than is the case for other models. All the publications on

this model have to my knowledge been by the developers themselves.

4.4.4 Molecular Simulation

In the last chapter MC and MD simulations were briefly introduced. In such

calculations the solvent molecules are explicitly represented and such models are

also called “explicit models” (while the continuum models are implicit). As noted

in the last chapter simulations are time consuming, the simulation time increasing

with the number of molecules being studied and the level of molecular

representation. Today most simulations are done with molecular mechanics

representation of solvent and solute. In both MD and MC there are techniques to

obtain the free energy of the solvation, one of the most common methods being

free energy perturbations.

As noted in the last chapter a key approximation made when using a molecular

mechanics representation is that charges are fixed. Polarization is handled

implicitly by using values for the charges intended to reflect the average

polarization in the liquid. Compared to a continuum model the polarization effects

are handled in a simpler manner in standard simulations.

Simulations are not packaged as models in the same way continuum models are.

Most simulation codes give the user great freedom in selecting the force field

parameters.

The parameters for many force fields are derived from fitting to empirical data.

The parameterization is usually based on reproducing liquid properties, and is thus

very different in nature from that used for the continuum models.


63

As indicated in the last chapter there is also many ways in which quantum

mechanical calculations can be used to determine force field parameters. The most

important use is in determination of molecular geometry and atomic charges.

As noted in the last chapter there are a number of ways in which partial atomic

charges can be derived from quantum mechanical calculations. What kind of

schemes will lead to more accurate solvation energies is still an open question.

In the last chapter it was also observed that polarizable force fields are available.

While such simulations are still too time-consuming to be done on a routine basis it

is clearly an option to consider if a more realistic solvent representation is desired.

With simulations the study of liquids composed of two or more components is in

principle no problem. As a system becomes less homogeneous it would however

seem very likely that the sampling required for satisfactory average values will

increase. Simulations can also quite readily be used to study systems with different

temperature. Pressure conditions can also be controlled, although this is still

perhaps somewhat more difficult than temperature control (Allen and Tildesley

1987).

4.4.5 RISM and RISM-SCF

In the statistical mechanics section of this chapter the RISM equations were

introduced. RISM can be regarded as an alternative to simulations, that when

combined with a molecular representation offers a solvent model from which the

free energy of solution can be calculated. Calculations where the solute and solvent

have a molecular mechanics representation is called a classical RISM calculation.

RISM-SCF (Hirata 2003 and references therein) combines a classical solvent

representation with a quantum mechanical solute representation. The calculation

procedure is analogue to the one described for the continuum models. From a

quantum mechanical calculation in the gas phase partial atomic charges are


64

calculated and a RISM calculation is carried out to determine the solvent structure

around the solute. From the solvent structure the reaction field is calculated and a

new quantum mechanical calculation is carried out to determine the atomic charges

in the presence of the field. This is repeated until convergence.

An RISM-SCF calculation has the virtue of combining the explicit solvent

representation of a classical simulation with the solute polarisation term found in

the continuum models. As in a standard simulation polarization of solvent

molecules is only included implicitly in present forms of RISM-SCF. As noted

previously the RISM equations involve some approximations, and compared to

simulations this adds a layer of uncertainty. The issues regarding force fields and

atomic charges are the same in RISM calculations as in simulations. In present

implementations of RISM-SCF (Kawata et al. 1996) the solute charges are

determined by fitting the charges to the electrostatic potential.

The complexity of the underlying equations and problems that can appear in

obtaining converged solutions have probably contributed to this type of model

seeing less use than continuum models and simulations.

4.4.6 Supermolecule Approach

The supermolecule approach is a term used for calculating the entire system

quantum mechanically. Traditionally this has been done by performing calculations

with some few solvent molecules in vacuum. While such an approach can be useful

in determining the direct effect of solvent molecules on the solute it is more

difficult to use such an approach for systematic calculations of solvation energy.

Solute molecules can vary in shape and size and the number of solvent molecules

that is needed to represent the main interactions will vary. As noted in the first part

of this chapter the observed properties of a liquid represent averages over large

numbers of configurations, it is clear that a calculation based on a single geometry

will often not reflect such averages.


65

A more advanced form of supermolecule calculations are QM/MD (Quantum

Mechanical Molecular Dynamics) and QM/MC (Quantum Mechanical Monte

Carlo) calculations. In such calculations simulations are carried out on molecules

represented at a quantum mechanical level. Such calculations are seeing increasing

use. The most famous, but far from the only, such approach is the Car-Parrinello

Molecular Dynamics scheme (Car and Parrinello 1985). Such calculations are

obviously very time-consuming and I am not aware of any such model being used

to calculate free energies of solution. Free energies from such simulations can

perhaps be determined by a scheme similar to what has been suggested for

QM/MM calculations (Cummins and Gready 1997).

4.4.7 Hybrids of Computational Chemistry approaches

Looking at a radial distribution function it is clear that the short-range and long-

range interactions are different in nature. At short range the interactions take on the

nature of weak bonding or repulsion, while at long range the solute molecule only

“sees” the averaged effect of a large number of solvent molecules. This would

suggest that one is perhaps best served by using a model that has a better solvent

representation at short range than at long range.

One such approach is to combine the supermolecule approach with continuum

models. A small number of explicit solvent molecules can be included inside the

cavity. While such calculations see some use there is an issue of how many solvent

molecules to include, and how to do it in a consistent way for molecules of

different size and shape (Cramer and Truhlar 1999).

Another form of hybridization is QM/MM models introduced in the last chapter.

In such models part of the system is described with a molecular mechanics

representation and other parts have a quantum mechanical representation. The

simplest form would involve representing the solute quantum mechanically and

using a MM representation of the solvent. In more advanced calculations some of


66

the solvent molecules closest to the solute can also be represented at a quantum

mechanical level. Calculations are carried out using some kind of simulation. To

obtain sufficient statistical sampling a simulation must usually be carried out for

many thousand steps, if one needed a QM calculation for each step and each QM

calculation took something like an hour, it is easy to see that such simulations can

become very time-consuming. One approach taken to reduce the time consumption

is to use very low level semi-empirical QM models (Kaminski and Jorgensen 1998

and Cummins and Gready 1997). Such an approach does on the other hand also

reduce the quality of the results obtained. Another interesting proposal is to use

MM simulations to calculate geometries and do set of QM calculations on energies

only (Wood et al. 1999). This proposal does suggest that there is room for

refinement of QM/MM methods by only using the QM calculations for the most

vital part of the calculations.

4.4.8 Descriptor Models

One of the approaches often taken in science when confronted with predicting a

certain property is to correlate it to another known property. While this approach

has perhaps not been used that much to determine the free energy of solvation

itself, it has often been used in estimating different equilibrium constants in

solution. An example of this can be found in the work of Eimer (1994) that finds a

correlation between an equilibrium constant and molecular weight, and uses this to

estimate the value for molecules where the equilibrium constant is not known. Such

applications involve a form of implicit estimation of solvation energies.

Approaches based on correlations with experimentally observable properties have

been in use for a long time and do not require any input from computational

chemistry.

Computational chemistry methods can however be used to determine a large

number of molecular characteristics that can otherwise not be obtained. This offers


67

new sets of descriptors that can be applied in finding correlations with the solvation

energy or equilibrium constants. A motivation for using such an approach is that

computational chemistry methods may calculate some property with greater

accuracy than the free energy itself can be calculated. One descriptor that can be

determined from simulations and that is used in finding correlations with solvation

energies is the solvent-accessible surface area (SASA) of a molecule, this can be

thought of as a form of “efficient surface area”. Duffy and Jorgensen (2000)

obtained encouraging results when looking at correlations between SASA, other

descriptors related to extent of hydrogen bonding and solvation energies. Another

model based on SASA has been developed by Kollman and coworkers (Wang et al.

2001). It can also be noted that some forms of the SM continuum models are

similar in nature to descriptor models.

4.4.9 Other Models

The outline and classification of models so far covers the most widely applied

approaches to determining solvation energies. There are however some methods

that do not fall within any of these categories. The most notable is perhaps the

Langevin-Dipole method (Warshel and Levitt 1976). The solvent is in this model

represented as a grid of dipoles. This method lies somewhere between a continuum

model and an explicit solvent model.

There are also a number of ways in which one can imagine combining different

approaches to calculating solvation energies. New variations do appear from time

to time in the literature, and combining aspects of different models is one way

forward to obtaining models that produce more accurate results within a given

timeframe.


68

4.4.10 Hybridization of Gibbs Energy Models and Computational Chemistry

Based Models

It is likely to take some time before computational chemistry methods can provide

robust a priori quantitative predictions of solvation energy for multi-component

systems. An option that might be worth exploring is to pursue a general semi-

empirical approach, drawing on whatever information is available experimentally

and using computational chemistry to fill in the gaps.

One way to do this would be to use methods in computational chemistry to

determine parameters for a lattice or equation of state model while at the same

maintaining the models reproduction of experimental observations.

Some early efforts along these lines are work by Jonsdottir et al. (1996) and Sum

and Sandler (1999). Both these works are based on determining the parameters for

the UNIQUAC model. The general problem with this work is that the UNIQUAC

parameters do not have any clear definition. Fischer (1983) warns against assigning

a physical meaning to these empirically determined parameters. Attempting to

predict ill-defined parameters is obviously a most unpromising line of research. I

comment in greater detail on the work by Sum and Sandler in a paper appearing as

a part of this thesis (da Silva 2004).

While UNIQUAC and similar equations are not suitable for combinations with

data from computational chemistry, more advanced models may be. The SAFT

equations would seem to be a promising candidate.

It would seem that there is a potential to combine information from

computational chemistry with some form of free energy model. This is however

likely to be a time-consuming task, requiring careful work and patience.


69

4.5 Comparison of Methods to Calculate the Free Energy of Solution

4.5.1 Methods

In the last section a fairly broad review was made of models available to calculate

the free energy of solvation. In the present section a direct comparison will be

made between a series of models in the calculation of amine basicity. This

comparison should give an idea of how far computational chemistry has come in

meeting the expectations of Jones and Arnett (quoted in the beginning of this

chapter).

In choosing models for this comparison an effort has been made to include as

many as possible of what seems to be the most promising methods. Not all solvent

models are however distributed as ready to use software. Some only exist as codes

in the laboratories developing the model, and can only be obtained by cooperation

with the researchers behind the model. Of such models the RISM-SCF model has

been included in the present comparison. Two of the models chosen are among the

widely used continuum models. The final models are MC simulations with free

energy perturbation. As noted in the previous chapter, there are numerous ways to

calculate the solute atomic charges from QM calculations. In the present work two

somewhat different types of charges are tested.

The comparison is intended to assess the models on an equal basis. All models

have been run with settings that were expected to be close to optimal, in general

that has meant using types of calculations similar to the ones in the papers first

describing the models. No effort has however been made to tune any of the models

to be in better agreement with the experimental data in consideration. It should be

emphasized that the present comparison does not attempt to address the overall

potential or quality of different models.


70

The RISM-SCF and simulation results appear in a paper in this thesis (da Silva,

Yamazaki and Hirata 2005). A detailed discussion of methods and results for these

calculations can be found in that paper.

PCM. In the present work the IEFPCM (Cances, Mennucci and Tomasi 1997)

model was used with its default settings in Gaussian 98 (Frisch et al. 1998) with 60

tesserae per atomic sphere. Calculations were carried out on HF/6-31G(d) gas

phase geometries (IEFPCM/HF 6-31G(d)//HF 6-31G(d)).

SM. The SM 5.42R model implemented in Gamesol (Xidos et al. 1993) has been

utilized. This model uses gas phase geometries and is parameterized for a series of

basis-sets. Calculations are carried out with HF/6-31G(d) gas phase geometries and

energies (SM 5.42R/HF 6-31G(d)//HF 6-31G(d)). Data in the Gamesol distribution

manual (Xidos et al. 1993) suggests that this level of calculation should be close to

optimal for the SM solvation model.

RISM-SCF. RISM-SCF calculations were carried out at the HF/6-31G(d,p) level.

The solute Lennard-Jones parameters are from the all-atom OPLS force field

(Jorgensen et al. 1996 and Rizzo and Jorgensen 1999) while the solvent was

represented with the TIP3P (Jorgensen et al. 1983) water model. Solute atomic

charges were determined by fitting to the electrostatic potential.

FEP-MK. A set of free energy perturbations were carried out with MK type

charges (described in the last chapter). The solute Lennard-Jones parameters are

from the all-atom OPLS force field (Jorgensen et al. 1996 and Rizzo and Jorgensen

1999) while the solvent in this case was represented with the TIP4P (Jorgensen et

al. 1983) water model. Both the solute and solvent representation in these free

energy perturbations were similar to what is utilized in the RISM-SCF calculation.

FEP-CM2. A second set of free energy perturbations were carried out with CM2

type charges (also described in the last chapter). The solute and solvent

representation was otherwise the same as for the FEP-MK simulations.


71

4.5.2 The Basicity

The property that has been chosen for the present comparison is the relative

basicity of amines. Amines are the family of molecules that are of main interest in

the present work. The basicity is in itself one of the amine properties of greater

interest. The calculation of basicity requires the calculation of solvation energy of a

neutral molecule and it’s protonated (and ionic) form and the gas phase basicity.

This can therefore provide a fairly rigorous test of how good a solvation model is,

provided accurate gas phase basicities are available. In addition there is accurate

experimental data available with which to compare the model results. For base

reaction the following equilibrium can be set up:

B Ha

BH

a aK

a+

+

= (4.16 )

The free energy of protonation in aqueous solution ( psG∆ ) is related to Ka by the

following equation:

2.303 logps aG RT K∆ =− (4.17)

The calculations are based on the following thermodynamic cycle.

Figure 4.5. Thermodynamic cycle.


72

Quantum mechanical calculations are used to determine gas phase basicities, while

solvation models are used to determine solvation energies ( sG∆ ). These results can

be added together to give the free energy in aqueous solution. In the present

comparison only the relative basicities will be studied. The quality of a model is

given by how close calculated relative basicities are to the relative experimental

values.

4.5.3 Amines

The amines included in the present study are shown in Figure 4.6. To reduce the

complexity of the comparison amines with uncertain conformer forms are not

included. This study does however include amine molecules that display significant

variations in geometry.

Figure 4.6 Amines in present study.


73

4.5.4 Results

In Table 4.1 the calculated gas phase basicity data are shown. These can be seen to

be in good agreement with experimental data.

Table 4.1 Relative Gas Phase Protonation Energies. Data in [kcal/mol].

Molecule Theoreticala Experimentalb

Ammonia 0.0 0.0

Methylamine 10.2 10.9

Ethylamine 14.3 14.1

Dimethylamine 17.9 18.5

Trimethylamine 22.2 23.7

Piperidine 24.2 24.4

Piperazine 23.3 22.9

Morpholine 17.0 17.3

Pyrrolidine 23.6 23.0

2,2,6,6-Tetramethyl-4-piperidinol (TMP) 29.7 a B3LYP/6-311++G(d,p) energy with thermal correction and ZPE calculated at HF/6-

31G(d) level.b Data from Hunter and Lias(2003).

In Table 4.2 and 4.3 the solvation energies determined with the different models

are shown. The simulations have only been used to calculate relative solvation

energies between the amines. To facilitate the comparison with the other data in the

tables the absolute energy from the SM continuum model has been added. The

RISM-SCF calculations have a systematic error that leads to an overestimation of

the size effect on the solvation energy (da Silva, Yamazaki and Hirata 2005). In

determining the basicity it is the difference of solvation energies between two


74

species of approximately the same size that is important and this error is therefore

expected to cancel out.

Table 4.2 Free Energy of Solvation for Neutral Amines. Data in [kcal/mol].

Molecule RISM-SCF FEP-MK FEP-CM2 PCM SM Exp.a

Ammonia -0.3 -4.87b -4.87b -4.30 -4.87 -2.41

Methylamine 5.1 -4.26 -6.72 -4.75 -5.14 -2.68

Ethylamine 10.1 -5.13 -6.36 -4.48 -4.90 -2.61

Dimethylamine 13.6 -1.40 -4.24 -4.30 -3.78 -2.41

Trimethylamine 23.3 1.44 -3.67 -2.76 -2.98 -1.34

Piperidine 24.1 -2.26 -4.65 -4.91 -4.33 -0.83

Piperazine 16.7 -7.41 -5.8 -10.65 -9.08

Morpholine 15.8 -5.34 -7.14 -9.01 -7.24

Pyrrolidine 21.5 -2.08 -9.50 -5.56 -6.03

TMP 47.9 -25.36 -6.98 -8.34 -5.62

a Data from Jones and Arnett (1974).b SM model values.


75

Table 4.3 Free Energy of Solvation for Protonated Amines. Data in [kcal/mol].

Molecule RISM-SCF FEP-MK FEP-CM2 PCM SM

Ammonia -57.6 -87.19a -87.19a -79.9 -87.19

Methylamine -43.5 -76.23 -80.90 -70.25 -76.39

Ethylamine -37.8 -75.48 -79.63 -67.79 -72.70

Dimethylamine -29.7 -69.14 -71.78 -65.45 -67.07

Trimethylamine -16.6 -62.60 -63.57 -59.12 -59.38

Piperidine -9.5 -61.60 -69.09 -62.35 -61.70

Piperazine -21.3 -61.60 -70.92 -69.22 -66.20

Morpholine -22.1 -72.43 -75.08 -71.78 -67.73

Pyrrolidine -17.2 -66.06 -70.89 -63.79 -63.91

TMP 23.9 -86.64 -65.29 -57.61 -56.23

a SM model values.

In Table 4.4 the relative free energy of protonation determined from experimental

data and the various solvation models are shown. All data are given relative to

ammonia.


76

Table 4.4 Basicity in solution. Data in [kcal/mol].

Molecule exptl pKa Gps

a Gpsa

exptl RISM-SCF FEP-MK FEP-CM2 PCM SM

Ammonia 9.24b 0.00 0.0 0.0 0.0 0.0 0.0

Methylamine 10.65b 1.92 1.5 -0.2 2.1 0.1 -0.9

Ethylamine 10.78b 2.10 5.0 2.3 5.3 2.0 -0.2

Dimethylamine 10.8b 2.13 3.9 3.3 3.1 3.5 -1.1

Trimethylamine 9.80b 0.90 4.8 3.9 -0.2 3.0 -3.7

Piperidine 11.12c 2.56 0.5 1.2 6.3 6.0 -0.8

Piperazine 9.83c 0.80 4.0 6.0 10.2 6.3 -1.9

Morpholine 8.49c -1.02 -2.3 1.7 2.6 4.2 -4.8

Pyrrolidine 11.30c 2.81 5.1 5.2 2.7 6.2 -0.9

TMP 10.05c 1.10 -3.5 8.6 5.7 3.4 -2.0

a Energies relative to ammonia. b Data from Jones and Arnett (1974). c Data from

Perrin (1965).

In Figure 4.7 the gas phase basicity is plotted against the experimental pKa. This

figure illustrates the importance of solvation energies in determining relative

basicities in solution. Figure 4.8 shows the results for the RISM-SCF, FEP-MK and

FEP-CM2 models. Finally in Figure 4.9 the PCM and SM results are shown.


77

Figure 4.7 Calculated gas phase basicity versus experimental pKa. The stippled

line indicates the theoretical trend (in solution) relative to ammonia.


78

Figure 4.8 Calculated solution phase basicity versus experimental pKa Crosshairs are

RISM-SCF, open circles are FEP-MK and squares are FEP-CM2. The stippled line

indicates the theoretical trend relative to ammonia.


79

Figure 4.9 Calculated solution phase basicity versus experimental pKa. Triangles are PCM

results while diamonds are SM model. The stippled line indicates the theoretical trend

relative to ammonia.

4.5.5 Conclusion

Looking at Figure 4.8 and 4.9 it is clear that none of the models produce results in

full agreement with experimental data. All the models do however successfully

close the large differences between relative basicities in gas phase and solution

(Figure 4.7). It must however be concluded that the expectation expressed by Jones

and Arnett (quotation in beginning of this chapter) over 30 years ago have only

partly been met.

Cramer and Truhlar (1999) did in their review note that accurately predicting the

relative basicity in solution between ammonia, methylamine, dimethylamine and

trimethylamine has proven to be difficult. Amines distinguish themselves from

most other functional groups in having varying number of hydrogen atoms, thereby


80

also having a varying potential to form intermolecular hydrogen bonds. None of the

present models are accurate enough to capture differences caused by such changes

at a quantitative level.

The agreement with experimental data is comparable for the different models.

The SM model does produce the best trend, the main error being in the solvation

energy of ammonia. A rather odd feature of Figure 5.8 is that the two continuum

models appear to have errors of same dimension and opposite sign for the different

molecules. Agreement with experimental data for the SM model is consistent with

its reported uncertainty for ionic species (Li et al. 1999). The level of agreement

with experimental data for the other models is also generally in line with what is

reported in the literature. It should be emphasized that all models are reasonably

robust in a qualitative sense, capturing larger trends in solvation energies.

5 Reaction Mechanisms and Equilibrium

81

5 Reaction Mechanisms and Equilibrium Kinetics is nature’s way of preventing everything from happening all at once.

S. E. LeBlanc

5.1 Introduction

This chapter is intended to give an overview of the reaction mechanisms of CO2

absorption in aqueous amine systems. On several key points it draws on my own

work. Most of it published (da Silva and Svendsen 2004a and da Silva and

Svendsen 2004b), but some not previously presented. This chapter also serves as a

review of observations in the literature. In addition to providing an overview of the

important aspects of CO2 capture, this chapter is also intended to show to what

extent central equilibrium constants can be modeled. This part is mainly based on

my own modeling work.

5.2 Reaction Mechanisms 5.2.1 Introduction

CO2 reacts in aqueous amine systems to form either bicarbonate or carbamate.

These species are shown in the figure below. The R groups in NR2 can be a proton

or any form of substituent group.

Figure 5.1 Bicarbonate and carbamate.


82

Bicarbonate is produced by the reaction of a CO2 molecule with a water molecule,

while carbamate is formed by the reaction of a CO2 molecule with an amine

molecule. CO2 in the liquid is bound almost entirely in one of these two forms, and

only a small fraction is found as free CO2.

5.2.2 Bicarbonate Formation

The formation of bicarbonate from CO2 and water is a well known reaction in

chemistry. There are three (related) mechanisms for this reaction.

2 2 2 3CO H O H CO+ (5.1)

2 3CO OH HCO− −+ (5.2)

2 3 3 2H CO OH HCO H O− −+ + (5.3)

Bicarbonate can again be deprotonated by a base molecule (B).

23 3HCO B CO BH− − ++ + (5.4)

The base molecule is usually an amine molecule or a hydroxyl ion (OH− ). By

itself bicarbonate formation is however a rather slow reaction. It has been observed

that this reaction proceeds more quickly in the presence of amine molecules, an

effect beside the direct effect of the amines acting as bases (Donaldsen and Nguyen

1980). It is also known that Brønsted bases can act to catalyze the formation of

bicarbonate (Sharma and Danckwerts 1963).

Calculations have been performed to identify a mechanism that might account for

this increased reaction-rate. These calculations were performed with PC Spartan

(1999) at the HF/6-31G(d,p) level. Calculations were performed with one water

molecule and one CO2 molecule in the presence of an ethanolamine molecule. In


83

this case the reaction coordinate chosen was O(H2O)-C(CO2). The determined

transition-state geometry is shown in Figure 5.2.

Figure 5.2 Transition state of bicarbonate formation.

The transition state identified in these calculations is consistent with the

mechanism proposed by Donaldsen and Nguyen (1980):

Figure 5.3

At the HF/6-31G(d,p) level this mechanism was found to have a barrier of 29.5

kcal/mol. For the bicarbonate formation in water a reaction-barrier of 42.5 kcal/mol

has been reported with the same type of calculation at the same level of theory

(Nguyen et al. 1997). The presence of base-molecules can therefore be seen to give

a significantly lower barrier to bicarbonate formation.


84

While this mechanism is usually mentioned in the context of tertiary amines I do

not believe it is unique to them. As observed above, it is known that base catalysis

can take place for a number of Brønstad bases. The calculations suggest that this

reaction will take place with any base molecule of appropriate strength. For

primary and secondary amines the kinetics will however often be dominated by

carbamate formation and base catalysis will play a lesser role and perhaps be more

difficult to detect experimentally. Base catalysis may however be significant for

primary and secondary amines in systems where bicarbonate formation dominates.

5.2.3 Carbamate formation

The carbamate formation is one of the main reactions of CO2 absorption. Two

mechanisms have been proposed for this in the literature. One is the zwitterion

mechanism originally proposed by Caplow (1968):

Figure 5.4

In this mechanism CO2 forms a bond to the amine functionality in a first step. In a

second step an amine-proton is transferred to a second molecule. In Caplows article

the second molecule was water, but this can be any base-molecule.

The intermediate species in the reaction is a zwitterion. Caplow assumed (as shown

in Figure 5.4) that a hydrogen bond is formed between the amine and a water

(base) molecule before the amine reacts with the CO2 molecule. This feature has

however been omitted in the recent literature, as can be seen in the work by

Danckwerts (1979), Versteeg et al. (1996) and Kumar et al. (2003).


85

Crooks and Donnellan (1989) proposed the following single-step mechanism:

Figure 5.5

Here B is a base molecule. In this mechanism the bonding between amine and CO2

and the proton transfer take place simultaneously.

It has been argued that the rate-expression of the zwitterion mechanism can be

better used to account for experimental observations such as broken order kinetics

in some solvents (Versteeg et al. 1996). In a paper appearing in this thesis (da Silva

and Svendsen 2004a) the experimental evidence was reviewed and quantum

mechanical calculations were carried out to determine the most likely mechanism.

A central finding from these calculations was that a CO2 molecule does not react

with an ethanolamine molecule in gas phase. The calculations strongly suggest that

base molecules must be present for CO2 to bond with amine molecules. This would

again suggest that if any reaction intermediate exists it can not be very stable and is

likely to be short-lived. Calculations also suggest that if a strong base (such as

another amine molecule) is interacting with the amine functionality there is no

barrier to the proton-transfer. This is consistent with a single-step mechanism.

What could not be resolved by the calculations is what would happen if the CO2-

amine complex was solvated entirely by water molecules. In this case it is possible

that the water molecules could transfer a proton to a base molecule located further

away. Alternatively the CO2-amine complex can remain stable, awaiting the

approach of a base molecule. The calculations, while not entirely conclusive,

suggest a single-step mechanism, or a short-lived reaction intermediate.


86

The two reaction mechanisms give rise to similar expressions for reaction

kinetics. It was found in the review (da Silva and Svendsen 2004a) that most

experimental data can be accounted for with both mechanisms. The zwitterion

mechanism based rate-expression is somewhat more flexible than expressions

based on the single-step mechanism, i. e. it can be fitted to a greater variety of data.

There is however no experimental data that I am aware of suggesting this flexibility

to be required. An argument against the zwitterion mechanism is that some

parameters at times take on values that do not seem plausible (Crooks and

Donnellan 1989 and Aboudheir et al. 2003). If the overall order of reaction is three

it follows from the zwitterion mechanism that a proton transfer is rate-determining,

a conclusion that would seem somewhat implausible.

The difficulty in drawing any definite conclusion as to what mechanism is correct

stems in part from the fact that they are very similar. The zwitterion mechanism

becomes equivalent to the single-step mechanism when the lifetime of the

zwitterion-intermediate approaches zero. This has been somewhat obscured in the

literature where the zwitterion mechanism has been written without hydrogen

bonds to base molecules. The calculations would suggest that while the zwitterion

mechanism is not necessarily wrong the single-step mechanism is more suited to

conveying the nature of the reaction taking place.

From the quantum mechanical calculations potential reaction-barriers were also

identified. The mechanism was found to have no intrinsic barrier. The kinetics is

therefore likely to be dominated by the need for molecular encounters for the

reaction to take place. One barrier may arise from the CO2 molecule having to

displace the solvation-shell around the amine functionality. A second barrier may

be caused by the need for the CO2, amine and a base-molecule to be aligned for

reaction to take place. A study on the liquid structure of ethanolamine-water

mixtures (da Silva, Kuznetosova and Kvamme 2005, also part of the present thesis)

suggest that the latter of these barriers is the most significant.


87

As can be seen from the mechanism in Figure 5.5, the carbamate-formation

involves the transfer of a proton from the amine functionality. It is well-known that

amines without such protons, such as tertiary amines, do not form carbamate

(Versteeg et al. 1996 and da Silva and Svendsen 2005).

5.2.4 Bases

A base molecule can by definition undergo the following reaction:

2B H O BH OH+ −+ + (5.5)

Amine molecules are all bases and they are usually the strongest bases present in

the system. Water itself is a weak base, the hydroxyl-ion (OH− ) is a strong base,

but usually present in small quantities. Bicarbonate is a very weak base. The

carbamate species might act as a base, bonding a proton to one of the CO2 oxygen

atoms. There is however nothing in the experimental data to suggest that such

protonation takes place.

5.2.5 Alcohol-Group Bonding to CO2

It has been suggested that at very high pH values, CO2 can bond to alcohol-groups

(Jørgensen and Faurholt 1954). To investigate the possibility of such a reaction

taking place calculations were carried out at HF/3-21G(d) level with PC Spartan

(1999). The calculations were carried out for two ethanolamine molecules and a

CO2 molecule in vacuum. Calculations were carried out with C(CO2)-

O(ethanolamine) as a restrained reaction coordinate. The results suggest a

mechanism analog to carbamate formation:


88

Figure 5.6

This reaction is however in general not expected to play a significant role in

industrial CO2 absorption processes as the pH of the system is usually not high

enough (Versteeg et al. 1996).

5.2.6 Carbamate as Reaction Intermediate

It has been suggested that carbamate undergoes a direct hydrolysis reaction (Smith

and Quinn 1979), meaning a direct reaction with water to form bicarbonate and

amine. The figure below shows a HF/3-21G(d) geometry of a water molecule

placed next to MEA carbamate.

Figure 5.7 Ethanolamine carbamate interacting with a water molecule.

From such calculations no reaction path or transition-state was found. It is

apparently not possible for a water molecule to bond to the CO2-group as long as it

remains bonded to the amine functionality. The water oxygen molecule must


89

interact with the CO2 group in the same site as it interacts with the amine-group. I

am also not aware of any experimental data that suggest that direct carbamate

hydrolysis takes place. Shifts in concentration between carbamate and bicarbonate

are not particularly fast and can be readily explained as the shift of equilibrium

through a set of reversible reactions. If equilibrium conditions change some

carbamate will revert back to amine and CO2. This CO2 can then go on to form

bicarbonate.

In general it would seem that the bonding of carbamate species is such that it is

unlikely to act as any form of reaction intermediate.

5.2.7 Molecules with Multiple Amine Functionalities

Molecules can have more than one amine functionality. Among the solvents being

considered for CO2 capture piperazine, and piperazine-derivatives have multiple

amine functionalities. So does N-(2-hydroxyethyl)ethylenediamine (AEEA) which

has received some attention recently (Ma’mun, Svendsen, Hoff and Juliussen 2004

and Bonenfant et al. 2005). The nature of the functional groups is the same in such

molecules as in simpler amines. The form of interactions with CO2 is therefore also

likely to be the same. In the case of multiple amine functionalities there is however

a greater number of species that can be formed. In Figure 5.8 the species that can

be formed by piperazine are shown.


90

Figure 5.8 Piperazine species.

In addition to the carbamate and protonated amine there is a diprotonated species, a

dicarbamate, and a form with combined protonation and carbamate formation.

Experimental work and analyses by Bishnoi (2000) suggest that these species can

exist in significant concentration. In piperazine the two amine functionalities are

equivalent, for AEEA and other molecules with non-equivalent amine sites the

number of potential species would be even greater. Systems with such amines are

more difficult to study experimentally, as the number of experimentally observable

properties often remains the same while the number of equilibrium constants to be

determined increases significantly.


91

5.2.8 Shuttle Mechanism

In the absorption process CO2 must be transferred from the gas-liquid interphase to

the bulk of the liquid. The CO2 can diffuse as a free molecule or in one of the

bound forms. The diffusion process takes a significant amount of time, and may

under some conditions determine the overall absorption rate.

It has been observed that mixtures of amines can absorb CO2 more quickly than

would be expected from considering the kinetics of the different species involved

(Versteeg et al. 1996). This has been explained as resulting from carbamate

forming species transporting CO2 from the interface to the bulk of the liquid, where

it goes on to undergo bicarbonate formation. This process has been demonstrated in

absorption models and it is referred to as the shuttle mechanism (Versteeg et al.

1990). This is not a chemical reaction, but rather a phenomenon arising from the

differing diffusion-rates of different species. The carbamate forming amine in this

process is usually referred to as a “promoter” or “activator”.

Figure 5.9 The shuttle mechanism.


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5.2.9 Summary and Conclusion

As is shown in this chapter the number of reactions involved in the CO2 absorption

process is quite small. It can not be ruled out that other reactions take place, but the

present set of reactions can to my knowledge account for all the observed behavior

of CO2 absorption in amine systems. Thus, all the reactions involving CO2 can be

generalized in the following simple form:

Figure 5.10

B is again a base molecule and AH is any molecule with a free-electron pair and a

hydrogen atom on the same site. If AH is an amine molecule and B is a water

molecule or a second amine molecule this is the carbamate formation mechanism.

If AH is a water molecule and B an amine molecule the reaction is base catalysed

bicarbonate formation. Finally with both AH and B as water the reaction becomes

standard bicarbonate formation.

Below is given a summary of the main reaction mechanisms. Alcohol-group

bonding to CO2 is in most conditions expected not to be significant, and is omitted

from this list.


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2 2CO Am B AmCO BH− ++ + + I

2 2 3CO H O B HCO BH− ++ + + II

2B H O BH OH+ −+ + III

2 2 2 3CO H O H CO+ IV

2 3CO OH HCO− −+ V

23 3HCO B CO BH− − ++ + VI

B is again used to indicate a base molecule, usually an amine molecule or hydroxyl

ion. This set of reactions is in itself quite small, and there are only four reactions (I,

II, III and VI) that are amine specific. Three of the four amine reactions depend on

the base strength of the amine, the final reactions depend on the stability of the

carbamate molecule formed by a given amine. The base strength is usually given as

the pKa, and the equilibrium constant for carbamate formation will be written as Kc.

The CO2 absorption process is usually based on temperature (T ) variation, and the

temperature dependency of the equilibrium constants is clearly required to predict

the performance of a given solvent. The equilibrium constants in the system do also

change as a function of the composition ( c ) of the liquid, and the concentration

dependency of the equilibrium constants is clearly also of importance. This means

that if ( ),apK T c and ( ),cK T c can be determined the absorption process for

different solvents can be predicted. In other (and more correct) words it means

determining the equilibrium constants, their temperature dependencies and the

activity coefficients of the various components present in the liquid. This is the

main goal of the present thesis. Tertiary amines do not form carbamate and for such

molecules the base strength is the only equilibrium constant governing the

reactivity towards CO2.


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5.3 Determining Equilibrium

5.3.1 Equilibrium and Kinetics

Comparison of calculated and experimental base strengths of a series of amines

(results in Chapter 4 and da Silva and Svendsen 2003) showed the models to be

reasonably accurate. Determination and prediction of base strength can however be

an easier task than implied by the results of these papers. Determination of base

strength is fairly routine experimental work and fairly accurate data is available for

a large number of molecules (Perrin 1965). Very often the pKa of a molecule being

considered as a solvent has been reported in the literature. In most of the cases

where the pKa for the molecule itself has not been reported, it has been reported for

some closely related substance. The modeling task can then be reduced to

determining the difference in base strength for two closely related compounds; this

can usually be done with a fairly high degree of confidence.

The modeling results for carbamate stability (da Silva and Svendsen 2005) appear

to be of the same quality as the results for base strength. The experimental

determination of carbamate stability is much more difficult than the determination

of base strength, and it is in this case much more difficult to draw on experimental

data to refine estimation of equilibrium constants for new molecules.

The set of modeling results for base strength and carbamate stability together

provide what can perhaps be summarized as a semi-quantitative model for new

solvents.

In modeling work (da Silva and Svendsen 2005) a linear correlation was found

between carbamate stability and rate of reaction. For tertiary amines a similar

correlation has been found between the base strength and rate of reaction (Versteeg

et al. 1996). This is not entirely surprising since all the molecules undergo analog

reactions. This simple relationship between equilibrium constants and reaction


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rates, suggest that predictions of equilibrium constants can also serve to predict

reaction rates.

CO2 in aqueous amine solutions reacts, as already noted, to form either carbamate

or bicarbonate. Carbamate formation is in general a far more exothermic reaction

than bicarbonate formation. It is in general faster than bicarbonate formation, but

more energy is also required to reverse the reaction in the stripper. Two amine

molecules are required to form a carbamate molecule. The loading (mol CO2/mol

amine solvent) will therefore not be much higher than 0.5 in a system dominated by

carbamate formation.

An issue I have not addressed so far is what the ideal values are for base strength

and carbamate stability, or to which extent carbamate formation or bicarbonate

formation is preferable. At present this remains unknown. This is not a question

that can be addressed with the tools of computational chemistry. A complete model

of the CO2 absorption process is required. While such models exist they have so far

not been applied to this question. In Chapter 7 I will look at what the ideal

characteristics might be.

5.3.2 Temperature Dependency of Equilibrium Constants

In the work on basicity (da Silva and Svendsen 2003) it was found that entropies

calculated from quantum mechanical calculations could be used to predict the

change in basicity over temperature. The quality of the correlation obtained was

very good. The results suggest that the change in basicity over temperature depends

on the nature of the intramolecular hydrogen bonding of a given molecule. Only

eight molecules were however included in the study of temperature effects. A

difficulty in expanding the comparison with experimental data is that experimental

data for basicity is not always consistent at higher temperatures (Kamps and

Maurer 1996). The prediction of changes in basicity over temperature can be a


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valuable tool, particularly for higher temperatures where very little, if any,

experimental data is available.

Predicting the change in the carbamate stability over temperature is more

difficult. Almost no experimental data of quantitative quality is available for

carbamate stability at any temperature, and this is required to obtain the change

over temperature (da Silva and Svendsen 2005). Computational chemistry could be

used to determine both the absolute equilibrium constant and absolute entropy

values, but without any experimental data with which to compare the results, the

quality of predictions made would be uncertain.

5.3.3 Activity Coefficients

The equilibrium constant models results are for infinite dilution, far from the

composition that is utilized in industrial CO2 absorption. There is therefore a need

to predict how the equilibrium constants change as function of system composition.

Such concentration dependency is usually given as activity coefficients for the

various components

I have made some effort to model the activity coefficients for the ethanolamine-

water mixture (da Silva 2004). The quality of the results was however not

particularly good, no effort had been made to find an optimal force field for

ethanolamine and the accuracy of the simulations could have been better. In later

work I have looked at force field parameterization for ethanolamine (da Silva,

Kuznetsova and Kvamme 2005), this force field has however yet not been applied

in determination of activity coefficients. While I am not entirely confident that the

force field presented in that paper will produce activity coefficients in full

agreement with values derived from experiment, I am confident that a force field

can be developed that reproduces both the properties of ethanolamine-water

mixtures and pure ethanolamine.


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The CO2 absorption system consists of many components, not only water and

ethanolamine. I am not aware of any work having been done to determine activity

coefficients in such multi-component systems. Long simulations would probably

be required to produce results with a reasonable degree of confidence; this is

something that can be carried out with sufficient patience and computer-resources.

Another issue is how accurate activity coefficients from simulations will be.

Vorholz et al. (2004) were able to demonstrate the salting-out effect in molecular

simulation. This is an interesting result, suggesting that simulations are able to

capture different effects of changing concentrations at a qualitative, if not a

quantitative level.

Activity coefficients are not likely to be one of the most important factors in

determining the overall performance of a solvent. A first approximation for a new

solvent could be to assume that the system has the same activity coefficients as

some structurally similar solvent for which experimental data is available.

5.3.4 Process Energy Consumption

I have not dealt specifically with modeling of the reaction energies and energy

consumption of the system, but it can be readily determined from the modeling

results for equilibrium constants. Once the constants are determined, reaction

energies can be derived with thermodynamic calculations.

Reaction energies determined from computational chemistry work in the present

thesis are not likely to be close to experimental values. As with the equilibrium

constants I believe the best results will be obtained by using computational

chemistry results to obtain relative values, these can then be anchored to results for

a solvent where experimental data are available.


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5.3.5 Summary

The models presented in this thesis can be used to predict the main equilibrium

constants for CO2 absorption in aqueous amine systems with a fair degree of

confidence. From such predictions the solvents effectiveness as an absorber for

CO2 capture can be estimated. Results also suggest that quantum mechanical

calculations can be used to predict changes in equilibrium constants over

temperature. Less work has been done on determining the activity coefficients of

the systems in question. Confident prediction of activity coefficients is likely to

require considerable simulation work. While knowledge of activity coefficients is

clearly desirable, they are not likely to be that important in predictions of the

relative differences between solvents.

6 Other Solvent Properties

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6 Other Solvent Properties Why, a four-year-old child could understand this. Someone get me a four-year-old.

Grocho Marx

6.1 Introduction

In the last chapter the reaction mechanisms and equilibrium of amine-CO2-water

systems were discussed. While the equilibrium is central to the applicability of an

amine solvent to CO2 absorption there are other issues that are also of importance.

The present chapter will deal with these other properties.

Properties is here used in a loose sense, issues ranging from solvability to cost

will be covered. The outline will follow a prioritized order, with the properties I

believe to be of greatest importance presented first. This chapter is essentially a

review; the current state of knowledge for each property will be briefly discussed

and the issue of modeling and prediction of behavior of new solvents will be

considered.

6.2 Solubility in Water

Loss of solvent by evaporation in the stripper and absorber can be a problem. If a

solvent has low solubility in water that will also limit the amine concentration

under which the process can be operated. The calculation of solvation energy has

been one of the main topics of my work, for the solvent itself (which is a neutral

molecule) any of the solvation models utilized in the present work can produce

results with a fairly high degree of confidence. The continuum models are

particularly well suited for this task.


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6.3 Solvent Degradation

There is in a aqueous amine system the possibility that the amine will undergo

undesirable side reactions. Such reactions can result in the amine molecules

degrading irreversibly. The degradation rate of the solvent can greatly influence the

overall cost of operating a CO2 absorption plant.

The solvent can be subject to three types of degradation: thermal, carbamate

polymerization and oxidative (Goff and Rochelle 2004). Exhaust gases usually

have a high content of oxygen, oxidative degradation can in such systems be

expected to be the main cause of degradation. Thermal degradation can however be

an issue for some solvent molecules (Nagao et al. 1998). Degradation is a problem

for several reasons (Goff and Rochelle 2004); because the solvent is degraded new

solvent must be added at regular intervals. Degradation products might also have

unfavorable characteristics that the solvent itself does not have; degradation

products may be toxic and corrosive. There is therefore an interest in understanding

degradation mechanisms.

Degradation reactions are inherently difficult to study. Experimental work can be

time-consuming as the reactions may be relatively slow, degradation may also be

catalyzed by impurities in the system. Experimental monitoring of degradation is

also made difficult by the lack of a priori knowledge of what degradation products

are formed in a given system.

It is today believed that the oxidation process proceeds by radical reactions (Chi

and Rochelle 2002 and Goff and Rochelle 2004). Radical chemistry is often

complex and a large number of different products can be formed. Goff and

Rochelle (2004) present a series of possible steps in degradation mechanisms for

ethanolamine, but the mechanism remains uncertain.

Blanc et al. (1982) did experimental work on the degradation of diethanolamine

and N-methyldiethanolamine. They separated the degradation products into basic

and acid products. The basic products were amine molecules of complex structure,


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while the acid products were small carboxyl acid molecules such as formic acid.

Ammonia is also known to be formed in amine degradation (Goff and Rochelle

2004).

There is little reliable data on the relative degradation of different amines in the

open literature. The work by Blanc et al. (1982) suggests that ethanolamine (a

primary amine) degrades more quickly than secondary and tertiary amines. Kohl

and Nielsen (1997) accepted this conclusion in their textbook. Substituent groups

on the amine functionality itself, or on neighboring atoms, appear to protect the

solvent from oxidative reactions. This insight can be used to make rough

predictions of the degradation rates of different amines. Another issue is if it is the

solvent molecule itself, the carbamate form or the protonated form that is most

vulnerable to oxidation. There is to my knowledge no work in the literature that has

brought any clear insight on this issue.

I do believe that computational chemistry calculations could be used to elucidate

the reaction mechanisms and gain some insight into how the degradation rate will

vary between different solvents.

For environmental reasons solvents that are biodegradable are preferable. It is

however possible that a solvent resistant to oxygen and water at high temperatures

is not going to degrade easily in nature. There is therefore a potential conflict

between the properties desirable in a solvent in the process and after disposal.

6.4 Corrosion

Kohl and Nielsen (1997) describe corrosion as the most serious problem affecting

amine gas absorption plants. They also observe that the corrosion rates vary with

amine solvent. Why this is so, is however not well-understood. It is known that

primary amines such as ethanolamine do have a high corrosion rate. Secondary

amines such as diethanolamine have a lower corrosion rate and even lower


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corrosion rates are observed for tertiary amines. It would seem, and is suggested by

Kohl and Nielsen (1997), that the corrosion rate depends on the concentration of

carbamate species (carbamate species often dominate in ethanolamine systems

while they are not formed by tertiary amines). Predictions of carbamate formation

can be obtained from the work in this thesis and this might serve to give a rough

estimate of the corrosion rate associated with different solvents.

The corrosion rate is probably not only a function of the solvent and operating

conditions, it can also depend on impurities in the system. Degradation products

formed may also contribute to corrosion in different ways than the solvent itself.

The extent of corrosion obviously depends not only on the solvent, but also on the

structure of the absorption equipment and the choice of materials.

6.5 Foaming

Kohl and Nielsen (1997) describe foaming as the most common problem in amine

treating plants. Foaming may result in higher loss of amine and reduced liquid-gas

interphase area, thereby reducing the efficiency of the separation.

Kohl and Nielsen (1997) attribute foaming to impurities in the system. Their

textbook, and much of the earlier literature on the amine absorption technology,

look at plants separating CO2 from natural gas. The amount and nature of

impurities is clearly different in exhaust gases, which is the application of interest

in the present work. It has been observed (Ma’mun, Svendsen, Hoff and Juliussen

2004) that 2-methylaminoethanol produces significant foam, while ethanolamine

foams much less.

Foaming is a fairly complex and an, at present, not entirely predictable

phenomenon (Morrison and Ross 2002). Foaming is caused by some components

acting as surfactants. In an aqueous solution, amines with hydrophobic

functionalities are therefore perhaps the most likely to act as surfactants and cause

foaming. Methods in computational chemistry can be used to determine the extent


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of hydrophobic and hydrophilic groups in a molecule. From data on hydrophobic

and hydrophilic groups some estimates can perhaps be made of the likelihood of an

amine contributing to foaming.

6.6 Toxicology

CO2 absorption is a large scale industrial process and it is clearly preferable that

solvents used are not highly toxic. The European Chemical Substances Information

System (ESIS, European Chemicals Bureau 2005) provide data on many amine

compounds. The ESIS data would suggest that most amines utilized in CO2

absorption are to some extent toxic. This is a consequence of the amines being

fairly strong organic bases. Some amines may however pose additional problems.

Piperazine is for example reported by ESIS to be harmful to aquatic organisms.

Some solvents are in wide use in the industry and for these it would seem likely

that issues regarding toxicology are well known. For amines that are not widely

used the effects of long term exposure might be unknown. I am not aware of any

correlation between amine structure and toxicology. Prediction of toxicology is

likely to be extremely difficult. This is however an important issue that must be

kept in mind during screening for new solvents.

6.7 Cost

The overall cost of a solvent depends on the cost of producing it and the

degradation rate. If a solvent is to be applied in an industrial scale process it is of

great importance that the solvent cost is not too high. The cost of producing an

amine depends on the synthesis process. Determining the optimal synthesis process

is a science in itself. For the solvents that are presently utilized on an industrial

scale it would seem likely that the production method has been carefully selected

and that costs will not change too much in the future.


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For solvents that are not presently produced on a large scale it would seem likely

that less work has gone into finding optimal synthesis routes. If demand for any

solvent was to rise, the cost might therefore go down. It is probably at present not

possible to predict the cost of producing a molecule on bulk scale. The cost of a

solvent is however likely to rise with molecular size and complexity.

6.8 Precipitations

It has been observed that in some absorption systems precipitations can be formed.

Some precipitations are probably the result of the amine itself precipitating as a

result of lowered solvability, there might also be circumstances where some form

of salt can be formed. Kumar et al. (2003) reported precipitations for CO2

absorption with amino acid salts. This is however an issue that has received little

attention in the open literature. For most solvents and under most operating

conditions this is probably not an issue.

7 Present and Potential Solvents

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7 Present and Potential Solvents “Tracking something,” said Winnie-the-Pooh very mysteriously.

”Tracking what?” said Piglet, coming closer

”That's just what I ask myself. I ask myself, What?”

A. A. Milne (From Winnie-the-Pooh)

7.1 Introduction

In the last two chapters the solvent properties of importance for the performance of

a CO2 capture process were reviewed. The extent to which to different properties

can be modelled and predicted was also discussed. The present chapter deals with

the likelihood of finding solvents better than the ones currently in use. The first part

of the chapter is a brief review of the most important solvents in use. In the second

part a discussion is made of what the ideal solvent properties are. Finally the

likelihood of finding a molecule with a set of properties that are ideal or at least

better than ethanolamine (which represents the benchmark to beat) is discussed.

7.2 Solvents in Use

7.2.1 Ethanolamine

Ethanolamine (MEA) is currently being provided commercially as a solvent for

exhaust gas CO2 capture. It is sold under the name Econamine by Fluor enterprises

(Reddy et al. 2003). The main problem with the ethanolamine processes is that the

energy consumption is fairly high. MEA is known to form a stable carbamate form

(da Silva and Svendsen 2005). The energy needed to free CO2 from the carbamate

form in the stripper is the cause of the high energy consumption. Ethanolamine is

highly solvable in water, not very toxic and does not cause significant foaming.


106

The molecule is noteworthy for being the second smallest of all alkanolamine

molecules.

Ethanolamine does have a high degradation rate and can cause corrosion. In

Econamine inhibitors are added to reduce degradation rates and limit corrosion.

7.2.2 Tertiary Amines

Tertiary amines do not form carbamate. They only act as bases, contributing to the

formation of bicarbonate. The advantage of tertiary amines is that the equilibrium

is more easily reversed in the stripper. Because the amine-CO2 stoichiometry of

bicarbonate formation is 1 to 1 tertiary amines do also have the potential to absorb

large amounts of CO2. As observed in the last chapter tertiary amines do also tend

to have low degradation rates. For natural gas treatment the tertiary amine N-

methyldiethanolamine (MDEA) is widely used (de Koeijer and Solbraa 2004). In

exhaust gases the fraction of CO2 in the gas phase is however lower and MDEA is

thought to have too low reactivity to work efficiently in such a case. Tertiary

amines are often combined with promoters in order to take advantage of the

shuttle-effect (Bishnoi and Rochelle 2002 and Zhang et al. 2003).

7.2.3 Sterically Hindered Amines

Amines with one or more substituent-group on the carbon-atoms bonded to the

nitrogen atom are called sterically hindered amines (Sartori and Savage 1983).

Such molecules tend not to form stable carbamate forms. They will therefore

mainly work as bases and contribute to bicarbonate formation. Their reactivity

towards CO2 is very similar to that of the tertiary amines. The sterically hindered

amine that has seen the greatest use is probably 2-amino-2-methylpropanol (AMP).

In addition to tertiary amines and sterically hindered amines there is likely to be

other amines that form less stable carbamate forms.


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7.2.4 Multiple Amine Functionalities

Some research has gone into molecules with multiple amine functionalities. Of

such molecules piperazine has probably seen the greatest use. Piperazine is usually

used as a promoter (Bishnoi and Rochelle 2002, Zhang et al. 2003 and Jenab et al.

2005). A problem with piperazine is that it has fairly low solvability in water.

Recent work (Ma’mun et al. 2004 and Bonenfant et al. 2005) has suggested that N-

(2-hydroxyethyl)ethylenediamine (AEEA) is a promising diamine solvent.

Multiple amine functionalities would suggest a potential to bind more CO2 with a

single solvent molecule. Further research is probably required to determine if there

is a particular benefit in using such solvents.

7.2.5 Ionic solvents

Some research has been done on the use of solvents where the active component is

an ionic amine species. Examples of this are potassium salts of taurine and glycine

(Kumar et al. 2003). One advantage of such ionic amines is that there is very little

loss of solvent through evaporation. The solution formed is in this case highly

ionic. There is to my knowledge no data in the open literature to support any

general conclusions on the merits of such solvents.

7.2.6 Patented Solvents

There are some amine systems for which data has been presented in some context

(publications in journals, patents or advertisement brochures) but where the

composition has been kept secret. Most notable among these are the solvents KS 1-

3 (Mimura et al. 1999) developed by Mitsubishi Heavy Industries. I believe KS 1

to be a mixture of AMP with a promoter. Less is known about KS 2 and 3. The

researchers at Mitsubishi have however done work on amino-amide molecules

(Nagao et al. 1998) and these could be possible ingredients.


108

The Canadian company Cansolv has recently filed a patent application for

absorbents for CO2 capture (Hakka and Ouimet 2004). This again appears to be a

promotor based system. In this patent tertiary amines are utilized. The promoter is

piperazine or a derivative of piperazine. The novel feature of this patent appears to

be the use of oxidation inhibitors and molecules with two tertiary amine

functionalities, such as N, N, N',N'-tetrakis(hydroxyethyl) 1,6-hexanediamine.

7.3 Ideal Solvent Properties

7.3.1 Equilibrium Constants

The chemistry of CO2 absorption is governed by the basicity and carbamate

stability of the solvent. Too high equilibrium constants will result in a too high

energy consumption, while too low equilibrium values will result in CO2 not being

absorbed to any significant degree. It is therefore not an issue of simply finding the

solvent with strongest or weakest bonding to CO2, there is rather some intermediate

values that will provide an optimum trade-off between uptake of CO2 and energy

consumption. I am however not aware of any work that provides insight into what

these optimal values are. This is not an issue that can be addressed by

computational chemistry. To answer the question of what the optimal equilibrium

values are a model of the entire absorption process is required. While such models

are available their application is not trivial and most are developed for a specific

solvent, rather than as general models. It does however seem likely that these

models, with some further development, can be utilized to answer this question.

While modelling work is required to determine optimal equilibrium constants

some suggestions can be made based on the performance of solvents presently in

use. The optimal process may utilize a single solvent or a mixture of different

solvent components. Use of solvents with multiple amine functionalities is a further

option. I will consider each option separately.


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Use of a single amine solvent is the simplest option. Two solvents for which the

performance is fairly well understood are MEA and MDEA. MEA forms a fairly

stable carbamate form and is regarded as having too high energy consumption.

MDEA only acts as a base and only bicarbonate is formed. This solvent is also a

relatively weak base having a pKa of only 8.5 (Perrin 1965) where as MEA has a

pKa of 9.5 (Perrin 1965). While use of MDEA results in a lower energy

consumption than is the case for MEA, it is regarded as having a too low capacity

to bind CO2 for the exhaust gas application. The ideal amine solvent should than

have base strength and carbamate stability somewhere between these two solvents.

It is not clear if a non-carbamate forming amine is suitable as a single solvent for

exhaust gas applications, if it were to work it would have to have a high base

strength. A carbamate forming molecule should probably have carbamate stability

somewhat lower than ethanolamine.

Mixtures of solvents are usually used to draw advantage of the shuttle-effect

described in Chapter 5. In such cases one amine works as a carbamate forming

promoter, while another amine mainly works to form bicarbonate. For the

bicarbonate forming molecule a stronger base than MDEA is probably preferable

(for the same reason as given for a single solvent system). The shuttle-mechanism

probably works optimally for some given level of carbamate strength. While it is

difficult to determine what that ideal carbamate stability is for this mechanism,

some tentative conclusions can perhaps be drawn from the promoters currently in

use. Both piperazine and MEA are used as promoters (Bishnoi and Rochelle 2002

and Aroonwilas and Veawab 2004). Both these molecules form relatively stable

carbamate forms (da Silva and Svendsen 2005). This would suggest that ideal

promoters are relatively strong carbamate formers. If KS1 (Mimura et al. 1999) is

indeed promoted AMP, its properties fall within the present recommendations,

AMP having a pKa of 9.7 (Perrin 1995).


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In addition to taking advantage of the shuttle-effect, solvent mixtures can also be

used to control the degree of CO2 capture or energy consumption. If a single

solvent does not have ideal performance, a mixture of solvents can be utilized. By

varying concentration ratios the overall performance can be controlled. In such a

case both solvents should have properties that would have made them viable in a

single component system.

Finally there is the use of solvents with multiple amine functionalities. These can

be utilized as a single solvent, or as promoter or bicarbonate former in a mixture of

solvents. The chemistry is in this case more complex than for a solvent with a

single amine functionality. The conditions given for a single amine functionality

solvent in terms of base strength and carbamate stability should also be met by a

solvent with multiple amine functionalities. I have however no basis to suggest

what the ideal equilibrium values for secondary protonation or carbamate

formation is. Some degree of chemical reactivity on all sites is probably preferable;

otherwise part of the molecule will be “dead weight”.

For the temperature dependence the issue is more straightforward; the greater the

fall in carbamate stability and base strength over temperature the better. Greater

temperature dependency increases the net amount of CO2 that can be transported

from the absorber to the stripper (the cyclical capacity). It could also be taken

advantage of to operate the stripper at lower temperature, thereby reducing the

energy consumption.

7.3.2 Other Properties

For the other properties discussed in the last chapter the ideal characteristics are

obvious. The solvent should have as high solvability in water as at all possible. It

should not foam, have low degradation rate, be inexpensive and not toxic.


111

7.4 Comparison with Ethanolamine

From these conclusions we can then turn to the crucial issue: What is the likelihood

of finding solvent molecules that are better than MEA. Since the ideal equilibrium

constants are not known, it is difficult to draw any conclusions as to how far

ethanolamine is from being an optimal solvent and how much room there is for

improvement. I suspect that a less stable carbamate form is optimal, but how much

the energy consumption can be lowered is hard to estimate.

MEA is probably the smallest and simplest solvent molecule that can be applied

in the CO2 capture process. It is for that reason likely to remain one of cheapest

solvents to manufacture. It is also not particularly toxic. MEA does however have a

high degradation rate (Blanc et al. 1982) and many other solvents are likely to offer

improvements over ethanolamine in this respect.

Overall this analysis would suggest that it is likely that solvents better than

ethanolamine can be found. The KS1 solvent (Mimura et al. 1999) has perhaps

already achieved this, and there is no reason to believe that this can not be

improved further upon. How great improvements that can be expected in terms of

energy consumption and operating cost is however difficult to estimate.

7.5 Conclusion

I have in this work not presented a specific list of candidate molecules for the

absorption process. To the question of what the ideal solvent molecule(s) is, the

present work provides a fairly detailed blueprint of how to answer the question, but

not the answer itself.

The screening process required to come up with a range of candidate molecules

would in itself be time-consuming. At the same time there have not been resources

available at our laboratory to test new candidate molecules resulting from such a

screening process.


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Some general rules for design of solvent molecules can however be proposed.

The ratio of hydrophilic to hydrophobic groups must be kept high, that usually

means high number of hydroxyl-groups and low number carbon-based groups. For

a reasonable basicity to be obtained there should be at least two carbon-groups

between hydroxyl- and amine-functionalities.

In general it appears that high basicity is desirable. High carbamate stability may

be desirable for promoters, but is probably not so for the main solvent component.

8 Future Work

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8 Future Work “Begin at the beginning,” the King said gravely, “and go on till you come to the

end; then stop.”

Lewis Carroll (from Alice in Wondeland)

8.1 Continuation of the Present Research

There are several ways in which the present work can be expanded and improved

upon. Degradation mechanisms are one particular area where I believe

computational chemistry could be applied to obtain greater insight. Computational

chemistry methods can also be utilized together with experimental spectroscopy

work to obtain a more detailed understanding of the various species present in a

CO2 absorption process.

On the issue of liquid structure and activity coefficients the present work is quite

limited. It should with simulations be possible to form a quite detailed

understanding of the liquid structure of amine-water systems. Such work can also

contribute to the determination of activity coefficients of various species.

Computers and the methods of computational chemistry are in continuous

development, and it is almost certain that the calculations of reaction energies

presented in this work can be improved upon.

The purpose of this work has been to contribute to the development of new

solvents. The next step should be to apply this model work in the selection of new

solvents for experimental work. New experimental data can also be used to validate

the modeling work, and offer guidance for further modeling.

8.2 Other Applications of Present Work

Determining free energies of solution and reactivity of organic molecules in

aqueous solution is a major topic in computational chemistry. My own work has to

8 Future Work

114

a large extent consisted of applying models in this area to the particular issue of

CO2 capture technology. The present work should therefore also be of interest as an

exercise in applying and validating models to calculate free energies in solution.

The present work has shown that computational chemistry tools can be

successfully applied to further the understanding of the CO2 absorption process.

While the work has been focused on the treatment of exhaust gases the work could

also be used to find optimal solvents for CO2 removal from natural gas. It is also

likely that the same methods as applied in the present work can be applied to study

other issues in gas processing.

8.3 Beyond Amines

My work has focused solely on absorbing CO2 with amine solvents. There are

however other chemical reactions resulting in CO2 being bonded, and some of

these reactions might perhaps be used to capture CO2. CO2 is captured in large

amounts in the natural photosynthesis process (Lawlor 2000). Another noteworthy

process is the catalyzed formation of CO2 from bicarbonate in the human body

(Palmer and van Eldik 1983). There are also other reactions where CO2 binds to

metal-complexes or organic compounds (Halmann 1993).

Many reagents or catalysts might turn out to be too expensive to be used in the

large scale capture of CO2. It would however seem worthwhile too carry out a more

general study of the various ways CO2 can interact with other molecules to see if

any mechanism can be taken advantage of in capture technology.

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Paper I

Prediction of the pKa Values of Amines Using ab Initio Methods and

Free Energy Perturbations

Eirik Falck da Silva and Hallvard F. Svendsen

2003

Ind. Eng. Chem. Res. 42, 4414-4421.

RESEARCH NOTES

Prediction of the pKa Values of Amines Using ab Initio Methods andFree-Energy Perturbations

Eirik F. da Silva* and Hallvard F. Svendsen

Department of Chemical Engineering, Norwegian University of Science and Technology,N-7491 Trondheim, Norway

A computational study has been performed on predicting the pKa values for amines andalkanolamines used in CO2 absorption processes. Gas-phase energies were calculated usingcommon basis sets at Hartree-Fock (HF), MP2, and B3LYP levels. Free energies of solvationwere calculated using continuum models and Monte Carlo free-energy perturbations. Resultsare compared with experimental pKa data. While the continuum methods could reproduce trendsbetween similar molecules, they failed to predict the overall trends for series involving amineswith different numbers of amine-group hydrogens and different numbers of intramolecularhydrogen bonds. Considerably better results were obtained using free-energy perturbations. Onthe basis of calculations of molecular vibrations, good estimates were also achieved for changesof pKa with temperature.

Introduction

As a measure for preventing global warming, thereis a steadily increasing interest in methods for removingcarbon dioxide from exhaust gases as well as naturalgas and refinery gases. Traditionally, absorption withalkanolamines in mixtures with promoters has beenused for this purpose. For high-pressure applications,N-methyldiethanolamine (MDEA)-based systems havebeen used successfully for many years. For exhaustgases, the most common amine has been ethanolamine(MEA). However, high energy demand for regenerationand high degradation rates makes this an undesirableamine to use for large fossil fuel power plants. Duringthe last years, new systems such as the PSR1-31 andKS1-32 have been developed and promise improvedperformance compared to the conventional MEA. Theinteractions between amino compounds and CO2 havebeen studied extensively using both experimental andtheoretical methods.3

For both CO2 reaction rate and absorption capacity,the pKa values of the conjugate acids of the alkanol-amines applied are important variables.4 Reasonableprediction of pKa values would therefore be of greatvalue when screening for new candidate compounds forexhaust gas CO2 removal.

A lot of work has been done in computational chem-istry on the prediction of pKa. While this is consideredto be a difficult task, works have been published thatshow good results for some sets of compounds.5,6 Thegeneral applicability of these methods would, however,still seem to be uncertain. The intention of this work isto explore the application of these models to the kindsof molecules used for CO2 recovery.

Several studies have been published on the basicityof methylamines.7-9 While these molecules are notdirectly relevant to the CO2 absorption process, theyclearly represent a closely related modeling task. Inclu-sion of these molecules in this work allows a moregeneral validation of the models being used.

Methods

The dissociation of the conjugate base of the aminecan be written as

When the mole fraction based activity of water isassumed to be 1 and H3O+ is written as H+, thefollowing equilibrium constant is obtained:

The definition of pKa is

The free energy of protonation in an aqueous solution(∆Gps) is related to Ka by the following equation:

This gives us the relation between pKa and ∆Gps.

Model predictions for ∆Gps should therefore give a linearcorrelation with the pKa.

* To whom correspondence should be addressed. Tel.: +4773594125. Fax: +47 73594080. E-mail: [email protected].

BH+ + H2O h B + H3O+ (1)

Ka ) aBaH+/aBH+ (2)

pKa ) -log Ka (3)

∆Gps ) -2.303RT log Ka (4)

pKa ) 12.303RT

∆Gps (5)

4414 Ind. Eng. Chem. Res. 2003, 42, 4414-4421

10.1021/ie020808n CCC: $25.00 © 2003 American Chemical SocietyPublished on Web 08/23/2003

The general approach to calculating ∆Gps is to use athermodynamic cycle such as8

The focus of this work is to reproduce trends in pKa.The energy of the proton (H+) itself is constant for allamines. It is therefore not relevant in this context andnot included in the present calculations. On the basisof the thermodynamic cycle, ∆Gps can be divided intotwo contributions:

where ∆Gpg is

and

While the gas-phase protonation energy and the freeenergy of solvation are expected to be the main con-tributors to the overall solvent-phase reaction energy,thermal and zero-point energy (ZPE) corrections are alsoincluded.

Computational Aspects

For the modeling of gas-phase protonation energies,standard ab initio calculations have been used. Geom-etry optimizations were performed using a series ofcommon methods and basis sets: HF/3-21G*, MP2/6-31G*, B3LYP/3-21G*, and B3LYP/6-311++G**. AllMP2 and B3LYP calculations were done using Gaussian98.10

The thermal corrections to the free energy, the ZPEs,and the entropies were all calculated at the HF/3-21G*level. These contributions are relatively small and arenot expected to change significantly with the level ofmodeling. To be consistent with how the gas-phaseenergy is calculated, the ZPE and thermal correctionsare calculated as the same relative difference as thatused for the protonation energy itself (eq 7). Thesecalculations were also done using Gaussian 98.

Molecular mechanics (MMFF) was used to generatean initial set of conformers. All conformers were thenoptimized at the HF/3-21G* level. Separate conformersearches were done for the amines and their protonatedforms. The effect of the solvation models on the relativeconformer stability was explored for some of the mainconformers. All calculations in this work were performedon the same set of conformers. Gas-phase conformersearch calculations were done with the Spartan pro-gram.12

For the calculation of solvation energies, severalmodels are available. The continuum models such asthe PCM models are probably the most common ones,13

but there are questions regarding their general ap-plicability. Of particular importance is their failure to

explicitly include hydrogen bonding.7,9 SM continuummodels have also been tested in this work. Calculationsbased on the explicit representation of the solvent usingfree-energy perturbation (FEP) simulations have alsobeen performed.

A wide variety of PCM models are available, andresults have been published using a number of differentbasis sets. There would, however, not seem to be anyclear guidelines as to whether some specific level ofcalculation would be more appropriate or, in general,more reliable. In this work, the IEFPCM model13 hasbeen chosen and all calculations were performed usingits default settings in Gaussian 98 with 60 tesserea peratomic sphere. These calculations will simply be referredto as PCM calculations.

Most calculations were done as single-point energycalculations on gas-phase geometry. Solvent-phase ge-ometry optimizations with the PCM models have alsobeen performed. While the geometries did changeslightly using solvent-phase optimization, the energychanges were relatively small. For larger basis sets, itwas also found that solvent-phase optimization resultedin some convergence problems in the calculations. Oneset of results using solvent-phase geometry optimizationhas been included in the Results and Discussion section.

The solvent-phase protonation energies (∆Gps) basedon continuum models presented in the Results andDiscussion section were calculated with the solvationenergy calculated on the same geometry as that usedto obtain the gas-phase energy. The B3LYP/6-311++G**gas-phase results were, however, added together withPCM results calculated at the B3LYP/3-21G* level.While the qualitative issues regarding gas-phase modelsand basis sets are fairly well understood, the solvationmodels are, in general, semiempirical, and it is not clearhow their performance changes with the level of geom-etry optimization. In general, it would therefore seembest to consider solvation energy calculation and gas-phase energy calculation as separate processes. Whilethey should be calculated on the same conformer, it isnot given that they should be calculated at the samelevel of geometry optimization.

The SM models are a series of semiempirical modelsto calculate the free energy of solvation. The SM5.4A11

model is parametrized to work with AM1 geometries.In this work, this model has been used to calculatesolvation energies using AM1 geometries in the Spartanprogram. In addition, SM5.42R/HF/6-31G* calculationswere performed with Gamesol 3.1.15

Simulations

As an alternative to the implicit solvent models (PCMand SM), classical Monte Carlo calculations were per-formed. Wiberg et al.16 have obtained good resultscombining gas-phase ab initio calculations with MonteCarlo calculations of the solvation energy to obtain freeenergy in solvation. In the present work a similarprocedure has been adopted. Wiberg et al.16 usedperturbations between the neutral forms of the mol-ecules and between the ionic forms of the molecules; i.e.,they only performed perturbations between moleculeswith the same charge. The molecules in the presentwork do, however, vary considerably in size and struc-ture, making perturbations between them difficult.Instead, the FEP calculations were done by perturbatingthe protonated form of the amine to the amine itself,

∆Gps ) ∆Gpg + ∆Gs (6)

∆Gpg ) Gg(B) - Gg(BH+) (7)

∆Gs ) ∆Gs(B) - ∆Gs(BH+) (8)

Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003 4415

giving the relative difference in free energy of solvation(∆Gs) directly.

These calculations were done with BOSS version 4.117

using procedures developed by Rizzo and Jorgensen.9A single solute molecule was placed in a periodic cubewith 267 TIP4P water molecules at 25 °C and 1 atm inthe NPT ensemble. Periodic boundary conditions wereapplied. A number of water molecules corresponding tothe number (n) of non-hydrogen atoms in the aminemolecule were removed, giving 267 - n water molecules.The perturbations were carried out over five windowsof double-wide sampling, giving 10 free-energy incre-ments that are summed up to give the total change infree energy of solvation. Each window had 500 000 stepsfor equilibration and another 500 000 for sampling.

Wiberg et al.16 used solution-phase B3P86/6-311+G**geometries. In the present work, similar solution-phaseB3LYP/6-311++G** geometries (optimized with PCM)were used. The same conformers as those for thecontinuum calculations were used, and simulations wereperformed using rigid geometries. The intermolecularinteractions between two molecules a and b wereevaluated using Coulomb and Lennard-Jones terms:

The Lennard-Jones σ and ε were taken from the OPLS-All atom force field.17

Wiberg et al.16 calculated atomic charges in the gas-phase and scaled these by a factor of 1.2 to obtain valuesappropriate for solution. In the present work, methodswere chosen that directly give solution-phase atomiccharges. Two different methods were tested for calculat-ing the charges. One was the CM2 model18 found inGamesol, while the other method used was the Merz-Kollmann (MK) scheme19 available in Gaussian. Both

models were used on HF/6-31G* gas-phase geometriesand basis sets. For the CM2 scheme, calculations weredone with the SM5.42R solvent field, while for the MKscheme, the PCM solvent field was used.

It should be noted that these simulations have astatistical uncertainty, unlike the continuum modelsthat are deterministic. On the basis of the batch meansprocedure available in BOSS, the statistical uncertain-ties were estimated to be on the order of (2 kcal/mol.This uncertainty is something that must be kept in mindwhen comparing results obtained by FEP and con-tinuum models.

Results and Discussion

In Table 1 are shown the amines used in this study,and in the table, it is indicated whether the amines areprimary (p), secondary (s), tertiary (t), or cyclic (c).Experimental pKa values at 25 °C are also shown. Thequality of the experimental data would seem to varysomewhat. For some molecules, different experimentalresults are available and variations between thesesuggest uncertainties in the order of (0.1 pKa unit.

The series NH3, NH2CH3, NH(CH3)2, and N(CH3)3 hasbeen the subject of several previous studies.7-9 In Table2, the gas-phase reaction energies for these moleculesare shown together with experimental values. TheB3LYP/6-311++G** results in particular are in goodagreement with the experimental data.

Solvation energies calculated using both continuummodels and FEPs are shown in Table 3. There isreasonable qualitative agreement between both the gas-phase energies and the solvation energies for all of thesets of results. In Table 4 are shown relative freeenergies of protonation in the solvent (∆Gps). Theexperimental data are based on eq 5 and data fromTable 1. The errors in the prediction of the solvent-phaseprotonation energy are larger than the errors in the gas-

Table 1. Experimental pKa Data

no. compd name typea hydrogen bondsb exptl pKa at 25 °C ref

1 NH3 0 9.3 202 NH2(CH3) p 0 10.657 213 NH(CH3)2 s 0 10.732 214 N(CH3)3 t 0 9.9 205 ethanolamine MEA p 1 9.51 216 1-amino-2-propanol MIPA p 1 9.47 217 3-amino-1-propanol MPA p 1 9.96 218 2-amino-2-methylpropanol AMP p 1 9.7 219 N-(2-hydroxyethyl)ethylenediamine AEEA p, s 1 9.82c 21

10 diethanolamine DEA s 2 8.95 2111 diisopropanolamine DIPA s 2 8.89 2112 morpholine s, c 0 8.7 2213 diethylenediamine piperazine s, c 0 9.83c 2114 N-n-butylethanolamine BEA s 1 9.9 2315 N-methyldiethanolamine MDEA t 2 8.63 2116 triethanolamine TEA t 2 7.78 21a p: primary amine. s: secondary amine. t: tertiary amine. c: cyclical amine. b Number of intramolecular hydrogen bonds for the

protonated form of the amine. c The first protonation constant.

Table 2. Gas-Phase Protonation Energies (All Results in kcal/mol)

B3LYP/3-21G* MP2/6-31G* B3LYP/6-311++G**

compd ∆Gpga rel ∆Gpg ∆Gpg

a rel ∆Gpg ∆Gpga rel ∆Gpg rel ∆GExptl

b

NH3 229.89 0.00 217.17 0.00 211.87 0.00 0.00NH2(CH3) 236.08 6.19 225.64 8.47 221.55 9.69 10.87NH(CH3)2 241.26 11.38 232.29 15.12 229.29 17.43 18.52N(CH3)3 244.80 14.92 236.42 19.25 234.23 22.37 23.69

a Thermal correction and ZPE calculated at the HF/3-21G* level included the value relative to that of NH3 (-9.38 kcal/mol).b Experimental data from Hunter and Lias.24

∆Eab ) ∑i

on a

∑j

on b{qiqje2

rij

+ 4εij[(σij

rij)12

- (σij

rij)6]} (9)

4416 Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003

phase energies, suggesting that the solvation energiesare not completely accurate.

We would argue that this series of four molecules istoo small to draw any firm conclusion as to the ap-plicability of any single model. The energy differencesthat one is attempting to reproduce are also relativelysmall. The FEP calculations used have an uncertaintythat is too large ((2 kcal/mol) to draw conclusions forthis small series.

Gas-phase conformer searches were done at the HF/3-21G* level and calculations on some of the more stableconformers were also done with the other models used.For the unprotonated forms of diisopropanolamine(DIPA), diethanolamine (DEA), MDEA, and N-n-butyl-ethanolamine (BEA), the most stable conformers didchange with the level of modeling. In these cases, themost stable conformers found at higher level have beenused. The most stable conformers for molecules 5-16are shown in Figure 1. The protonated forms of theamines were found to have a strong tendency to formhydrogen bonds between amine hydrogens and oxygenatoms on the alcohol groups. For MDEA, the most stableconformer without hydrogen bonds was 5 kcal/mol lessstable than the most stable hydrogen-bonded conformer(at the HF/3-21G* level). For some of the smallermolecules such as MEA, only a hydrogen-bonded con-former was found. In Table 1, the number of such bondsfound for each amine in the protonated form is indi-cated.

On the basis of the results of the conformer searches,a general qualitative explanation for the trends seen inthe experimental pKa data can be suggested. The alcoholgroups in the molecules are electron-withdrawing,destabilizing the protonated form of the amine. Thiseffect is mitigated by the alcohol groups forming hydro-gen bonds to the amine protons. Most of the alkanol-amines therefore have pKa values slightly lower thanthose of methylamines of the same order. Morpholinehas an electron-withdrawing oxygen but cannot formhydrogen bonds and has therefore a relatively low pKa.Triethanolamine (TEA) has three ethanol groups thattogether have a strong electron-withdrawing effect. Inthe protonated form, there is, however, only one amineproton that these groups can bond with, limiting thestabilizing effect of the hydrogen bonding. One mightthink of the hydrogen-bonding effect as reaching a formof saturation, giving a significant drop in the pKa.

For the neutral amines, the most stable conformerswere also found to have different forms of hydrogenbonding. Hydrogen-bonded gauche-MEA was, for ex-ample, found to be 4 kcal/mol more stable than the transconformer (at the HF/3-21G* level).

These conformer searches have been based on gas-phase calculations. The intramolecular hydrogen bondsfound to dominate in the gas phase will in the solventcompete with hydrogen bonding to water molecules. Thecalculations done with solvent models (PCM and SM5.4A)do, however, suggest that these intramolecular hydro-gen bonds are favored even in the solvent, particularlyfor the protonated forms of the amines. Molecules 9-11and 14-16 have many free dihedral angles and havemany potential conformers. For these molecules inparticular, we see that the most stable conformer canchange with the level of modeling; the energy differencesbetween the conformers are, however, expected to berelatively small because the effects of intermolecularhydrogen bonds and intramolecular hydrogen bondscancel out.

In Table 5, gas-phase energies for molecules 5-16 areshown together with experimental values. The resultsfrom the different calculations are in reasonable quali-tative agreement. When compared with the experimen-tal energies, the B3LYP/6-311++G** results are in goodquantitative agreement for 3-amino-1-propanol (MPA),morpholine, and piperazine. For DEA, the protonationenergies are, however, overestimated by 4 kcal/mol,suggesting that the strength of the intramolecularhydrogen bonds for the protonated form of the moleculeare overestimated. For MEA, all models show too lowprotonation energy, suggesting that the strength of thehydrogen bond of the protonated form of the moleculein this case is underestimated. The uncertainty in theestimation of the hydrogen bond strength was also seenin the optimized geometries: BEA had an intramolecu-lar hydrogen bond [H(O)-N] varying between 2.0 Å(B3LYP/3-21G*) and 2.3 Å (B3LYP/6-311++G**).

No direct correlation was found between the gas-phase protonation energy (∆Gpg) and the pKa, and thisstrongly suggests that the solvation energy is crucialfor predicting the relative pKa for these compounds. InTable 6, the free energies of solvation calculated withvarious models are shown. The different PCM resultscan be seen to be quite similar; in particular, it can beseen that the effect of solvent-phase optimization issmall. The FEP results are, however, quite different;while they show some qualitative agreement with thePCM results, the relative differences between the vari-ous molecules is much larger than those calculated withPCM.

Table 7 shows calculated and experimental solvent-phase protonation energies. Experimental data arebased on eq 5 and data in Table 1. The overall qualityof the results with continuum models is quite disap-

Table 3. Solvation Energies (All Results in kcal/mol)

compd PCM/MP2a PCM/B3Lb PCM/B3Lsc FEP-CM2 FEP-MK

NH3 75.6 76.1 76.0 76.4 74.1NH2(CH3) 65.7 65.9 66.0 67.1 61.7NH(CH3)2 61.5 60.9 61.3 58.1 60.2N(CH3)3 56.8 56.0 56.2 50.6 55.4

a PCM/MP2/6-31G*//MP2/6-31G*. b PCM/B3LYP/3-21G*//B3LYP/3-21G*. c Optimization in solution: PCM/B3LYP/3-21G*//PCM/B3LYP/3-21G*.

Table 4. Relative Solvent-Phase Protonation Energies (All Results in kcal/mol)

gas-phasea

MP2/6-31G* B3LYP/6-311++G**

compd PCM/MP2b FEP-CM2 FEP-MK PCM/B3Lc FEP-CM2 FEP-MK exptl

NH3 0.00 0.00 0.00 0.00 0.00 0.00 0.00NH2(CH3) -1.47 -0.77 -4.00 -0.53 0.44 -2.78 1.85NH(CH3)2 1.07 -3.15 1.21 2.14 -0.84 3.52 1.95N(CH3)3 0.44 -6.49 0.55 2.21 -3.37 3.67 0.82

a Thermal correction and ZPE calculated at the HF/3-21G* level included the value relative to that of NH3 (-9.38 kcal/mol). b PCM/MP2/6-31G*//MP2/6-31G*. c PCM/B3LYP/3-21G*//B3LYP/3-21G*.


pointing. At the B3LYP/6-311++G** level, one can, forexample, see that the molecule with the lowest experi-

mental value (TEA) in the data set has the highest valuein the calculated results.

Figure 1. Conformers of molecules 5-16.

Table 5. Gas-Phase Protonation Energies (All Results in kcal/mol)

B3LYP/3-21G* MP2/6-31G* B3LYP/6-311++G**

no. compd ∆Gpga rel ∆Gpg ∆Gpg

a rel ∆Gpg ∆Gpga rel ∆Gpg rel ∆Gexptl

b

5 MEA 245.43 15.55 231.96 14.79 227.55 15.69 18.596 MIPA 247.30 17.41 233.42 16.25 229.27 17.407 MPA 254.02 24.14 238.44 21.27 234.96 23.09 23.498 AMP 254.33 24.45 239.02 21.85 234.56 22.699 AEEA 264.68 34.80 246.83 29.67 240.43 28.56

10 DEA 256.53 26.65 246.73 29.56 240.25 28.39 24.1411 DIPA 257.50 27.62 245.48 28.31 243.17 31.3112 morpholine 240.69 10.80 231.23 14.07 228.52 16.65 17.2613 piperazine 247.71 17.83 237.71 20.54 234.76 22.89 22.8714 BEA 252.90 23.01 241.45 24.28 238.98 27.1115 MDEA 257.85 27.96 249.06 31.89 243.61 31.7416 TEA 243.54 13.65 241.89 24.72 244.92 33.05

a Thermal correction and ZPE calculated at the HF/3-21G* level included the value relative to that of NH3 (-9.38 kcal/mol).b Experimental data from Hunter and Lias.24


As noted previously, this data set contains moleculeswith very differing bonding. Given the uncertainty inthe estimation of hydrogen bonds already noted and theuncertainty regarding the PCM model’s ability to ac-count for hydrogen bonding with the solvent, it is ofinterest to look at how the models perform in predictingthe relative pKa values of molecules with similarhydrogen bonding. To have similar bonding, the mol-ecules must have the same number of hydrogens on thenitrogen and the same number of intramolecular hy-drogen bonds. All of the primary alkanolamines (mol-ecules 5-8) have such a similarity, and so do the twocyclic molecules (12 and 13) and DEA and DIPA(molecules 10 and 11). These groups are marked inTable 7. The other PCM results are also reasonablygood. The order between piperazine and morpholine isalso predicted correctly by all models. For the orderbetween DEA and DIPA, all of the models are wrong;the B3LYP/6-311++G** results are, for example, off byabout 2 kcal/mol.

Calculations with the SM continuum models, ingeneral, gave results similar to those obtained with thePCM model.

Using FEP solvation energies gave a better overalltrend in the results. For the full set of 16 molecules,the FEP-CM2 results in combination with MP2/6-31G*gas-phase energies gave an overall correlation coef-ficient of 0.45; in combination with B3LYP/6-311++G**energies, a correlation coefficient of 0.42 was obtained.In Figure 2, this FEP set of results is shown togetherwith the best set of results for the PCM model. The samegas-phase energy (MP2/6-31G*) together with the PCM

solvation energy gave no overall correlation. In Table7, however, it can be seen that the results with FEPsolvation energies have larger relative differences thanthose seen in the experimental data set.

While the B3LYP/6-311++G** gas-phase energies, ingeneral, seem to be fairly accurate, there is an uncer-tainty in the estimation of the strength of intramolecu-lar hydrogen bonds. Given the uncertainty in the gas-phase energies, we cannot draw any firm conclusionsas to the performance of the models used to calculatethe solvation energies. The present work does, how-ever, suggest that FEP simulations are a promisingtool for the solvation energy calculations for thesealkanolamines. More accurate free-energy calculationswill, however, be needed to better assess the perfor-mance of these simulations.

Temperature Effects

Ab initio calculations can be used to calculate themolecular vibration frequencies and thereby obtain gas-phase entropies. With an estimate of the entropy, thetemperature changes in the pKa can be predicted byusing the following equation:25

In this work the vibration frequency calculations were


no. compd PCM/MP2a PCM/B3Lb PCM/B3Lsc FEP-CM2

5 MEA 60.5 58.2 58.9 56.76 MIPA 59.3 56.4 57.4 60.17 MPA 55.5 51.5 52.2 57.98 AMP 53.8 51.7 52.3 54.79 AEEA 52.1 48.2 50.0 44.9

10 DEA 51.4 47.9 49.8 43.111 DIPA 49.0 46.7 47.5 42.412 morpholine 63.0 62.1 62.7 54.713 piperazine 59.8 58.0 58.1 50.314 BEA 53.6 51.2 52.3 47.415 MDEA 47.6 46.9 47.8 38.116 TEA 51.0 49.9 50.2 36.6

a PCM/MP2/6-31G*//MP2/6-31G*. b PCM/B3LYP/3-21G*//B3LYP/3-21G*. c Optimization in solution: PCM/B3LYP/3-21G*//PCM/B3LYP/3-21G*.

Table 7. Relative Solvent-Phase Protonation Energies (All Results in kcal/mol)

gas-phasea

B3LYP/3-21G* MP2/6-31G* B3LYP/6-311++G**

no. compd PCM/B3Lb FEP-CM2 PCM/MP2c FEP-CM2 PCM/B3Lc FEP-CM2 exptl

5 MEA -2.76 -4.44 -0.67 -5.20 4.25 2.57 0.276 MIPA -2.53 0.91 -0.28 -0.25 -2.30 1.14 0.227 MPA -0.72 5.48 0.97 2.62 -1.58 4.62 0.908 AMP -0.87 1.84 -0.86 -0.76 -1.74 0.98 0.579 AEEA 5.51 1.97 4.75 -3.16 0.63 -2.91 0.71

10 DEA 0.11 -4.87 2.52 -6.49 0.14 -4.84 -0.4611 DIPA 1.64 -2.92 2.73 -4.61 1.90 -2.66 -0.5612 morpholine -3.63 -11.29 1.04 -8.03 2.64 -5.02 -0.8213 piperazine -1.00 -8.89 4.10 -6.18 4.71 -3.18 0.7214 BEA -1.67 -5.68 2.32 -4.60 2.16 -1.86 0.8215 MDEA -0.06 -9.06 1.77 -8.42 3.87 -5.13 -1.0616 TEA -9.98 -23.50 2.74 -12.43 6.80 -6.72 -2.10

a Thermal correction and ZPE calculated at the HF/3-21G* level included the value relative to that of NH3 (-9.38 kcal/mol). b PCM/B3LYP/3-21G*//B3LYP/3-21G*. c PCM/MP2/6-31G*//MP2/6-31G*.

Figure 2. Calculated protonation energies in solution versusexperimental pKa values.

-d(pKa)/dT ) (pKa + 0.052∆S0)/T (10)


done at the HF/3-21G* level at 20 and 60 °C using theGaussian program. The same conformer search routineas that described previously was used for these alkanol-amines. To get a reasonable estimate of the totalentropy, we calculated the entropy of reaction given byeq 1 including the values for H2O and H3O+. Calculatedentropies together with the experimental pKa valuesused are given in Table 8. The entropies were assumedto vary linearly with temperature, and eq 10 was solvednumerically, doing a stepwise calculation from 20 to60 °C. Figure 3 shows these estimated values at 60 °Cplotted against experimental pKa values at 60 °C.

While the agreement is very good, it should be notedthat using eq 10 even without the entropy contributionalso gives good results. The entropy term does, however,improve the correlation. We believe that molecules thatdepend on intramolecular hydrogen bonding for theirhigh pKa are more sensitive to temperature variations.The data are, however, too limited to draw any firmconclusion.

We see that the estimated pKa values are systemati-cally lower than the experimental ones. This can beattributed to systematic errors in the entropy estimationand/or to changes in the solvent with temperature thatare not accounted for in the model.

Conclusions

Calculations have shown that intramolecular hydro-gen bonds play a crucial part in determining the pKavalues of alkanolamines. These same hydrogen bondsmake the accurate modeling of these molecules difficult.Continuum solvent models were found to be useful inpredicting the relative pKa strengths between amineswith similar solvation behavior, i.e., with the same

number of amine hydrogens and the same number ofintramolecular hydrogen bonds. The full set of amineswas, however, not successfully modeled with any of thecontinuum models tested. Reasonable results wereobtained using FEPs to calculate the solvation energy.It was also found that gas-phase entropy change calcu-lations could be used to expand the data to temperaturesother than those experimentally available. We proposethat the differences in temperature dependency ofdifferent amines can be attributed to differences inintramolecular hydrogen bonding.

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(3) Jamroz, M. H.; Dobrowolski, J.; Borowiak, M. Ab initio studyon the 1:2 reaction of CO2 with dimethylamine. J. Mol. Struct.1997, 404, 105.

(4) Versteeg, G. F.; van Dijck, L. A. J.; van Swaaij, W. P. M.On the kinetics between CO2 and alkanolamines both in aqueousand nonaqueous solutions. An overview. Chem. Eng. Commun.1996, 144, 113.

(5) Liptak, M.; Shields, G. Accurate pKa calculations for car-boxylic acids using complete basis set and Gaussian-n Modelscombined with CPMC continuum solvation methods. J. Am. Chem.Soc. 2001, 123, 7314.

(6) Schuurmann, G.; Cossi, M.; Barone, V.; Tomasi, J. Predic-tion of the pKa of carboxylic acids using the ab initio continuum-solvation model PCM-UAHF. J. Phys. Chem. A 1998, 102,6706.

(7) Kawata, M.; Ten-no, S.; Kato, S.; Hirata, F. Theoreticalstudy for the basicities of methylamines in aqueous solution: ARISM-SCF calculation of solvation thermodynamics. Chem. Phys.1996, 203, 53.

(8) Tunon, I.; Silla, E.; Tomasi, J. Methylamines BasicityCalculations. In Vacuo and in Soultion Comparative Analysis. J.Phys. Chem. 1992, 96, 9043.

(9) Rizzo, R. C.; Jorgensen, W. L. OPLS All-Atom Model forAmines: Resolution of the Amine Hydration Problem. J. Am.Chem. Soc. 1999, 121, 4827.

(10) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G.E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery,J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam,J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.;Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.;Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G.A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A.D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J.V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz,P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith,T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe,M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres,J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A.Gaussian 98, revision A.9; Gaussian, Inc.: Pittsburgh, PA, 1998.

(11) Chambers, C. C.; Hawkins, G. D.; Cramer, C. J.; Truhlar,D. G. Model for aqueous solvation based on class IV atomic chargesand first solvation shell effects. J. Phys. Chem. 1996, 100, 16385.

Table 8. Experimental pKa Data and Calculated Entropies (Data Given in cal/mol)

compd exptl pKa(20 °C)a exptl pKa(60 °C)a ∆S(20 °C)b ∆S(60 °C)b

MDEA 8.76 7.99 -3.156 -4.045DMMEA [2-(dimethylamino)ethanol] 9.23 8.36 -0.593 -0.699DGA [2-(2-aminoethoxy)ethanol] 9.62 8.60 1.046 0.961DEMEA [2-(diethylamino)ethanol] 9.76 8.71 0.336 0.247AMP 9.88 8.78 0.844 0.07MMEA [2-(methylamino)ethanol] 9.95 8.94 -0.416 -0.501DIPMEA [2-(diisopropylamino)ethanol] 10.14 9.13 0.330 0.269TBAE [2-(tert-butylamino)ethanol] 10.29 9.28 -0.429 -0.521

a Experimental data from Littel et al.26 b Reaction entropies calculated at the HF/3-21G* level.

Figure 3. Plot of experimental versus calculated pKa values at60 °C.


(12) PC SPARTAN, version 1.0.7; Wavefunction, Inc., 18401Von Karmen Ave. #370, Irvine, CA 92715.

(13) Tomasi, J.; Persico, M. Molecular Interactions in Solu-tion: An overview of methods Based on Continuous Distributionsof the solvent. Chem. Rev. 1994, 94, 2027.

(14) Cances, M. T.; Mennucci, V.; Tomasi, J. A new integralequation formalism for the polarizable continuum model: Theo-retical background and applications to isotropic and anisotropicdielectrics. Chem. Phys. 1997, 107, 3032.

(15) Xidos, J. D.; Li, J.; Zhu, T.; Hawkins, G. D.; Thompson, J.D.; Chuang, Y.-Y.; Fast, P. L.; Liotard, D. A.; Rinaldi, D.; Cramer,C. J.; Truhlar, D. G. Gamesol, version 3.1, University of Minnesota,Minneapolis, MN, 2002, based on the General Atomic and Molec-ular Electronic Structure System (GAMESS) as described in:Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.;Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen,K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J.Comput. Chem. 1993, 14, 1347.

(16) Wiberg, K. B.; Clifford, S.; Jorgensen, W. L.; Frisch, M. J.Origin of the Inversion of the Acidity Order for Haloacetic Acidson going from the Gas Phase to Solution. J. Phys. Chem. A 2000,104, 7625.

(17) Jorgensen, W. L. BOSS, version 4.3; Yale University, NewHaven, CT, 1989.

(18) Li, J.; Zhu, T.; Cramer, C. J.; Truhlar, D. G. A new ClassIV Charge Model for Extracting Accurate Partial Charges fromWawe Functions. J. Phys. Chem. A 1998, 102, 1820.

(19) Bash, P. A.; Singh, U. C.; Langridge, R.; Kollman, P. A.Free Energy Calculations by Computer Simulation. Science 1987,236, 564.

(20) Pearson, R. G. Ionization Potentials and Electron Affinitiesin Aqueous Solution. J. Am. Chem. Soc. 1986, 108, 6109.

(21) Perrin, D. D. Dissociation Constants of Organic Bases inAqueous Solution; Butterworths: London, 1965; Supplement,1972.

(22) Bishnoi, S. Dissertation, University of Texas, Austin, TX,2000; p 100.

(23) Hoff, K. A. Unpublished results from work at the Depart-ment of Chemical Engineering, NTNU.

(24) Hunter, E. P.; Lias, S. G. Proton Affinity Evaluation;National Institute of Standards and Technology, Gaithersburg,MD, 2003; http://webbook.nist.gov.

(25) Perrin, D. D.; Dempsey, B.; Sejeant, E. P. pKa predictionfor organic acids and bases; Chapman and Hall: London, 1981.

(26) Littel, R. J.; Bos, M.; Knoop, G. J. Dissociation constantsof some alkanolamines at 293, 303, 318, and 333 K. J. Chem. Eng.Data 1990, 35, 276.

Received for review October 16, 2002Revised manuscript received July 29, 2003

Accepted August 5, 2003

IE020808N


Paper II

Ab Initio study of the reaction of carbamate formation from CO2 and

alkanolamines


2004

Ind. Eng. Chem. Res. 43, 3413-3418.

GENERAL RESEARCH

Ab Initio Study of the Reaction of Carbamate Formation from CO2

and Alkanolamines


Department of Chemical Engineering, Norwegian University of Science and Technology,N-7491 Trondheim, Norway

Ab initio calculations and a continuum model have been used to study the mechanism forformation of carbamate from CO2 and alkanolamines. The molecules studied are ethanolamineand diethanolamine. A brief review is also made of published experimental observations relevantto the reaction mechanism. The ab inito results suggest that a single-step, third-order reactionis the most likely. It would seem unlikely that a zwitterion intermediate with a significant lifetimeis present in the system. A single-step mechanism also seems to be in good agreement with theexperimental data.

Introduction

The absorption of CO2 by alkanolamines in aqueoussolutions is a well-established technology, and both theequilibrium and kinetics of the reactions involved havebeen studied extensively.1 It is also well-known that CO2reacts to form carbamate and/or bicarbonate, with therelative ratio of these depending on the nature of thealkanolamine and process conditions such as tempera-ture and CO2 loading (mol of CO2 absorbed/mol ofamine). The mechanism of the carbamate formation has,however, been the subject of some controversy, and theorigin of the reaction barrier in carbamate formationhas not been satisfactorily explained in the literature.

Versteeg et al.1 cite the following two-step reactionfor the formation of carbamate from CO2 and alkanol-amines:

where B is a base, usually a second amine molecule. Thefirst step of the reaction is bimolecular, and the productof the first reaction step is a zwitterion. The mechanismis usually referred to as the zwitterion mechanism. Incases where an overall second-order reaction is ob-served, one would assume the first step to be rate-determining. Versteeg cites Caplow2 as the one whoproposed this mechanism and also notes that it waslater reintroduced by Danckwerts.3 The notation usedby Versteeg is, however, somewhat different from the

original one used by Caplow:2

A key feature of eq 3 that is lost in eqs 1 and 2 is thatCaplow assumed that a hydrogen bond is formedbetween the amine and a water molecule before theamine reacts with the CO2 molecule. It would also seemthat such a hydrogen bond could be formed between theamine and any basic species.

An alternative mechanism was suggested by Crooksand Donnellan:4

Again B is used to represent a base molecule. In thismechanism, the bond formation and proton transfer tothe base take place simultaneously, giving a single-step,

* To whom correspondence should be addressed. Tel.:+47 73594125. Fax: +47 73594080. E-mail: [email protected].

CO2 + R1R2NH h R1R2N+HCOO- (1)

R1R2N+HCOO- + B h R1R2NCOO- + BH+ (2)

3413Ind. Eng. Chem. Res. 2004, 43, 3413-3418

10.1021/ie030619k CCC: $27.50 © 2004 American Chemical SocietyPublished on Web 05/25/2004

third-order reaction. While this mechanism appears tobe quite different from mechanisms 1 and 2, it is seento be quite similar to eq 3 (with water as the base in eq3).

In this work, simple ab initio calculations were doneto investigate which mechanism is the more probableone. Experimental results relevant to the determinationof the reaction mechanism are also reviewed.

It would be instructive to do calculations for alkanol-amines that display different kinetics and attempt toaccount for the differences between them. We have herechosen ethanolamine (MEA) and diethanolamine (DEA).MEA is known to have overall second-order kinetics inan aqueos solution, while DEA shows overall third-orderkinetics.1 These molecules show markedly differentbehavior, at the same time they both are among themore common alkanolamines used for absorption pur-poses.

Methods

In this work, we have used HF/3-21G* calculationson the alkanolamines. The solvent effects were studiedby the use of a continuum (implicit) solvation model andthe inclusion of a small number of water molecules. Acontinuum model represents the effects of the solventas a dielectric continuum. It captures the overall sol-vation effects and some of the effects of hydrogenbonding. Such a model cannot be used to model interac-tions with the solvent such as proton transfer, and itonly captures the average effect of the solvent ratherthan explicit interactions between a single solventmolecule and the solute. To study such explicit interac-tions, water molecules have been added.

The carbon (CO2)-nitrogen (in amine) bond lengthwas identified as the key reaction coordinate. Thereactions were, therefore, modeled by doing a series ofcalculations where this bond length was kept constantwhile the rest of the geometry was optimized. This isshown in Figure 1. For the stable configurations identi-fied, calculations were done without any restraints onthe geometry.

All calculations were initially done as calculations onthe explicit molecules at the HF/3-21G* level in avacuum. Single-point calculations with the SM 5.4A5

solvation model were done on the optimized gas-phaseconfigurations. The total energy calculated in thesecases, referred to as SM in the figures, is then the sumof the HF/3-21G* gas-phase energy and SM 5.4A energy(SM 5.4A//HF/3-21G*), with the total energy shown thenbeing the free energy in the solution. All calculationswere done using PC Spartan Pro, version 1.0.7.6

Calculations were done with one and three watermolecules and with a second alkanolamine moleculeacting as a base. The water molecules were placed inpositions where they would constitute a representativemodel of the solvent interactions with the amine func-

tionality. In the case of a single water molecule, it wasplaced such that it would interact as a base with theamine functionality (water oxygen facing the aminehydrogen). In the case of three water molecules, twomolecules were placed to interact as bases with theamine nitrogen and one water molecule was placed sothat one hydrogen atom forms a hydrogen bond withthe free-electron pair of the nitrogen. The hydrogenatoms on the alcohol groups can form hydrogen bondsboth with the CO2 oxygens and with the water moleculeoxygen. In the present work, we have chosen, somewhatarbitrarily, to use conformers of MEA and DEA withno alcohol group-CO2 interaction.

In the Results and Discussion section, one set ofcalculations is shown for the full transfer of the protonto the base, giving the final products. The calculationsare for two MEA molecules. Modeling of the proton-transfer step is somewhat difficult when using clustersof molecules in a vacuum because the molecules tendnot to separate. The final configuration often showsprotonated molecules and carbamate bonded to eachother (particularly when water is used as a base). It is,however, known from the equilibrium states of thesystem that the final carbamate product is more stablethan any intermediate state, and it is this observationthat will be used in the discussion.

It should be emphasized that the purpose of this workis to achieve a qualitative understanding of the reactionmechanism. The uncertainty in choice of conformers,level of ab initio calculation, and representation of thesolvent all contribute to making it difficult to draw anyquantitative conclusions from this work. The need tohave a consistent and accurate representation of bothintermolecular and intramolecular hydrogen bonds forthese molecules represents a particularly difficult issue.7We do, however, believe that the present level ofmodeling is adequate to identify stable intermediatesand reaction barriers between the unreacted amine,CO2, and the final reaction product.


Optimizations were initially done for the unreactedmolecules placed next to each other. The energiesobtained for these starting configurations were definedto be zero for all calculations, and all other energies aregiven relative to these. The plots in Figures 2-4, 6, and7 all show the energy as a function of the carbon-nitrogen bond length. The energy is plotted from thestarting configuration to the energy minimum (orslightly longer) along the reaction coordinate. In Figure8, the energy is plotted as a function of the distance

Figure 1. Approach of CO2 to MEA. Hydrogens on carbon arenot shown.

Figure 2. Approach of CO2 to MEA in a vacuum (open circles)and in a solvent field (SM, black circles).


between a hydrogen atom on the nitrogen and the baseatom it is being transferred to.

Figure 2 shows the results for the approach of CO2 toa single MEA molecule in a vacuum and in the con-tinuum solvation model (SM). In a vacuum, no stableproduct is formed, while in the solvent field, a stableconfiguration is produced. In Figure 3, the results of CO2approaching MEA in the presence of one water molecule

are shown, and Figure 4 shows the results with MEAin the presence of three water molecules. As in Figure2, energies both in a vacuum and in the solvent fieldare shown. It can be seen that in the presence of onewater molecule in a vacuum the reaction proceedswithout a barrier. This suggests that the reaction hasno intrinsic barrier. In the case of three water molecules,one of them is hydrogen bonded to the free electron pairon the nitrogen. For the CO2 to bond, this hydrogen bondmust first be displaced, and this gives rise to a reactionbarrier. The same kind of barrier can be seen with thesolvent field calculations (Figures 2 and 3), suggestingthat with both presentations of the solvent the reactionbarrier is caused by the CO2 molecule having to displacethe solvation shell of the amine functionality.

When the energies of the products in Figures 2-4 arecompared, it can be seen that, in the cases where base(water) molecules are included explicitly in the calcula-tions, the formed product is much more stable. Thisstrongly suggests that the presence of the base isnecessary for the reaction to proceed. In all cases it wasalso found that the bond lengths of the amine hydro-gen(s) changed during the reaction. In the case of theMEA reaction with CO2 in the presence of a single watermolecule, the amine hydrogen had an initial H-N bondlength of 1.008 Å and was at a distance of 2.006 Å fromthe oxygen in the water molecule. Once the CO2 hadbonded to the amine, the H-N bond length increasedto 1.026 Å, while the hydrogen’s distance from theoxygen decreased to 1.765 Å. These changes in bondlengths suggest a gradual proton transfer as the CO2reacts with the amine molecule.

In Figure 6, the results for CO2 approaching DEA inthe presence of three water molecules are shown (theconfiguration of this approach at a C-N distance of 3.2Å is shown in Figure 5). In this case there are appar-

Figure 3. Approach of CO2 to MEA and one water molecule in avacuum (open circles) and in a solvent field (SM, black circles).

Figure 4. Approach of CO2 to MEA and three water moleculesin a vacuum (open circles) and in a solvent field (SM, black circles).

Figure 5. Approach of CO2 to DEA in the presence of three watermolecules. Hydrogens on carbon are not shown.

Figure 6. Approach of CO2 to DEA and three water molecules ina vacuum (open circles) and in a solvent field (SM, black circles).

Figure 7. Approach of CO2 to two MEA molecules in a vacuum(open circles) and in a solvent field (SM, black circles).

Figure 8. Transfer of proton between two MEA molecules to formcarbamate and protonated MEA. Open circles are results in avacuum, and black circles are results in a solvent field (SM).


ently two reaction barriers. The first one (at around 3.2Å) is caused by the displacement of the water moleculesaround the amine functionality and is of the samenature as the barrier identified for MEA. When the CO2molecule approaches the amine functionality, the watermolecules reorganize. In this set of DEA calculations,the water molecule hydrogen bonded as a base to theDEA is displaced while the water molecules reorganize,and it this displacement that results in the secondbarrier seen. However, in these calculations we wereonly looking at single set of configurations of the DEAmolecule and the water molecules. The second barrieris probably a result of the particular set of configura-tions that we have chosen and is probably not repre-sentative of the DEA formation reaction barrier. It doeshowever (again) show that the presence of a basemolecule is necessary for a stable product to be formed.

While not shown, calculations with CO2 approachingDEA without the presence of water molecules and CO2approaching DEA in the presence of one water moleculehave been performed. These calculations show a quali-tative agreement with the results shown for MEA. Whilethe present calculations are not accurate enough tomake any quantitative comparison between MEA andDEA, the results do suggest that their reaction with CO2proceeds along the same reaction path.

In Figure 7 is shown the approach of CO2 to MEA,with a second MEA molecule working as the base. Thetwo MEA molecules were oriented toward each otherso they only interact through the amine functionality.Because of sterical repulsion, the amine functionalitiesmaintain an N-N distance of around 3 Å. This limitsthe degree of hydrogen bonding between them, whichresults in no stable intermediate being formed in thegas phase. In Figure 8, the transfer of the proton fromthe carbamate to the base is shown. In this figure, thex axis shows the distance between the proton beingtransferred and the amine group (nitrogen atom) it isbeing transferred to; the starting configuration is iden-tical with the final products in Figure 7. From thisfigure, it is seen that such a proton transfer can takeplace without any reaction barrier.

These results strongly suggest that, for the CO2 toreact with an amine center, basic solvent moleculesmust be present. On the basis of this observation, wecan see two possible reaction mechanisms.

One possibility is the mechanism proposed by Crooksand Donnellan (eq 4), i.e., amine bonding to CO2 andproton transfer taking place simultaneously. In a gen-eral way, this can be written as

A second alternative is that the CO2 bonds to the amine,with the solvent molecules stabilizing the zwitterion-like intermediate with hydrogen bonds. Such an inter-mediate is, however, likely to have a very short lifetime.If a strong base molecule (usually an amine molecule)appears in the vicinity, the proton would be transferredto the base and carbamate is formed; if the reaction tocarbamate is not completed, the zwitterion-like inter-mediate is likely to revert back to free CO2 and amine.

While this second alternative is a form of the zwit-terion mechanism, it must be emphasized that anyzwitterion-like intermediate would have a very shortlifetime and we would argue that the single-step mech-

anism is in any case the most suited to conveying thenature of the reaction taking place.

Review of the Experimental Data

As shown in the Introduction to this paper, there hasbeen considerable discussion in the literature regardingthe reaction of carbamate formation. Most of the discus-sion has been based on the analysis of experimentalkinetic data. For the zwitterion mechanism, Versteeget al.1 have presented the following expression for thereaction rate:

If the zwitterion formation is rate-determining, theexpression reduces to

This expression can explain the first-order kinetics withrespect to amine observed for aqueous MEA. For second-order kinetics, as for cases with DEA, one needs toassume that the deprotonation is rate-determining,leading to the following expression:

Here B is any base in the system. With amine, water,and other bases B, eq 8 can be written as

If the amine deprotonation term dominates in eq 9, thisequation becomes

This gives a reaction order of 2 with regard to the amine.Reaction orders between 1 and 2 are explained by a mixbetween the two cases. Arrhenius expressions based onthis are in the literature1,8 presented not only for k2 butalso for k2kam/k-1 and k2kH2O/k-1. The deprotonationconstants kam and kw, however, cannot be obtained alonebut only in the groups given.

The consequence of the direct third-order formulationis that water, amine, and other bases can influence thereaction in parallel. With water and amine as thedominating bases, we get

Here k3am and k3

H2O are real third-order rate constants.However, for practical purposes, eq 11 is the analogueto eq 9 with k2kam/k-1 and k2kH2O/k-1 equal to k3

am andk3

H2O, respectively.From eq 11, two extreme cases can be defined. If

k3H2OcH2O . k3

amcam, then water is the dominating base.Because water is the solvent, this will be observed as a

CO2 + R1R2NH‚‚‚B h R1R2NCOO-‚‚‚BH+ (5)

RCO2) -k2[CO2][R1R2NH]/(1 + k-1/∑kB[B]) (6)

RCO2) -k2[CO2][R1R2NH] (7)

RCO2)

-k2∑kB[B]k-1

[CO2][R1R2NH] (8)

RCO2)

-k2

k-1(kam[R1R2NH] + kH2O[H2O] +

∑kB[B])[CO2][R1R2NH] (9)

RCO2)

-k2

k-1kam[CO2][R1R2NH]2 (10)

RCO2) -(k3

am[R1R2NH] + k3H2O[H2O])[CO2][R1R2NH]

(11)


first-order reaction in amine:

If k3amcam . k3

H2OcH2O, then the amine itself is thedominating base and the reaction is second-order withrespect to the amine, as observed for DEA.

This is identical with the third-order reaction rateexpression for the zwitterion mechanism, eq 10. Asalready seen, eq 12 is the same reaction rate equationas that for the second-order zwitterion mechanism, eq7. The two reaction mechanisms can, therefore, be seento give identical rate functions, and any set of experi-mental kinetic data can be fitted to either mechanism.The same observation has also been made by Kumar etal.9 This clearly means that it is very difficult to deducethe reaction mechanism from kinetic studies.

Some arguments have however been made in theliterature on the nature of the reaction based on thekinetics, and these will be discussed presently.

Kumar et al.9 observed that in some systems, suchas DEA in water, the reaction rate can change with theamine concentration in the system.10 In the case of DEA,the reaction order apparently falls at low concentration.They claimed that this change in reaction order couldonly be accounted for with the zwitterion mechanism.We propose an alternative explanation for this observa-tion. Starting with eq 11, an expression for the apparentreaction order with respect to amine can be derived bydifferentiating the equation

At high DEA concentrations, the effect of the amine asthe base will be strong, and k3

amcam . k3H2OcH2O in eq 14.

This is seen to lead to a reaction order of n ) 2 in eq12. When the DEA concentration is lowered, the twoterms in the denominator become more equal. At verylow concentrations, then k3

amcam , k3H2OcH2O and an

order of n ) 1 is predicted.It would also seem that all amines can contribute to

base catalysis of bicarbonate formation. This reactionis first-order in amine concentration, and while it isslower than carbamate formation, the reaction mightbe significant at low amine concentrations. If significant,the bicarbonate formation would contribute to a lower-ing of the observed overall reaction order.

It has previously been argued that a single-step, third-order mechanism cannot explain the broken-order ki-netics observed for some systems. When eq 11 is lookedat, it is, however, clear that this is not the case. Theextent to which water, or another solvent, works as abase will vary (as explained above), and this can directlyaccount for the broken-order kinetics observed.

Equation 11 also suggests that when the solvent ischanged to a weaker base, the reaction order in theamine will increase. This depends on the autoprotolyticconstant of the solvent. For water, pKw is 14, whereasfor ethanol, pKEtOH is 19, and this effect is indeed

observed for MEA (and other alkanolamines) whensolvents such as methanol and ethanol are changed.1

We are not aware of any physical explanation havingbeen offered in the framework of the zwitterion mech-anism to account for the different alkanolamines dis-playing different reaction order.

For the single-step, third-order reaction, an explana-tion will presently be suggested. Sartori and Savage11

reported in an NMR study that MEA forms a morestable carbamate than DEA, a conclusion that can alsobe inferred from kinetic data. Because MEA has a morestable carbamate form, even a weak base, such as water,might be enough to drive the reaction forward. For DEA,a stronger base might be required, giving an overallthird-order reaction. This would suggest that aminesthat form stable carbamates, in general, will have lowerreaction order than amines with less stable carbamateforms. Only limited data have been published forcarbamate stability, but it would seem reasonable to usethe reaction rate as a proxy parameter for carbamatestablity; i.e., a high reaction rate indicates strongcarbamate formation. In their review, Versteeg et al.1report a high reaction rate and an overall second-orderreaction for diglycolamine, 1-amino-2-propanol, 2-(meth-ylamino)ethanol, and 3-amino-1-propanol. For di-2-propanolamine, the same authors report a low reactionrate and an overall third-order reaction. These observa-tions are all consistent with the present explanation.

While a solvent such as water might be a strongenough base to (locally) allow the formation of carbam-ate for amines such as MEA, it is also clear that thepresence of stronger bases in the system (usually otheramine molecules) is required to shift the equilibriumtoward the formation of carbamate. Water, or othersolvents, might be thought of as transporting protonsto bases not placed immediately next to the reactingamine group.

In a recent paper, Aboudheir et al.12 argued that asingle-step, third-order mechanism is best suited toexplain all observed kinetic phenomena. They arguedthat when data are fitted to the expression for thezwitterion mechanism, some parameters take on un-physical values.

Spectroscopic techniques and NMR would seem tooffer the most direct experimental insight into whatspecies are present in a given system. Ohno et al.13 havereported a detailed spectroscopic study of 2-(N-methyl-amino)ethanol and its reaction with CO2 in an aqueoussolution. Looking specifically at the issue of the zwit-terion formation, they found no evidence of its existenceand suggested that only the carbamate and base formsof the alkonolamine were formed. This observation isconsistent with a single-step mechanism.

On the basis of the present conclusions, we canattempt to identify the origin of the reaction barriers.In the case of MEA and other molecules showing second-order kinetics in water, it would seem that the onlybarrier comes from the CO2 molecule having to dislodgethe solvent molecules in the solvation shell of the aminegroups. For the systems where stronger bases arerequired, the need for a base molecule to approach theamine functionality clearly represents a barrier to thereaction taking place. We believe this effect to bedominant for molecules displaying an overall third-orderreaction.

RCO2) -k3

H2O[H2O][CO2][R1R2NH] )

-2k2[CO2][R1R2NH] (12)

RCO2) -k3[CO2][R1R2NH]2 (13)

n )∂ ln rCO2

∂ ln cam) 1 +

k3amcam

k3amcam + k3

H2OcH2O

(14)


ConclusionIn studying the formation of carbamate from CO2 and

alkanolamines in solution, we find a single-step, third-order reaction mechanism to be the most likely. Such amechanism is consistent with both ab initio calculationsand experimental observations on these systems.

The apparent second-order mechanism for MEA inwater can be explained by water acting as a base. Thevarying extent as to which the solvent can act as a basewould also seem to account for the broken-order kineticsobserved for this reaction. Overall third-order kineticsis most likely to be displayed by amines having lessstable carbamate forms.

The barriers for this reaction could either originatefrom the CO2 molecule having to displace the solvationshell around the amine group before reacting with theamine functionality and/or from the need for a basemolecule to approach the amine functionality beforereaction can take place.

Further studies are needed before any quantitativeestimates of the various aspects of the reaction can bemade. More advanced modeling of solvent effects for thisreaction will then be needed.

AcknowledgmentFinancial support for this work by the Norwegian

Research Council is greatly appreciated. Gratitude isalso expressed to Dr. Karl Anders Hoff for helpfuldiscussions.

Literature Cited(1) Versteeg, G. F.; van Dijck, L. A. J.; van Swaaij, W. P. M.

On the Kinetics Between CO2 and Alkanolamines both in Aqueousand Non-Aqueous Solution. An Overview. Chem. Eng. Commun.1996, 144, 113.

(2) Caplow, M. Kinetics of Carbamate Formation and Break-down. J. Am. Chem. Soc. 1968, 90, 6795.

(3) Danckwerts, P. V. The Reaction of CO2 with Ethanolamines.Chem. Eng. Sci. 1979, 34, 443.

(4) Crooks, J. E.; Donnellan, J. P. Kinetics and Mechanism ofthe Reaction beween Carbon Dioxide and Amines in AqueousSolution. J. Chem. Soc., Perkins Trans. 2 1989, 331.

(5) Chambers, C. C.; Hawkins, G. D.; Cramer, C. J.; Truhlar,D. G. Model for aqueous solvation based on class IV atomic chargesand first solvation shell effects. J. Phys. Chem. 1996, 100, 16385.

(6) PC SPARTAN, version 1.0.7; Wavefuncion, Inc.: Irvine, CA,2001.

(7) da Silva, E. F.; Svendsen, H. F. Prediction of the pKa Valuesof Amines Using ab Initio Methods and Free-Energy Perturba-tions. Ind. Eng. Chem. Res. 2003, 42, 4414.

(8) Xu, S.; Wang, Y.-W.; Otto, F. D.; Mather, A. E. Chem. Eng.Sci. 1996, 51, 841.

(9) Kumar, P. S.; Hogendoorn, J. A.; Versteeg, G. F.; Feron, P.H. Kinetics of the reaction of CO2 with aqueous potassium salt oftaurine and glycine. AIChE J. 2003, 49, 203.

(10) Versteeg, G. F.; Oyevaar, M. H. The reaction between CO2and Diethanolamine at 298 K. Chem. Eng Sci. 1989, 44, 1264.

(11) Sartori, G.; Savage, D. W. Sterically Hindered Amines forCO2 Removal from Gases. Ind. Eng. Chem. Fundam. 1983, 22,239.

(12) Aboudheir, A.; Tontiwachwuthikul, P.; Chakma, A.; Idem,R. Chem. Eng. Sci. 2003, 58, 5195.

(13) Ohno, K.; Matsumoto, H.; Yoshida, H.; Matsuura, H.;Iwaki, T.; Suda, T. Reaction of Aqueous 2-(N-Methylamino)ethanolSolutions with Carbon Dioxide. Chemical Species and TheirConformers Studied by Vibrational Spectroscopy and ab initioTheories. J. Phys. Chem. A 1998, 102, 8056.

Received for review July 29, 2003Revised manuscript received March 19, 2004

Accepted March 30, 2004

IE030619K


Paper III

Use of Free Energy Simulations to predict Infinite Dilution Activity

Coefficients


2004

Fluid Phase Equilibria, 221, 15-24 and

Erratum Fluid Phase Equilibria 231, 252-253.

1

Use of Free Energy Simulations to Predict Infinite Dilution Activity Coefficients

Fluid Phase Equilibria, 221, 15-24 and Erratum Fluid Phase Equilibria 231, 252-253.

Eirik F. da Silva*

Department of Chemical Engineering, Norwegian University of Science and Technology,

N-7491 Trondheim, Norway

Abstract

An important challenge in applied thermodynamics is the prediction of mixture

phase behavior without the use of experimental data. Current group contribution methods

are sometimes, but not always successful in this regard. In the present work Monte Carlo

free energy perturbations are used in calculating the free energies of solvation for pure

component and infinite dilution using the OPLS force field. Infinite dilution activity

coefficients are calculated by pure simulation and simulations used in combination with

experimental vapour-pressures. The activity coefficients are then used to fit the parameters

in Wilson’s equation thereby giving overall predictions of activity. Results are compared

with free energies and activity coefficients based on experimental values. The systems

studied are methanol + water, ethanol + water, acetonitrile + water, formic acid + water

and ethanolamine (MEA) + water.

Keywords: Vapour-liquid equilibria; Activity coefficient; Molecular Simulation;

Ethanolamine

2

Introduction

Knowledge of chemical activity is an important component in understanding

various chemical processes, chemical gas-absorption being one example of this [1]. Infinite

dilution activity coefficients can for example be used to make overall predictions of

activity and approximate vapour-liquid equilibrium curve.

Traditionally Gibbs excess free energy models have been used to model activity

coefficients. The only predictive models have been group contribution models such as

UNIFAC [2]. These models are to some extent limited by access to experimental data. In

systems with a large number of chemical species and limited experimental data such as in

gas-absorption the use of such models becomes difficult.

The value of models that can predict activity coefficients is therefore clear. And it

should be emphasized that even models that are only qualitative can in some cases be a

useful tool, particularly in understanding complex systems.

The ideal would be some form of ab initio (quantum mechanical) model without

any need of parameterization to experimental data. It is however clear that treating the

condensed phase at a quantum mechanical level is computationally very expensive. Guillot

[3] reports a vaporization enthalpy for water of 7.38 kcal/mol calculated using ab initio

molecular dynamics (Car-Parrinello), while the experimental vaporization enthalpy for

water is around 11 kcal/mol [3]. While this result is encouraging it is clear that many

issues remains before ab initio molecular dynamics methods can be used for quantitative

predictions of solvation.

In a recent work Sum and Sandler [4] use ab initio calculations on clusters of eight

molecules to calculate parameters for an excess Gibbs energy model (UNIQUAC). The

results presented in the article show very good agreement with experimental data. The

procedure does however involve a number of approximations and uncertainties that are not

fully acknowledged in the article. The ab initio method used is Hartree-Fock, involving

approximations that usually makes it unsuited for obtaining absolute bonding energies [5].

It is also assumed that the interactions of a cluster of eight molecules is representative of

the interactions in a liquid. The size of the cluster at the same time also results in a very

small number of data for the statistical averaging that is done. Finally there is the

approximation in the use of the UNIQUAC equation itself which is known not to be

generally accurate [6,7]. It is therefore difficult to reconcile the large uncertainties and

3

numerous approximations in the method with the apparent high quality in the results. This

work does not in any case represent any true ab initio modeling of the condensed phase.

Classical simulations have been central in developing the understanding of the

condensed phase. Despite their fairly long history it has been observed [8] that their use for

the practical prediction of chemical activity is at an early stage. There are two main issues

regarding use of simulations:

One is the representation of the molecule used. Some models such as OPLS

(Optimized Parameters for Liquid Simulation) [9] include polarization only implicitly,

while some other force fields are polarizable. There are also differences in the flexibility of

molecules and the number of sites used. Force fields such as OPLS can be thought of as

offering a molecular level group contribution method [10].

There are numerous choices in how to optimize a force field model. There are also

many ways ab initio calculations can be used to parameterize force fields. Examples are

determination of torsional potential parameters [11] and atomic charges [12].

The second issue is how accurate data for the free energy can be achieved for a

given molecular representation. There are a number of calculation schemes based on forms

of thermodynamic integration and free energy perturbation [10,13]. For each scheme there

is usually also a number of simulation parameters to set. There would not seem to be any

general agreement on which methods are superior. Particularly if one considers the

tradeoffs between accuracy and simulation time it is difficult to know what methods to

choose.

In this work Monte Carlo free energy perturbations are used with OPLS force field

representation of the molecules. The simulation method is one of the most widely used, its

main appeal being that it is relatively inexpensive in terms of computation time.

The focus of this work is on binary systems with water. Methanol, ethanol,

acetonitrile and formic acid are chosen because parameters for them are available in the

OPLS force field and because experimental data is available for binary systems with water.

Ethanolamine, also known as MEA, is an important molecule in gas-purification

[1,14]. For ethanolamine itself considerable experimental data is available, for other

alkanolamines the data is however often very limited. If a molecular force field (such as

OPLS) was found to offer parameters that could be transferred to alkanolamines it could be

used in modeling of a number of systems of importance in gas-purification.

4

Theory

The difference between the chemical potential in a mixture and the ideal gas-phase

is called the residual chemical potential and at infinite dilution is directly related to the

activity coefficient [10] by the following equation:

( ) ( ) ( )1 12 12 12 22 22 11ln res res reskT ∞γ = µ −µ = µ −µ + µ −µ (1)

Where 12µ is the chemical potential of a molecule of type 1 in a pure solvent of type 2. The

equation is valid for constant temperature (T) and pressure, k is the Boltzmanns constant.

There are several ways in which data can be obtained to solve Eq. (1). One can

directly calculate the free energy of a single particle by insertion or removal. This can for

example be done stepwise:

( ) ( )21 21 11 11 01res resresµ = µ −µ − µ −µ (2)

The subscript 0 is used to indicate that a particle does not exist in the system, it has either

been removed or will be inserted. The experimental vapour-pressures can also be used to

calculate the difference in the residual free energy of the pure components by use of the

following equation [10]:

( )0

1 122 11 0

2 2

( )ln ln( )

satres

sat

f P TkT kTf P T

⎛ ⎞ ⎛ ⎞⎟ ⎟⎜ ⎜⎟ ⎟µ −µ = ≈⎜ ⎜⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜⎝ ⎠ ⎝ ⎠ (3)

where f is the fugacity and satP is the saturation pressure. Lazaridis and Paulaitis [15]

used Eq. (3) in combination with equation 1 to obtain activity coefficients at infinite

dilution.

In the present work the free energy of solvation will be calculated. While

differences in the residual chemical potential and the free energy of solvation are the same

at infinite dilution their relative values for pure components is different. The free energy

of solvation (s∆µ ) has the following relationship to the saturation pressure[16]:

ln( / )sats s skT P M RTdµ∆ = (4)

5

where Ms is molar mass and ds is density. To obtain the difference in residual free energies

for the pure components from solvation energies the Ms/ds ratio for each component must

be subtracted.

For the pure component there are also other techniques available for the calculation

of the free energy. Hermans et al. [17] and Mezei [18] have presented results based on

thermodynamic integration of the entire ensemble.

Once both infinite dilution activity coefficients in a binary system are estimated the

data can be fit to any two-parameter Gibbs excess model such as Wilson’s or UNIQUAC

to get an estimate of activity coefficients for all compositions, a possibility mentioned by

Haile [19]. In this work the Wilson equation has been chosen [6]:

( ) 12 211 1 12 2 2

1 12 2 2 21 1

ln( ) ln x x xx x x x

⎛ ⎞Λ Λ ⎟⎜ ⎟γ =− +Λ + +⎜ ⎟⎜ ⎟⎜ +Λ +Λ⎝ ⎠ (5)

6

Methods

The free energy perturbation (FEP) approach centers on the relationship [20]:

( )[ ]00101 expln EEkTAA −−−=− β (6)

The equation expresses the free energy difference between systems 0 and 1 by an average

of a function of their energy difference that is evaluated by sampling based on E0. This

calculation works if the two systems are similar to each other. A coupling parameter is

introduced to allow gradual interconversion of the potential functions and geometries. This

interconversion can be represented by the following equation [20]:

( ) ( )0 1 0ξ λ ξ λ ξ ξ= + − (7)

Where is any feature of the system. In the present work the “double-wide” sampling

technique described by Jorgensen and Ravimohan [20] will be used. This is a so-called

single-topology method.

The calculation of absolute free-energy is somewhat more difficult than calculating

relative free-energies. In obtaining absolute free energies insertion schemes are considered

superior to deletion schemes[21]. Standard double-wide calculations involve both deletion

and insertion steps and are their use in this context is therefore questionable. In this work

staged insertion of argonlike particles will therefore be used to obtain the absolute free-

energy of solvation. A very similar approach has been used previously by Jorgensen et al.

[22] in obtaining the absolute free energy of solvation of TIP4P water, the method was in

that work called single solvent perturbation.

As an alternative approach the free-energies of the pure components can be

determined from experimental vapour-pressure (Eq. 3). The simulations are then only used

to obtain relative free-energies of solvation.

In BOSS [23] the potential energy is expressed as the sum of Lennard-Jones and

Coulomb potential functions:

∑∑∑<<<

+−=ji ij

ji

ji ij

ji

ji ij

ji

rqq

rCC

rAA

U 612 (8)

7

where the sums are over all pairs of interaction sites, Ai=(4 i iε σ 12)1/2 ,Ci=(4 i iε σ 6)1/2 , qi is

the partial electric charge of interaction site i and rij is the separation between interaction

sites.

The interaction sites are usually atoms; however, non-polar hydrogens bonded to carbon

atoms can be combined with the carbon atom to form a single «united» atom (UA).

For the water molecule two representations were used: the TIP3P model [24] for

water as solute and the TIP4P for water as solvent. The TIP4P model has a total of four

interaction sites: the oxygen atom, the two hydrogen atoms, and a center for the negative

charge located along the dipole vector. The TIP3P model was chosen as solute because the

three-center model can more easily be used in perturbations. Calculations have also been

done on TIP4P as solute to offer comparison with data reported in the literature.

Internal rotations were included for ethanol, formic acid and ethanolamine. The

rotational potential is represented by the Fourier series in Eq. (9):

( ) ( )( ) ( )( ) ( )( )1 2 21 1 11 cos 1 cos 2 1 cos 32 2 2

V V V Vφ = + φ + − φ + + φ (9)

where V is a coefficient and φ is the torsional angle. Following Jorgensen et al. [11] the

intramolecular energy interactions between molecules separated by 3 bonds (1-4

interactions) were scaled down by a factor of 2. Coefficients for internal rotations are

given in Table 1.

Table 1 Fourier Coefficients (in kcal/mol)

Molecule Dihedral Angle V1 V2 V3

ethanol H-O-CH2-CH2 0.834 -0.116 0.747

formic acid H-O(H)-C-O 0.000 0.000 0.000

ethanolamine H-O-CH2-CH2 0.834 -0.116 0.747

N-CH2-CH2-O 9.900 0.000 0.000

H(N)-N- CH2-CH2 -0.190 -0.417 0.418

OPLS geometries published by Jorgensen et al. were used for TIP4P [24], TIP3P [24], UA

methanol [25], UA ethanol [25] and UA acetonitrile [26]. For formic acid unpublished

geometry included in the BOSS program distribution [23] was used. Bond lengths for

formic acid were 1.2258 Å (C=O), 1.356851 (C-O(H)), 1.09 (C-H) and 0.943611 (O(H)-

8

H). Angles are 119.277520 ( O(H)-C-O), 108.159159 (H(O)-O(H)-C) and 124.451989

(H(C)-C-O). It should be noted the formic acid parameters in BOSS were for a fully

flexible molecule, in the present work the parameters are used with rigid bond-lengths and

angles.

For ethanolamine no OPLS parameterization has been published. The amine

parameters are taken from Rizzo and Jorgensen [9] and for the alcohol functionality the

UA ethanol parameters are used. The CH2 group neighboring the amine group is given the

same Lennard-Jones parameters as the ethanol functionality CH2 group, finally the charge

of this group is chosen to give the molecule a total charge of zero. Geometry parameters

are based on mixture of HF/6-31G* ab initio geometry and AM1 semiemprical geometry.

Bond-lengths are set to 1.012 Å (N-H), 1.45 Å (N-CH2), 1.53 Å (CH2-CH2), 1.43 Å (CH2-

O) and 0.945 (O-H). Angles are 108.5 (H-CH2-O), 112 (CH2-CH2-O) 108.46( N-CH2-CH2)

and 109.69 (H-N-CH2). Ethanolamine has four dihedral angles. The relative positions of

the amine-group hydrogens are fixed by setting the dihedral angle H1(N)-N-CH2-H2(N) to

121.68. The three other dihedral angles are chosen to be flexible. Using HF/6-31G* ab

initio calculations on a single ethanolamine molecule the most stable gauche conformer

was found to be 2.81 kcal/mol more stable than the most stable trans conformer. Following

Jorgensen et al. [11] the coefficients for the rotations are set to reproduce this conformer

energy difference. For the alcohol-group the same coefficients as used for ethanol are

chosen. The coefficients are given in Table 1. All Lennard-Jones and charge parameters for

the molecules studied are listed in Table 2.

9

Table 2 Force Field Parameters Molecule United

Atom

(Å)

(kcal/mol) Q

(Electron units) argon 3.401 0.2339 0.000 water O 3.15365 0.155 0.000 (TIP4P) H 0.000 0.000 0.520 M 0.000 0.000 -1.040 water O 3.15061 0.1521 -0.834 (TIP3P) H 0.000 0.000 0.417 methanol O 3.070 0.170 -0.700 CH3 3.775 0.207 0.265 H 0.000 0.000 0.435 ethanol CH3 3.905 0.175 0.000 CH2 3.905 0.118 0.265 O 3.070 0.170 -0.700 H 0.000 0.000 0.435 acetonitrile C 3.650 0.150 0.280 CH3 3.775 0.207 0.150 N 3.200 0.170 -0.430 formic acid C 3.750 0.105 0.520 O 2.960 0.210 -0.440 H(C) 2.420 0.015 0.000 O(H) 3.000 0.170 -0.530 H(O) 0.000 0.000 0.450 ethanolamine N 3.300 0.170 -0.900 H(N) 0.000 0.000 0.360 CH2(N) 3.905 0.118 0.180 CH2(O) 3.905 0.118 0.265 O 3.070 0.170 -0.700 H(O) 0.000 0.000 0.435

Formic acid and ethanolamine have an intramolecular contribution to the free energy. To

obtain the free energy of solution the intramolecular free energy in the gas-phase must be

subtracted from the value in solution. Results in this work will be presented with the gas-

phase contribution subtracted.

The OPLS force field is intended to offer transferable parameters for molecules

both as solute and solvent, they are usually fitted to density and vaporization enthalpy. The

representations for water (TIP4P), UA methanol, UA ethanol and UA acetonitrile are all

reported to reproduce fairly accurately densities and heats of vaporization for pure

components (see Table 3).

The particle insertion simulations were done by growing a uncharged (UC) TIP4P

molecule in the ensamble. The particle was not grown from zero but from a small particle

with negligible free-energy. This particle had a Lennard-Jones σ=0.01 Å and a ε =0.015

kcal/mol. Most of the other simulations were done directly between the solutes and a water

molecule. The size difference between the ethanolamine molecule and water is however

10

very large, in this case ethanolamine was first perturbed to an argonlike uncharged (UC)

ethanolamine molecule. This uncharged molecule was then perturbed to UC TIP4P.

Boxes with 267 solvent molecules were used. All solvent boxes were equilibrated

for at least 10 million configurations before use. Double-wide perturbations were done

with ∆λ = +/-0.05, with λ =0.05, 0.15, 0.25, 0.35,0.45,0.55,0.65,0.75,0.85 and 0.95. Each

step had 500 000 configurations of equilibration and 500 000 configurations of averaging.

The particle insertions were done with ∆λ = +0.05 and same amount of sampling and

equilibration for each step as for the double-wide perturbations.

Periodical boundary conditions were used. Preferential sampling of the solvent near

the solute [20] was used for the double-wide sampling calculations based on the following

weighting:

( )2

1r wkc+

(10)

Following recommendations in the BOSS documentation [23] wkc values between 200 and

300 were used. This procedure was however not used for the particle insertion

calculations. All simulations were done in a NPT ensemble at a pressure of 1 atmosphere,

the ethanolamine simulations were done at 60°C, while the other simulations were done at

25 °C. Attempts to change the volume of the system were done every 700-1625

configurations. Lowest frequency of volume changes was for ethanolamine while the

highest was for TIP4P. Each volume change was 130 Å3. New configurations are

generated by selecting a molecule, translating it randomly in all three Cartesian directions,

rotating it randomly about a randomly selected axis and performing any internal rotations.

Ranges for translations are set at 0.15 Å while ranges for angular rotations and dihedral

rotations are set at 15 degrees.

Interactions were cut off with a quadratic “switching” function. The same cutoffs as

previously used by Jorgensen et al. were used: 8.5 Å for water (TIP4P) [22], 9.5 Å for

methanol [25], 11.0 for ethanol [25], 10 Å for acetonitrile [26] and 12 Å for formic acid

(value used for acetic acid [27]). Ethanolamine is a larger molecule and in this case a

cutoff of 14 Å was chosen. The same cutoffs were chosen for solvent-solvent interactions

and solute-solvent interactions, except in water where a 10 Å solute-solvent interaction

was chosen. The statistical uncertainty was estimated by the batch means procedure [9]

and standard deviations from the total energy of separate runs using different starting

configurations. For each free energy difference three separate simulations from different

11

staring configurations were used. Each free energy calculation took between 2 and 12

hours on a single processor PC.

The heat of vaporization to the ideal gas has been calculated to make comparison

with experimental data and with previous work by Jorgensen et al. (Table 3). It is

calculated according to the following equation [27]:

( ) ( ) ( )( )intra intravap iH E g E l E l RT∆ = − + + (11)

where ( )intraE g and ( )intraE l are the intramolecular rotation energies for the gas and the

liquid, ( )iE l is the intermolecular energy for the liquid. There has apparently not been

published any estimates for the enthalpy of vaporization of ethanolamine except at the

boiling temperature. Antoaine equations have however been published and in the present

work this will be used to estimate the experimental vaporization enthalpy using the

Clapeyron equation:

vap

vap

HdPdT T V

∆=

∆ (12)

where P is the pressure and vapV∆ is the molar volume change upon vaporization. The

calculation will be done assuming ideal gas and neglecting the molar volume in the liquid

phase.

12


In Table 3 densities and vaporization enthalpies for the solvents studied are shown.

While some of the experimental vaporization enthalpies are not for ideal gas, the energy

differences between ideal gas and real gas are in these cases small.

Table 3 Densities and Energy Results

Solvent T [°C]

d [g/cm3] ∆Hvap [kcal/mol]

Calcd Calcd Exptl Calcd Calcd Exptl water (TIP4P) 25 1.012 0.999 [24] 0.997 [28] 10.60a 10.66 [24] a 10.51 [24] methanol 25 0.720 0.759 [25] 0.786 [28] 8.97 a 9.05 [25] a 8.94 [25] ethanol 25 0.741 0.748 [25] 0.785 [28] 9.90 a 9.99 [25] a 10.11 [25] acetonitrile 25 0.750 0.765 [26] 0.776[28] 7.57 a 8.03 [26] a 8.01 [31]a formic acid 25 1.236 1.214 [28] 12.39 a 11.03 [31]a

ethanolamine 25 1.056 1.012 [29] 14.59 a ethanolamine 60 1.029 0.984 [30] 13.59 a 13.79b a: Heat of vaporization to ideal gas. b: Obtained by using the Clapeyron equation (Eq. 12) with Antoaine equation data given in [32].

For TIP4P, methanol, ethanol and acetonitrile the simulation results are in good agreement

with the experimental values, reflecting the fact that the OPLS force field has been

parameterized to reproduce these properties. The results are slightly different from those

obtained for the same systems by Jorgensen et al. The number of molecules in the

simulation boxes is in the present study different (in all cases larger) than used in the

original studies and this probably explains part of the discrepancy. It should also be noted

that the present simulations with use of preferential sampling are not optimal for estimating

overall solvent properties.

The agreement for formic acid is slightly worse reflecting that this model has not

been parameterized in the same way.

For ethanolamine the parameters are taken from other molecules, it is therefore

very encouraging to see the good agreement with the experimental data. The densities are

overestimated by around 4.5% at both temperatures. The agreement with the vaporization

enthalpy is even better. These results suggest that the OPLS force field has reasonable

transferability to alkanolamines.

In Table 4 the results for the separate free energy calculations based on double-

wide sampling are shown. For most calculations free energy differences have been

calculated using three simulations based on different starting configurations, the result

shown is the average of all simulations. The uncertainty given with the result is the

standard deviation over subsets in the calculations, again the average for all runs is shown

13

(the standard deviation not varying that much from run to run). The standard deviation of

the total free energy from repeated runs is shown in a separate column.

Table 4 Free Energy Differences (Results in kcal/mol)

Solvent T [°C] ∆Gcalca S.D.b

methanol→waterc waterd 25 -1.97 +/-0.21 0.26 waterd→UC water waterd 25 8.25 +/-0.15 0.54 waterc→UC water waterd 25 8.93 +/-0.18 0.30 methanol→waterc methanol 25 -0.53 +/-0.16 0.31 waterc→UC water methanol 25 6.43 +/-0.19 0.15 ethanol→ waterc waterd 25 -1.97 +/-0.37 0.38 ethanol→ waterc ethanol 25 0.36 +/-0.25 0.44 waterc→UC water ethanol 25 5.64 +/-0.17 0.76 acetonitrile→ waterc waterd 25 -3.49 +/-0.46 0.49 acetonitrile→ waterc acetonitrile 25 1.07 +/-0.15 0.12 waterc→ UC water acetonitrile 25 4.57 +/-0.06 0.12 formic acid→waterc waterd 25 -0.22 +/- 0.51 0.23 formic acid→waterc formic acid 25 0.59 +/-0.33 1.52 waterc→UC water formic acid 25 10.26 +/-0.13 1.11 MEAe →UC MEAe waterd 60 11.40 +/-0.20 0.40 MEAe→ UC water waterd 60 0.39 +/-0.16 f waterc→UC water waterd 60 8.82 +/-0.14 0.47 MEAe →UC MEAe MEAe 60 7.90 +/-0.20 0.61 UC MEAe→ UC water MEAe 60 0.57 +/-0.33 f waterc→UC water MEAe 60 7.07 +/-0.17 0.76 a Standard deviation from batch means procedure. b Standard deviation of total free energy for three separate simulations. c TIP3P.d TIP4P. e ethanolamine. f Single simulation.

For the methanol to water (TIP3P) in water Lazaridis and Paulaitis [15] obtained a value of

-1.77 kcal/mol using almost identical method. While the difference in the results is

significant it is in fact within the uncertainties observed both in the work by Lazaridis and

Paulaitis and in the present one. The present result is based on greater sampling and is

probably the more accurate value. Using slightly different molecular representation

Slusher [33] obtained a value of -1.58 kcal/mol for the same energy difference.

For the methanol to water free energy difference in methanol Slusher [33] obtained

a value of -1.65 kcal/mol using somewhat different molecular representation. The present

result is –0.53 kcal/mol and the difference is clearly greater then can be accounted for by

the uncertainties in the calculations.

The standard deviations based on calculations from repeated runs are in general

somewhat higher then those based on the subsets of a single run.

In Table 5 the results of the particle insertion calculations are shown. In the

appendix underlying simulation results are shown for the insertion calculations together

14

with results based on deletion. Results from the present work do not give grounds to draw

general conclusions regarding insertion and deletion. As noted in the Methods section

double-wide sampling involves both deletion and insertion steps and should only be used

when deletion and insertion are equivalent. Further work might therefore be required to

clarify under which conditions double-wide sampling and insertion are equivalent.

Table 5 Free Energy of Insertion (Results in kcal/mol)

Solvent T [ °C] ∆Gcalca S.D.b

0→ argon waterc 25 2.44 +/-0.19 0.13 0→UC water waterc 25 2.51 +/-0.18 0.30 0→UC water methanol 25 1.1 +/-0.10 0.09 0→UC water ethanol 25 0.95 +/-0.10 0.27 0→UC water acetonitrile 25 1.29 +/-0.12 0.15 0→UC water formic acid 25 2.93 +/-0.19 0.77 0→UC water waterc 60 2.98 +/-0.17 0.36 0→UC water ethanolamine 60 2.83 +/-0.18 0.49 a Standard deviation from batch means procedure. b Standard deviation of total free energy for three separate simulations. c TIP4P.

Adding together the free energy differences from Table 4 and Table 5 the total free energy

of solvation at infinite dilution, or for pure component can be calculated. In Table 6 total

simulation free energies are compared with values estimated from experimental data. The

present result for water (TIP4P) is in good agreement with a Helmoltz free energy of

TIP4P obtained by Thermodynamic Integration reported by Hermans et al. [17]. They

reported a Helmoltz free energy of –5.3 kcal/mol that translates to a Gibbs free energy of

–5.9 kcal/mol, while the present result is –5.74 +/-0.24. Using a method very similar to the

one used in the present work Jorgensen [22] obtained a value of –6.06 kcal/mol for the free

energy of solvation of TIP4P.

15

Table 6 Free Energy of Solvation (Results in kcal/mol)

Solute Solvent T [°C] ∆Gs,calca ∆Gs,exp

b calc∞γ c calc

∞γ d exp∞γ

argon watere 25 2.44+/-0.19 2.002 watere watere 25 -5.74 +/-0.24 -6.324 waterf watere 25 -6.42 +/-0.26 methanol watere 25 -4.45 +/-0.33 -5.1 4.0 5.2 1.74g waterf methanol 25 -5.33 +/-0.21 2.8 2.2 1.57h methanol methanol 25 -4.80 +/-0.26 -4.859 ethanol waterb 25 -4.45 +/-0.46 -5.05 9.1 11.3 3.91g waterf ethanol 25 -4.69 +/-0.19 5.7 4.6 ethanol ethanol 25 -5.06 +/-0.32 -5.079 acetonitrile watere 25 -3.78 +/-0.52 7.8 1758 11.1g waterf acetonitrile 25 -3.28 +/-0.16 68.3 29 acetonitrile acetonitrile 25 -4.35 +/-0.31 formic acid watere 25 -7.02 +/-0.42 9.6 0.1 0.64g waterf formic acid 25 -7.33 +/-0.23 0.1 10.1 formic acid formic acid 25 -7.92 +/-0.41 -5.538 waterf watere 60 -5.85 +/-0.22 ethanolamine watere 60 -8.81 +/-0.31 0.02 0.0002 0.27i

waterf ethanolamine 60 -4.24 +/-0.25 4.4 333.6 0.51i ethanolamine ethanolamine 60 -5.65 +/-0.43 a Standard deviation from batch means procedure. b Ref. [16]. c Pure simulation activity coefficients (sim).d Activity coefficients based on simulations and experimental vapour pressures (sim-P). e TIP4P. f TIP3P. g Data from Kojima et al. [34]. h Data from Slusher [33]. i Data from fitting of vapour-liquid equilibria to UNIQUAC [35].

The overall agreement between FEP results and experimental free energies is quite good.

Only in the case of formic acid does the energy deviate by more than 1 kcal/mol. This

overestimation of the free energy of formic acid is probably due to the use of a molecular

representation that gives too high vaporization enthalpy (Table 3).

Comparing infinite dilution activity coefficients calculated from the simulations

with experimental values good overall agreement is found in most cases. In the case of

ethanolamine the agreement is however poor. The results suggest that the simulated

solvation energies in pure ethanolamine are too low both for water and ethanolamine itself,

leading to the activity coefficient of water being too high in ethanolamine and at the same

time giving too low activity coefficient for ethanolamine in water.

Figures 1-4 show activity coefficients based on simulations together with

experimental activity coefficients. Two different estimates of the activity coefficients are

shown.

Using the data in Table 4 and Table 5 with Eq. (1) and the molar mass-density

correction from Eq. (4) the infinite dilution activity coefficients are obtained. Density data

16

are from references given in Table 3. Using these values one can determine the parameters

for Wilson’s Eq. (4) and thereby obtain a general prediction for the activity coefficients.

Results based on this calculation are referred to as simulation (sim) in Figures 1 to 4.

The other approach is to use Eq. (3) with experimental data for the saturation

vapour pressure [35] to obtain the free energies for the pure components and only use the

simulations for the free energy differences in the same solvent ( )21 11resµ −µ . This gives the

activity coefficients at infinite dilution, which again can be used to fit the parameters in

Wilson’s equation. Results based on this are shown as sim-P in Figures 1-4. The infinite

dilution activity coefficients obtained using this method are shown in Table 6.

With experimental liquid composition-vapour pressure data and liquid

composition-vapour composition data a set of equations is obtained that can be solved to

obtain the activity coefficients. The experimental results shown in figures 1-4 are based on

this approach. Data from Gmehling et al. [35] has been used. Experimental methanol +

water and ethanol + water systems were at 25 C, while acetonitrile + water and formic acid

+ water systems were at 30 C. To obtain the activity coefficients the data for formic acid +

water were corrected for vapour phase association of formic acid following Gmehling et al.

[35].

For ethanolamine isothermal vapour-composition data are not available. In this case

only the vapour pressure is shown. Here the activity coefficients from the simulations have

been used together with experimental vapour pressures for pure components to obtain a

vapour-liquid equilibrium curve on the same form as the experimental data. Experimental

vapour pressures are from Nath and Bender [29] (same data given in Gmehling et al. [35] ),

while vapour pressures for pure components are from Antoaine equations given in

Gmehling et al. [35]. Plots are shown in figure 5.

Experimental activity coefficients are obtained from liquid composition-vapour pressure

data and vapour composition data.

17

Figure 1. Activity coefficients for methanol + water at 25 C. Points are experimental data. Dashed lines are activity coefficients based purely on simulations (sim). Solid lines are based on simulations and experimental vapour pressures (sim-P).

Figure 2. Activity coefficients for ethanol + water at 25 C. Points are experimental data. Dashed lines are activity coefficients based purely on simulations (sim). Solid lines are based on simulations and experimental vapour pressures (sim-P).

18

Figure 3. Activity coefficients for acetonitrile + water at 30 C. Points are experimental data. Dashed lines are activity coefficients based purely on simulations (sim). Solid lines are based on simulations and experimental vapour pressures (sim-P).

Figure 4. Activity coefficients for formic acid + water at 30 C. Points are experimental data. Dashed lines are activity coefficients based purely on simulations (sim). Solid lines are based on simulations and experimental vapour pressures (sim-P).

19

Figure 5. Vapour pressure for ethanolamine + water at 60 C. Points are experimental data. Dashed line is from activity coefficients based purely on simulations (sim).

In the fitting process it was found that not all sets of infinite dilution activity coefficients

could be fit easily to Wilson’s equation. Particularly in the fitting of the ethanolamine

system extreme parameters (10-74) were needed, and even this does not produce a perfect

fit with the activity coefficients from the simulations. This problem arises because the

parameters in Wilson’s equation are strongly coupled and the equation is inherently better

in fitting to some forms of data.

The pure simulation (sim) and simulations in combination with experimental

vapour-pressures (sim-P) are quite good for methanol + water, ethanol + water and

acetonitrile + water. For the formic acid + water system the pure simulation results (sim)

are wrong while the sim-P results are inconclusive. The difference between the sim and

sim-P results are for formic acid dramatic, but this can be easily understood in terms of the

uncertainties in the simulations and the use of Wilson’s equation to fit the data. Formic

acid + water is also a highly non-ideal system and data obtained at infinite dilution might

be insufficient to describe the system at all compositions.

For ethanolamine +water there is only limited agreement. Part of the problem might

be the isssue regarding use of Wilson’s equation mentioned previously but the agreement

with experimental data at infinite dilution is in this case also poor (Table 6). Further

studies are needed for this system.

20

The methanol + water system has also been studied by Crozier and Rowley [36]

using different molecular representation, the results from the present work would appear to

be in better agreement with experimental data.

In general the results can be said to be fairly good suggesting that the OPLS force

field based on parameterization to density and enthalpy of vaporization is useful in

predictions of activity coefficients.

The present simulations do not have the same precision as work by Slusher [33]

and by Crozier and Rowley [36], but when comparing the quality of the results it must be

kept in mind that the simulations used in the present work are relatively inexpensive in

terms of simulation time. Further studies are needed to determine which method can

deliver the most precise results for a given amount of CPU time.

For highly non-ideal systems such as formic acid + water it would appear that data

at infinite dilution and for pure component are insufficient basis for predicting the full

equilibrium. One possibility along the lines of the present work would be to also do free

energy perturbations in mixtures of the solvents.

As noted previously there are a number of ways in which a force field can be

optimized. While the present work uses TIP4P for water and UA OPLS for methanol,

Slusher [8] uses SPC water and a different UA methanol model. The results of the present

work suggest that the difference between the models is significant. It is however not clear

if any type of force field parameterization is in general superior with respect to obtaining

free energies.

It should also be noted that systems involving hydrogen bond forming molecules

and water are among the more difficult to model. In work on binary systems with osmotic

molecular dynamics Crozier and Rowley [36] in general obtained better results for systems

involving alkanes than for systems involving molecules such as methanol and water.

At present it would seem that it is not possible to a priori predict how well a given

force field will reproduce experimental data. A semi-qualitative reproduction of

experimental data is perhaps what can be expected.

21

Conclusion

In this paper free energy perturbations have been used to calculate free energies of

solvation for pure components and solutes at infinite dilution. The results were used to fit

the parameters in Wilson’s equation to give overall predictions of activity coefficients for

mixtures. Results are shown both for pure simulation results and for simulations used in

combination with vapour pressure over pure component. For the systems methanol +

water, ethanol +water and acetonitrile + water reasonable agreement was found with

experimental data. For formic acid + water the comparison with experimentally based data

is ambiguous. For the system ethanolamine + water only partial agreement with

experimentally based data was obtained. Apparently the ethanolamine representation used

gives too low solvation energies. The present work suggests that the OPLS force field is

sufficiently accurate to give useful predictions of overall vapour-liquid equilibrium.

22

References

[1] D. M. Austgen, G. T. Rochelle, Ind. Eng. Chem. Res., 28 (1989) 1061.

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Elsevier, Amsterdam, 1977.

[3] B. Guillot, J. Mol. Liq., 101 (2002) 219.

[4] A. K. Sum, S. I. Sandler, Fluid Phase Equilibria, 158-160 (1999) 375.

[5] C. J. Cramer, Essentials of Computational Chemistry, John Wiley & Sons, 2002.

[6] J. Prausnitz, R. Lichtentaler, E. Gomes de Azevedo, Molecular Thermodynamics of Fluid-

Phase Equilibria, 3rd ed., Prentice Hall 1999.

[7] J. Fischer, Fluid Phase Equilibria, 10 (1983) 1.

[8] J. T. Slusher, J. Phys. Chem. B, 103 (1999) 6075.

[9] R. C. Rizzo, W. L. Jorgensen, J. Am. Chem. Soc., 121 (1999) 4827.

[10] J. T. Slusher, Fluid Phase Equilibria, 153 (1998) 45.

[11] W. L. Jorgensen, D. S. Maxwell, J. Tirado-Rives, J. Am. Chem. Soc., 118 (1996) 11225.

[12] A. Jakalian, D. B. Jack, C. I. Bayly, J. Comp. Chem., 23 (2002) 1623.

[13] P. Kollman, Chem. Rev., 93 (1993) 2395.

[14] G. F. Versteeg, L. A. J. van Dijck, W. P. M. van Swaaij, Chem. Eng. Commun., 144 (1996)

113.

[15] T. Lazaridis, M. E. Paulaitis, AIChE J., 39 (1993) 1051.

[16] A. Ben-Naim, Y. Marcus, J. Chem. Phys., 81 (1984) 2016.

[17] J. Hermans, A. Pathiaseril, A. Anderson, J. Am. Chem. Soc., 110 (1988) 5982.

[18] M. Mezei, J. Comp. Chem., 13 (1992) 651.

[19] J. M. Haile, Fluid Phase Equilibria, 26 (1986) 103.

[20] W. L. Jorgensen, C. Ravimohan, J. Chem. Phys., 83 (1985) 3050.

[21] D. A. Kofke, P. T. Cummings, Molecular Physics, 92 (1997) 973.

[22] W. L. Jorgensen, J. F. Blake, J. K. Buckner, Chemical Physics, 129 (1989) 193.

[23] W. L. Jorgensen, BOSS version 4.3, Yale University, New Haven, CT(1989a)

[24] W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W Impey, M. L. Klein, J. Chem.

Phys., 79 (1983) 926.

[25] W. L. Jorgensen, J. Phys Chem., 90 (1986) 1276.

[26] W. L. Jorgensen, J. M. Briggs, Molecular Physics, 63 (1988) 547.

[27] J. M. Briggs, T. B. Nguyen., W. L. Jorgensen, J. Phys. Chem., 95 (191) 3315.

[28] J. A. Riddick, W. B. Bunger, T. K. Sakano, Organic Solvents, 4th ed., Wiley, New York,

1986, Vol, II, 360.

[29] A. Nath, E. Bender, J. Chem. Eng. Data, 28 (1983) 370.

23

[30] R. M. DiGullio, R.-J. Lee S. T. Schaeffer, L. L. Brasher, A. S. Teja, J. Chem. Eng. Data, 37

(1992) 239.

[31] D. D. Wagman, W. H. Evans, V. B. Parker, R. H. Schumm, I. Halow, S. M. Bailey, K. L.

Churney, R. L. Nuttall, J. Phys. Chem. Ref. Data, Suppl. 2 (1982) 11.

[32] S.-B. Park, H. Lee, Korean J. Chem. Eng., 14 (1997) 146.

[33] J. T. Slusher, Fluid Phase Equilibria, 154 (1999) 181.

[34] K. Kojima, S. J. Zhang, T. Hiaki, Fluid Phase Equilibria, 131 (1997) 145.

[35] J. Gmehling, U. Onken, W. Arlt, Vapour-Liquid Equilibrium Data Collection, DECHMA,

Frankfurt, 1977 and onwards.

[36] P. S. Crozier, R. L. Rowley, Fluid Phase Equilibria, 193 (2002) 53.

25

Appendix

In the table data are shown for simulations with overlapping double-wide sampling.

In such a simulation each perturbation step is covered in both (insertion and deletion)

directions. From this total free energies are obtained for insertion and deletion, the average

of these two values would correspond to two double-wide sampling calculations. Some of

the data are the basis for the averaged results shown in table 5. Results are shown for singe

simulations.

Table 7 Free Energy of Insertion and Deletion (Results in kcal/mol)

Solvent T [°C] Insertion Deletion watera →methanol(1) waterb 25 2.49 +/-0.21 2.54 +/-0.25 watera →methanol(2) waterb 25 2.11 +/-0.19 2.11 +/-0.22 watera →methanol(3) waterb 25 2.12 +/-0.16 2.02 +/-0.15 watera →methanol(1) methanol 25 0.32 +/-0.15 0.23 +/-0.16 watera →methanol(2) methanol 25 0.70 +/-0.12 0.54 +/-0.10 watera →methanol(3) methanol 25 0.82 +/-0.15 0.77 +/-0.16 0→UC water(1) waterb 25 2.22 +/-0.16 2.08 +/-0.17 0→UC water(2) waterb 25 2.73 +/-0.24 2.72 +/-0.22 0→UC water(3) waterb 25 2.57 +/-0.17 2.43 +/-0.16 0→UC water(1) methanol 25 1.09 +/-0.09 1.11 +/-0.11 0→UC water(2) methanol 25 1.19 +/-0.10 1.17 +/-0.11 0→UC water(3) methanol 25 1.02 +/-0.10 0.89 +/-0.10 0→UC water(1) ethanol 25 1.20 +/-0.16 1.18 +/-0.15 0→UC water(2) ethanol 25 0.99 +/-0.08 0.86 +/-0.10 0→UC water(3) ethanol 25 0.66 +/-0.06 0.66 +/-0.08 0→UC water(1) acetonitrile 25 1.31 +/-0.12 1.18 +/-0.12 0→UC water(2) acetonitrile 25 1.43 +/-0.14 1.24 +/-0.12 0→UC water(3) acetonitrile 25 1.12 +/-0.11 1.07 +/-0.12 0→UC water(1) formic acid 25 2.04 +/-0.14 1.60 +/-0.12 0→UC water(2) formic acid 25 3.45 +/-0.18 2.91 +/-0.15 0→UC water(3) formic acid 25 3.30 +/-0.25 2.84 +/-0.18 0→UC water(1) ethanolamine 60 2.46 +/-0.12 2.10 +/-0.14 0→UC water(2) ethanolamine 60 3.38 +/-0.22 2.85 +/-0.21 0→UC water(3) ethanolamine 60 2.64 +/-0.18 2.61 +/-0.15 0→UC water(1) waterb 60 2.71 +/-0.13 2.59 +/-0.13 0→UC water(2) waterb 60 3.38 +/-0.22 2.85 +/-0.21 0→UC water(3) waterb 60 2.84 +/-0.15 2.79 +/-0.16 a TIP3P. b TIP4P.

Paper IV

Comparison of Quantum Mechanical and Experimental Gas Phase

Basicities of Amines


2005

J. Phys. Chem. A 109, 1603-1607.

Comparison of Quantum Mechanical and Experimental Gas-Phase Basicities of Amines andAlcohols

Eirik F. da Silva*Department of Chemical Engineering, Norwegian UniVersity of Science and Technology,N-7491 Trondheim, Norway

ReceiVed: October 19, 2004; In Final Form: NoVember 25, 2004

A comparison was made between the experimental and B3LYP relative gas-phase basicities and proton affinitiesof a series of 9 amine, 3 alcohol, and 3 alkanolamine molecules. While agreement is good for most of thespecies studied, it is poor for the alkanolamines and 1,2-ethanediol. A series of calculations were undertakenat the B3LYP and MP2 levels using various basis sets to see if the uncertainties in the calculations canaccount for the discrepencies. The results suggest that this is unlikely and that the theoretical values arelikely to be reasonably accurate. Calculations are also presented for the dimer formation energies ofalkanolamine molecules, diamine molecules, and 1,2-ethanediol. These calculations suggest that all of thesespecies can form proton-bound dimers. The alkanolamines and 1,2-ethanediol also appear to have relativelyhigh formation energies for neutral dimers.

Introduction

Gas-phase basicities and proton affinities have been thesubject of substantial experimental1 and theoretical2-4 work.These properties offer a useful benchmark for quantum me-chanical calculations, and high-level calculations have beensuccessful in reproducing experimental data. Calculations havealso been used to interpret the experimental data.5 In additionto the inherent interest in gas-phase basicities, they are alsoimportant when studying properties in solution. If gas-phasebasicity, solution-phase basicity, and the free energy of solvationof the neutral solute are known, then the free energies ofsolvation of the ionic form can be derived. This quantity isotherwise difficult to estimate.6 Accurate quantum mechanicalcalculation of the gas-phase basicity is also required forpredicting basicities in solution.

Amines are organic bases of importance in many contexts.Our interest lies in the application of amines for the removal ofCO2 from exhaust gases. Alkanolamines are of particular interestin this context.7 In a previous study,8 poor agreement was foundbetween the experimental and calculated gas-phase basicitiesfor some alkanolamine molecules; the present work is intendedto further study the accuracy of the calculated and experimentalvalues.

Methods

Calculations for the gas-phase basicity have been carried outat the B3LYP and MP2 levels. The propensity to formintramolecular hydrogen bonds8 is an important feature of thealkanolamines. The accurate calculation of the energies ofspecies containing hydrogen bonds is not trivial; one of thedifficulties is the basis-set superpositon error (BSSE). Whilethe counterpoise correction can be applied for bonding betweendifferent molecules, it cannot easily be applied to intramolecularbonds.9,10The effect of BSSE is, however, expected to decreasewith the increasing size of the basis set and with the inclusion

of diffuse basis functions.10 In this work, relatively large basissets will be used to limit the effect of BSSE and the resultsfrom different basis sets will be compared.

Experimental data are at 298 K and zero-point energies, andtherefore, thermal corrections should be added to the calculatedvalues. They are calculated at the HF/6-31G(d) level.

Calculations are also carried out to determine the likelihoodof the alkanolamines forming dimers in the gas phase. Theyare carried out at the HF/6-311++G(d,p) level. They areintended to give a quantitative picture of dimer formation. Theomission of electron correlation in the HF calculations meansthat the energies calculated with this method are less accuratethan the gas-basicity calculations. For the ethanolamine, a dimercalculation was also carried out at the MP2/6-311++G(2d,2p)//HF/6-311++G(2d,2p) level.

All calculations were carried out in Gaussian 98.11


Figure 1 shows the conformers that were identified as themost stable at the B3LYP/6-311++G(d,p) level for the alkanol-amines, diamines, 1,2-ethanediol, and their protonated forms.For the neutral forms of the three alkanolamines, the conformersare characterized by hydrogen bonding between the alcohol andamine functionalities. The H(O)-N bond seems to be the mostenergetically favored. For the protonated forms, only H(N)-Ohydrogen bonds are found. The conformers of the diamines and1,2-ethanediol are also characterized by intramolecular hydrogenbonds. The lengths of these bonds are given in Table 1.

The selected conformers are drawn from a conformer searchat the HF/3-21G(d) level.8 Some of the most stable conformersidentified at that level have also been studied at the B3LYP/6-311++G(d,p) level, and it seems likely that these are, in fact,the most stable conformers at this level of theory. It should,however, be noted that a full study of the conformers at theB3LYP/6-311++G(d,p) level has not been undertaken. Diethanol-amine has a large number of potential conformers, and therefore,for the neutral form of this molecule, there is less confidence* E-mail: [email protected].

1603J. Phys. Chem. A2005,109,1603-1607

10.1021/jp0452251 CCC: $30.25 © 2005 American Chemical SocietyPublished on Web 02/04/2005

in the determination of the most stable conformer. The conform-ers for neutral ethanolamine are consistent with those found,both theoretically and experimentally, by other authors (Tuber-gen et al.13 and Vorobyov et al.12 and the references therein).The conformer identified for 3-amino-1-propanol is in agreementwith theoretical work by Kelterer and Ramak.14

In Table 2 the relative basicity of these amines together withother amine and alcohol molecules calculated at the B3LYP/6-311++G(d,p) level is shown. Data are given relative toammonia. For piperazine, calculations were done on the chairconformer. The conformers of ethanol are shown in theSupporting Information, and the other molecules have only oneconformer form.

The data in Table 2 show good agreement for most of themolecules. For the alkanolamines, there is, however, a significantdisagreement between the experimental data and the calculatedresults. The experimental and theoretical gas-phase basicitiesdiffer by 2.4 kcal/mol for ethanolamine and by 4.1 kcal/mol

for diethanolamine. The relative basicity for these two alkanol-amines differs by 6.5 kcal/mol. A similar trend can be seen forthe proton affinities of these molecules. For 3-amino-1-propanol,the final alkanolamine in this study, there is also a considerabledifference between the experimental and theoretical protonaffinities. However, the gas-phase basicities, in this case, are

Figure 1. Stable conformers of alkanolamines, diamines, and 1,2-ethanediol. Dashed lines indicate hydrogen bonds.

TABLE 1: Hydrogen Bond Lengths

molecule bond length (Å)a

ethanolamine H(O)-N 2.273ethanolamine(H+) H1(N)-O 2.034

diethanolamine H(O1)-N 2.296H(N)-O2 2.433

diethanolamine(H+) H1(N)-O1 2.084H2(N)-O2 2.084

3-amino-1-propanol N-H(O) 2.0333-amino-1-propanol(H+) H1(N)-O 1.7601,2-ethylenediamine H1(N2)-N1 2.5081,2-ethylenediamine(H+) H1(N1)-N2 1.9061,3-propanediamine H1(N1)-N2 2.3051,3-propanediamine(H+) H1(N1)-N2 1.6841,2-ethanediol H(O2)-O1 2.3031,2-ethanediol(H+) H1(O1)-O2 1.642

a B3LYP/6-311++G(d,p) geometry.

TABLE 2: Relative Gas-Phase Basicities and ProtonAffinities a

gas basicity proton affinity

molecule theoreticalb experimentalc theoreticalb experimentalc

ammonia 0.0 0.0 0.0 0.0ethanolamine 16.2 18.6d 16.2 18.3d

diethanolamine 28.2 24.1e 28.4 23.8e

3-amino-1-propanol

23.4 23.5d 23.6 26.0d

1,2-ethylene-diamine

22.8 22.3d 23.2 23.4d

1,3-propane-diamine

29.9 28.9d 30.6 31.9d

methylamine 10.2 10.9 11.0 10.9ethylamine 14.3 14.1 14.4 14.0dimethylamine 17.9 18.5 18.0 18.1trimethylamine 22.2 23.7 22.3 22.8piperidine 24.2 24.4 24.3 24.0piperazine 23.3 22.9 23.5 21.5morpholine 17.0 17.3 17.2 16.9pyrrolidine 23.6 23.0 23.7 22.6methanol -23.1 -22.6f -23.2 -23.7f

ethanol -17.0 -17.4 -17.3 -18.51,2-ethanediol -13.1 -10.9g -12.6 -9.0g

a Results in kcal/mol.b B3LYP/6-311++G(d,p) energy with thermalcorrection and zero-point energy calculated at the HF/6-31G(d) level.c Data from Hunter and Lias,1 also available at webook.nist.gov.15

Original papers indicated for alkanolamines, diamines, and 1,2-ethanediol.d Data from Meot-Ner et al.16 e Data from Sunner et al.17

f Value is theoretical.g Data from Chen and Stone.18

1604 J. Phys. Chem. A, Vol. 109, No. 8, 2005 da Silva

in better agreement. For 1,2-ethanediol, significant differencescan also be seen between the experimental and theoreticalvalues.

As the largest deviations occur for molecules displayingintramoleculer hydrogen bonds, this would suggest that theremight be errors in the calculation of strengths of these bonds.

To explore the method and basis-set dependency of theresults, the basicities of the alkanolamines, 1,2-ethanediol, andammonia were calculated with different basis sets and usingboth the MP2 and B3LYP level of theory. The results are shownin Table 3.

From the values in Table 3, one can see that there is somevariation in the results with variation in the level of theory andsize of the basis set. However, the B3LYP/6-311++G(d,p)results are in fairly good agreement with MP2 calculations withlarger basis sets. More importantly, the relative basicity of thealkanolamines and 1,2-ethanediol remains almost unchanged.Therefore, it seems unlikely that there is any level of quantummechanical calculation that will be in agreement with theexperimental data. The MP2/Aug-cc-pVTZ//B3LYP/6-311++G-(d,p) calculations use the largest basis set, and these results areprobably the most accurate.

Gas-Phase Dimer Formation.Quantum mechanical calcula-tions were performed to investigate the likelihood of thealkanolamines, diamines, and 1,2-ethanediol forming dimers.Calculations are carried out both for proton-bound dimers andneutral dimers.

The initial geometries were based on conformers that wouldgive the largest number of hydrogen bonds, in particular theH(O)-N-type bonds that appear to be the most energeticallyfavored for alkanolamines. The determination of conformers wasnot based on any rigorous exploration of the potential dimersof these molecules; for diethanolamine, in particular, there area large number of potential dimers. The ethanolamine dimer isthe same as that reported to be the most stable in calculationsby Vorobyov et al.12 The 1,2-ethanediol dimer geometry is fromwork by Bako et al.19

Calculations are carried out at the HF/6-311++G(d,p) level,and only the binding energy of the dimer is calculated. This isthe energy difference between the dimers and the monomerscalculated at the same level. The dimers are shown in Figure 2and Figure 3, and the hydrogen bond lengths are given in Table4. The dimer formation energy is given in Table 5.

The geometries and the data in Table 5 suggest that all ofthese molecules form stable proton-bound dimers. They, ap-parently, can act as bidentate ligands to a protonated molecule.Proton-bound dimers have also been observed experimentallyfor diethanolamine17 and 1,2-ethanediol.18 In the experimentalwork on 1,2-ethanediol,18 it was also proposed that one moleculeacts as a bidentate ligand. In the same paper, it was observed

that 1,2-ethanediol had a stronger propensity to form proton-bound dimers than diols with longer carbon chains. A similartrend can be seen in Table 5; the results suggest that 1,3-propanediamine forms a weaker proton-bound dimer than 1,2-ethanediamine. Apparently, 3-amino-1-propanol also forms aless stable proton-bound dimer than ethanolamine. It appearsthat molecules with longer carbon chains can form less strainedintramolecular hydrogen bonds, and therefore, the additionalstability gained by bonding to a second molecule is less.

At the MP2/6-311++G(2d,2p)//HF/6-311++G(2d,2p) level,the dimer binding energy of ethanolamine is calculated to be-11.00 kcal/mol. As a comparison, the dimer formation energyof water has been calculated to be-5.18 kcal/mol using a

Figure 2. Dimers optimized at the HF/6-311++G(d,p) level. Dashedlines indicate hydrogen bonds.

TABLE 3: Gas-Phase Basicities and Proton Affinities Relative to Ammoniaa

ethanolamine diethanolamine 3-amino-1-propanol 1,2-ethanediol

B3LYP/6-311++G(d,p)//b

B3LYP/6-311++G(d,p)16.2 16.2 28.2 28.4 23.4 23.6 -13.1 -12.6

B3LYP/6-311++G(3df,2p)//B3LYP/6-311++G(3df,2p)

16.8 16.8 28.7 28.9 23.8 24.0 -12.3 -11.8

MP2/6-311++G(d,p)//B3LYP/6-311++G(d,p)

14.8 14.8 26.7 26.9 21.9 22.0 -14.6 -14.1

MP2/6-311++G(2d,2p)//B3LYP/6-311++G(d,p)

15.9 15.9 27.7 27.9 22.9 23.0 -13.9 -13.4

MP2/Aug-cc-pVTZ//B3LYP/6-311++G(d,p)

16.1 16.1 28.0 28.2 23.0 23.2 -12.9 -12.5

experimental 18.6 18.3 24.1 23.8 23.5 26.0 -10.9 -9.0

a Results in kcal/mol.b Same data as in Table 1.

Gas-Phase Basicities of Amines and Alcohols J. Phys. Chem. A, Vol. 109, No. 8, 20051605

similar level of theory.20 This would suggest that the alkanol-amines and 1,2-ethanediol have relatively stable dimers. Thediamines appear to form weaker dimers.

Experimental Values

The experimental basicity and proton affinity data forethanolamine, 3-amino-1-propanol, 1,2-ethanediamine, and 1,3-propanediamine are from pulsed high-pressure mass spectrom-etry work by Meot-Ner et al.16 The diethanolamine data arefrom fast atom bombardment mass spectroscopy work by Sunneret al.,17 and the 1,2-ethanediol data are from pulsed electronbeam high-pressure mass spectrometry experiments.18 It wasnoted in the work on 1,2-ethanediol that the presence of proton-bound dimers created problems in determining the protonaffinity and basicity of this molecule. The present work suggeststhat all of the alkanolamines have a comparable propensity toform dimers. While the basicity of these molecules wasdetermined with different experiments, it seems that dimer

effects may have affected the experimental results for all ofthese molecules. The relatively low volatility of these alkanol-amines may also make the experimental determination of theirgas-phase basicities more difficult. Therefore, it appears thatthere is considerable uncertainty regarding the experimental datafor alkanolamines and 1,2-ethanediol.

Conclusion

Gas-phase basicities from quantum mechanical calculationsare generally shown, in this article and work of other authors,to be in good agreement with experimental data. However, pooragreement was observed for a series of alkanolamines and 1,2-ethanediol. Calculations using the MP2 and B3LYP methodswith different basis sets revealed some method and basis-setdependency in the results, but these uncertainties cannot accountfor the differences between the calculated results and theexperimental data. Therefore, the current MP2/Aug-cc-pVTZresults are probably the most reliable estimate of the basicityof these molecules.

Calculations on dimer forms suggest that the alkanolamines,diamines, and 1,2-ethanediol form stable proton-bound dimers.Less stable neutral dimers can also be formed. Dimer effectsand low volatility suggest high uncertainty in the experimentalbasicities for the alkanolamines and 1,2-ethanediol.

Acknowledgment. This work has received support from TheResearch Council of Norway (Program for Supercomputing)through a grant of computing time.

Supporting Information Available: Underlying values fordata in Table 2 and Table 3, geometric parameters and Cartesiancoordinates of the alkanolamines, and illustrations of otherconformers of diethanolamine. This material is available freeof charge via the Internet at http://pubs.acs.org.

References and Notes

(1) Hunter, E. P. L.; Lias, S. G.J. Phys. Chem. Ref. Data1998, 27,413.

TABLE 4: Dimer Hydrogen Bond Lengths

dimer bond length (Å) dimer(H+)a bond length (Å)

ethanolamine N1-H(O2) 2.119 ethanolamine O1-H1(N1) 2.249H(O1)-N2 2.118 H2(N1)-N2 1.913H1(N1)-O1 2.628 H3(N1)-O2 2.092H2(N2)-O2 2.627 diethanolamine H1(N1)-O4 2.321

diethanolamine H(N1)-O4 2.361 H2(N1)-N2 2.112N1-H(O3) 2.017 H2(N1)-O3 2.319H(O1)-O3 2.094 O1-H(O3) 2.505H(O2)-N2 2.100 H(O2)-O4 2.109H(O4)-O2 2.065 3-amino-1-propanol O1-H3(N1) 1.989

3-amino-1-propanol N1-H(O2) 2.080 H1(N1)-N2 1.965H(O1)-N2 2.069 H2(N1)-O2 1.993H1(N1)-O1 2.252 1,2-ethanediamine N1-H1(N2) 2.285H2(N2)-O2 2.295 H2(N2)-N3 1.999

1,2-ethanediamine N1-H3(N3) 2.560 H3(N2)-N4 2.041H1(N1)-N2 2.625 1,3-propanediamine N1-H1(N2) 2.069H2(N2)-N4 2.544 H2(N2)-N3 1.967H4(N4)-N3 2.776 H3(N2)-N4 2.003

1,3-propanediamine N1-H3(N3) 2.405 1,2-ethanediamine O1-H1(O2) 2.286H1(N1)-N2 2.399 H1(O2)-O3 1.789H2(N2)-N4 2.447 H2(O3)-O4 1.632H4(N4)-N3 2.336

1,2-ethanediamine H(O1)-O4 2.051O1-H(O3) 2.155H(O1)-O2 2.699O2-H(O4) 2.160H(O3)-O4 2.748

a Proton-bound dimer.

Figure 3. 1,2-Ethanediol dimers optimized at the HF/6-311++G(d,p)level. Dashed lines indicate hydrogen bonds.

TABLE 5: Dimer Binding Energiesa

neutral dimer proton-bound dimer

ethanolamine -5.9 -25.2diethanolamine -5.3 -14.83-amino-1-propanol -4.7 -23.21,2-ethanediamine -2.3 -26.21,3-propanediamine -2.9 -23.21,2-ethanediol -5.4 -32.2

a Results in kcal/mol.

1606 J. Phys. Chem. A, Vol. 109, No. 8, 2005 da Silva

(2) Smith, B. J.; Radom, L.J. Am. Chem. Soc.1993, 115, 4885.(3) East, A. L. L.; Smith, B. J.; Radom, L.J. Am. Chem. Soc.1997,

119, 9014.(4) Pokon, E. K.; Liptak, M. D.; Feldgus, S.; Shields, G. C.J. Phys.

Chem. A2001, 105, 10483.(5) Pople, J. A.; Curtiss, L. A.J. Phys. Chem.1987, 91, 155.(6) Pearson, R. G.J. Am. Chem. Soc.1986, 108, 6109.(7) Versteeg, G. F.; van Dijck, L. A. J.; van Swaaij, W. P. M.Chem.

Eng. Commun.1996, 144, 113.(8) da Silva, E. F.; Svendsen, H. F.Ind. Eng. Chem. Res.2003, 42,

4414.(9) Reiling, S.; Brickmann, J.; Schlenkrich, M.; Bopp, P. A.J. Comput.

Chem.1996, 17, 133.(10) Lii, J. H.; Ma, B.; Allinger, N. L.J. Comput. Chem.1999, 20,

1593.(11) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,

M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.;Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A.D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi,M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.;Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick,D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.;Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz,P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-

Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P.M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.;Head-Gordon, M.; Replogle, E. S.; Pople, J. A.Gaussian 98, revision A.9;Gaussian, Inc.: Pittsburgh, PA, 1998.

(12) Vorobyov, I.; Yappert, M. C.; DuPre, D. B.J. Phys. Chem. A2002,106, 668.

(13) Tubergen, M. J.; Torok, C. R.; Lavrich, R. J.J. Chem. Phys.2003,119, 8397.

(14) Kelterer, A. M.; Ramak, M.THEOCHEM1991, 232, 189.(15) NIST Chemistry WebBook, NIST Standard Reference Database

Number 69; Linstrom, P. J., Mallard, W. G., Eds.; National Institute ofStandards and Technology: Gaithersburg, MD, http://webbook.nist.gov,March 2003.

(16) Meot-Ner(Mautner), M.; Hunter, E. P.; Hamlet, P.; Field, F. H.Proceedings of the 28th Annual Conference on Mass Spectrometry andAllied Topics, May 25-30, 1980, 233.

(17) Sunner, J. A.; Kulatunga, R.; Kebarle, P.Anal. Chem. 1986, 58,1312.

(18) Chen, Q. F.; Stone, J. A.J. Phys. Chem.1995, 99, 1442.(19) Bako, I.; Grosz, T.; Palinkas, G.; Bellissent-Funel, M. C.J. Chem.

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J. Chem. Phys.1986, 84, 2279.

Gas-Phase Basicities of Amines and Alcohols J. Phys. Chem. A, Vol. 109, No. 8, 20051607

Paper V

Study of the Carbamate Stability of Amines Using ab Initio Methods

and Free-Energy Perturbations


2005

Accepted in Ind. Eng. Chem. Res.

1

Study of the Carbamate Stability of Amines Using ab Initio Methods and Free Energy

Perturbations


Department of Chemical Engineering, Norwegian University of Science and Technology, N-

7491 Trondheim, Norway

Abstract The relative carbamate stability of a series of amines used in CO2 absorption

processes have been studied with different solvation models and gas phase energies

calculated with the B3LYP density functional method. The solvation energies were

calculated with Monte Carlo free energy perturbations and continuum models.

Comparison between calculated energies and experimental NMR and kinetic data

shows reasonable agreement. The trends in carbamate stability can apparently not be

explained in terms of any single molecular characteristic.

Keywords: ab initio calculations, solvation energy, carbamate, amines

Introduction

As a measure for preventing global warming there is a steadily increasing interest in

methods for removing carbon dioxide from exhaust gases. Absorption with

alkanolamines in mixtures with promoters has traditionally been used for the removal

of carbon dioxide from natural gas and refinery gas and the same technology is an

option for the treatment of exhaust gases. For high-pressure applications, N-

methyldiethanolamine (MDEA) based systems have been used successfully for many

years. For exhaust gases, the most common amine has been ethanolamine (MEA).

The high energy demand for regeneration and relatively high degradation rates for this

amine are however unfavorable for large fossil fuel power plants. During the last

years, new systems like the PSR 1-31 and Mitsubishi KS 1-32 have been developed

and promise improved performance compared to the conventional MEA. At the same

time it should also be noted that improvements in performance have been reported for

MEA.3

*Tel.: +47 73594125, Fax.: +47 73594080 e-mail: [email protected]

2

In the chemical absorption of CO2 in aqueous amine systems the CO2 is bound

as either bicarbonate or carbamate.4 If the equilibrium constants governing the

formation of these species is known or can be predicted the overall performance of a

solvent can to a large extent be predicted.

For the formation of carbamate there is the following reaction:4

2 2 2 2CO R NH B R NCO BH− ++ + + (1)

where B indicates a base molecule and 2R NH is any primary or secondary amine

molecule. For bicarbonate formation there is the following reaction:

2 2 3 32CO H O HCO H O− ++ + (2)

While no amine molecule appears in equation 2, the extent to which this reaction will

proceed is in fact governed by the strength of the amine as a base:

2 3BH H O B H O+ ++ + (3)

The present work will deal with the modeling of carbamate stability. A number of

models are available for the base strength. If the carbamate stability can be modeled

in similar fashion the performance of different amine solvents can be predicted.

For the carbamate formation an alternative equilibrium can be set up that does

not involve the base molecule:

3 2 2 2 2HCO R NH R NCO H O− −+ + (4)

If the mole fraction based activity of water is assumed to be 1 and if H3O+ is written

as H+ the following equilibrium constant is obtained for equation 3:

B Ha

BH

a aK

a+

+

= (5)

Similarly, the following equilibrium constant is obtained for carbamate formation

(equation 4):

2 2

2 3

R NCOc

R NH HCO

aK

a a−

−

= (6)

The carbamate equilibrium constant from equation 1 (Kc2) can be expressed as a

product of the equilibrium constants of equation 2,3 and 4:

22

cc

a

K KK

K= (7)

3

where K2 is the equilibrium constant of equation 2. The interactions between an amine

species and CO2 in solution can therefore be described by two equilibrium constants:

Ka and Kc. While there are also other reactions that take place4 these are independent

of the amine present in the system.

From knowledge of these two equilibrium constants the amount of CO2

captured and energy consumption of the process can be estimated. As will be shown

in the present work knowledge of the equilibrium constants can also be used to predict

the reaction rates. Models that can predict these equilibrium constants are therefore

likely to be very useful in efforts to improve the absorption process in terms of energy

consumption and overall efficiency.

The equilibrium constant Ka is usually presented in the form of the pKa

( aa KpK log−= ). Well-established methods exist for the experimental determination

of the pKa and the determination can be done with a fairly high degree of accuracy.

Substantial data on the pKa for alkanolamines and other organic bases are also

available in the literature.5

For the carbamate stability (Kc) the situation is however very different. The

carbamate species only appear in significant concentrations in systems where

several other species are also present in significant concentrations. The carbamate

species is also in equilibrium with solvated CO2. Because the solvated CO2 is only

present in small quantities its concentration can be difficult to establish. The only

direct experimental route to obtaining this carbamate equilibrium constant appears to

be NMR-techniques. The NMR-experiments are however very demanding and data

has only been published for a small number of molecules.6-8 The uncertainty in the

results are also much larger than for pKa measurement. To compare NMR results

obtained under different conditions, estimates for activity coefficients are also

required. As already noted these systems have many components, several of them

ionic, making the estimation of activity coefficients challenging. In summary it can be

observed that the experimental determination of carbamate stability is a more

demanding task than the determination of the pKa and the quality of the results that

can be obtained is inferior.

Although the experimental tasks of determining pKa and carbamate stability

are very different, the modeling tasks are very similar. In both cases one is attempting

to calculate the free energy difference in aqueous solution between an ionic species

4

and a closely related neutral species. The present authors have used quantum

mechanical calculations and free energy perturbations to estimate trends in the pKa. 9

In the present work we will use essentially the same models to predict trends in

carbamate stability. While some theoretical work has been published on carbamate

species10-13 the present work is to our knowledge the first modeling work on relative

carbamate stability.

5

Methods

For equation 4 the following thermodynamic cycle can be set up:

On the basis of the thermodynamic cycle the reaction energy in solution csG∆ can be

divided into two contributions.

cs cg sG G G∆ =∆ +∆∆ (8)

where cgG∆ is:

2 2 2 2 3( ) ( ) ( ) ( )cg g g g g gG G R NCO G H O G R NH G HCO− −∆ = + − − (9)

and

2 2 2 2 3( ) ( ) ( ) ( )s s s s g sG G R NCO G H O G R NH G HCO− −∆∆ =∆ +∆ −∆ −∆ (10)

Molecular mechanics (MMFF) was used to generate an initial set of conformers. All

conformers were then optimized at HF/6-31G(d) level. Separate conformer searches

were done for the amines and the carbamate forms. The conformers found to be the

most stable in the gas phase were also assumed to be the most stable in solution and

all calculations in this work were performed on the same set of conformers. Gas phase

conformer search calculations were performed with PC Spartan Pro version 1.0.7.16

Calculation of gas phase reaction energies were carried out at B3LYP/6-

311++G(d,p) and MP2/6-31G(d) levels. Our previous work with pKa9 suggest that the

B3LYP/6-311++G(d,p) method produces results in better agreement with

experimental data. It has also been noted in the literature14 that this level of theory

reproduces experimental properties quite well. The presence of intramolecular

hydrogen bonds in the amines identified in our previous work means that they can not

reliably be modeled with the small basis-set in the MP2 calculation. B3LYP and MP2

calculations were performed with their implementations in Gaussian 98.15

6

Thermal corrections and zero-point energies have been calculated at HF/3-

21G(d) level. While this method is not very accurate it should be noted that these

contributions to the gas phase energy are relatively small. These calculations were

also performed with Gaussian 9815 implementations.

In the calculation of solvation energy three different models are used. One is a

free energy perturbation scheme while the two others are widely used continuum

models.

The free energy perturbation scheme is similar to what we have previously

used in the modeling of pKa. A approach that was modeled on work by Wiberg et

al.17 In the present work free energy perturbations have been performed as two

separate series, one between the neutral form of the amines, the second between the

carbamate forms of the molecules. All perturbations were therefore between species

of the same charge, this is the same form as used by Wiberg et al.17 and more accurate

than the form used in our previous work on pKa.

In the present work simulations were carried out on rigid gas phase B3LYP/6-

311++G(d,p) geometries. The intermolecular interactions between two molecules a

and b were evaluated using Coulomb and Lennard-Jones terms: 12 62on a on b

4i j ij ijab ij

i j ij ij ij

q q eE

r r r

⎧ ⎫⎡ ⎤⎪ ⎪⎛ ⎞ ⎛ ⎞σ σ⎪ ⎪⎢ ⎥⎟ ⎟⎜ ⎜⎪ ⎪⎟ ⎟⎜ ⎜∆ = + ε −⎨ ⎬⎢ ⎥⎟ ⎟⎜ ⎜⎟ ⎟⎪ ⎪⎟ ⎟⎜ ⎜⎢ ⎥⎝ ⎠ ⎝ ⎠⎪ ⎪⎣ ⎦⎪ ⎪⎩ ⎭∑∑ (11)

The Lennard-Jones σ and ε for alcohol, alkane and amine groups were from the

OPLS-All atom force field.18, 19 For CO2 the EPM220 parameters were chosen: σ (C)=

2.757 Å, σ (O)= 3.033 Å, ε (C)= 0.066 [kcal/mol] and ε (O)= 0.170 [kcal/mol].

Partial atomic charges were determined by using solvent phase (SM 5.42R21 ) CM222

charges implemented in the Gamesol23 program. These charges were calculated on

HF/6-31G(d) geometries. It should be noted that atomic charges are not uniquely

defined and a number of schemes for their calculation are available.24, 25 The

calculation of charges is one of the main uncertainties when using simulations to

determine free energies.

The perturbations were carried out between the amines closest in size. To

allow smooth transitions no more than one non-hydrogen atom was deleted in a single

simulation. Series of up to three simulations were therefore used to transform larger

solutes to smaller ones.

7

These calculations were performed with BOSS version 4.126 using procedures

developed by Jorgensen et al.27 A single solute molecule was placed in a periodic

cube with 267 TIP4P water molecules at 25°C and 1 atmosphere in the NPT

ensemble. A number of water molecules corresponding to the number (n) of non-

hydrogen atoms in the amine molecule were removed, giving 267 - n water

molecules. The perturbations were carried out over ten windows of double-wide

sampling giving 20 free energy increments that are summed up to give the total

change in free energy of solvation. Each window had 500000 steps for equilibration

and another 500000 for sampling. The present free energy perturbations have a

statistical uncertainty of around ±1 kcal/mol.

This combination of B3LYP gas phase energies and solvation energies from

free energy perturbations is essentially the same as the one presented in our work on

pKa. It should be emphasized that the model involves no form of adjustment to obtain

agreement with experimental data.

The first of the two continuum models used to calculate the solvation energies

is the IEFPCM model.28 Calculations were carried out with 60 tesserae per atomic

sphere and other default settings in Gaussian 98. Calculations were performed as

single point calculations on gas phase MP2/6-31G(d) geometries (IEFPCM/ MP2/6-

31G(d)// MP2/6-31G(d)). This model was also utilized in our work on pKa modeling.9

The other continuum model is the SM 5.42R21 model, in this case single-point

calculations on the HF/6-31G(d) level were carried out (SM 5.42R/ HF/6-31G(d)//

HF/6-31G(d)). The IEFPCM and SM 5.42R calculations were carried out in Gaussian

9815 and Gamesol23 respectively. The IEFPCM model has also been used to determine

the solvation energies of 3HCO− , 2CO and 2H O .

Results

In Table 1 are listed the molecules studied. In the table it is indicated weather amines

are primary or secondary. Tertiary amines do not form carbamate species and are

therefore not included in the present study. It is also indicated in the table if the

molecule has any substituent-groups on the carbon(s) adjacent to the amine. This

particular characteristic has been used to rationalize carbamate-stability and we will

look at this characteristic in the discussion. Experimental pKa’s are also given in

Table 1, they will be used to convert data from Kc to Kc2 and they are also relevant to

8

the discussion of explanations given for carbamate stability. Finally we have given

some references to the amines in the CO2 absorption literature and included references

to NMR-results when these are available.

Table 1. Experimental pKa data

No. Compd Name Typea Exptl pKa

(25 C)

Kinetics/NMR

references

1 Ethanolamine MEA p 9.51b 4, 31, 7,e 8e

2 3-Amino-1-Propanol MPA p 9.96 b 4

3 2-(2-Aminoethoxy)Ethanol DGA p 9.46c 4

4 Ethylendiamine EDA p 9.92 b, d 31

5 1-Amino-2-Propanol MIPA p 9.46b 4

6 N-(2-Hydroxyethyl)Ethylenediamine AEEA p, s 9.82 b, d

7 2-Amino-2-Methylpropanol AMP p* 9.7 b 31, 7e

8 2-Amino-2-Methyl-1,3-Propanediol AMPD p* 8.8 b 31, 6e, 7e

9 2-Amino-2-Ethyl-1,3-Propanediol AEPD p* 8.8 b 7e

10 Diethanolamine DEA s 8.95 b 4, 6e

11 Diisopropanolamine DIPA s 8.89 b 4

12 2-(Methylamino)Ethanol MMEA s 9.77 b 4, 8e

13 Morpholine s, c 8.49 b 31

14 Piperazine s, c 9.83 b, d 30

15 Piperidine s, c 11.12 b 31

a: p: primary amine, s: secondary amine, c: cyclical amine, *: subsituent group on atom neighboring

the amine functionality. b: Data from Perrin.5 .c: Data from Littel et al.29 (extrapolated from data at

20C). d: The first protonation constant. e: Reference to NMR data.

The compounds chosen for this study covers a fairly large part of the amines

commonly used in CO2 absorption. Almost all amines covered in a review by

Versteeg et al.4 are included. In addition we have attempted to cover amines in the

literature that seem promising or that display particularly interesting behavior.

The geometry of the most stable conformers found for the carbamate forms of

MEA, 2-amino-2-methylpropanol (AMP) and piperidine are shown in Figure 1. The

most stable carbamate conformers of the other amine molecules are shown in Figure

2. For N-(2-hydroxyethyl)ethylenediamine (AEEA) conformers are shown for

bonding to both amine functionalities. The conformers of the amines themselves are

9

shown in the supporting information, most of these conformers were also presented in

our previous work on pKa.9

Figure 1. Carbamate forms of ethanolamine (MEA), 2-amino-2-methylpropanol (AMP) and piperidine.

Stippled lines indicate hydrogen bonds.

Figure 2. Carbamate forms of amines. Stippled lines indicate hydrogen bonds.

10

To look at the most likely form of intramolecular hydrogen bonding for carbamate

species the potential conformer forms of 3-amino-1-propanol (MPA) have been

studied in greater detail. There can be conformers with hydrogen bonding between

alcohol-group and carbamate oxygens, between alcohol-group and nitrogen atom and

finally there are conformers without any hydrogen bonds. In Figure 3 the conformers

identified as the most stable of each type in the gas phase are shown and energies for

these conformers are shown in the tables. In Table 4 reaction energies are shown for

these different carbamate conformers of MPA (all calculated relative to the same

conformer of MPA itself). Results with different solvation models all suggest that the

carbamate conformer found to be most stable in gas phase (Table 2) remains the most

stable in solution.

Figure 3. Conformers of 3-amino-1-propanol (MPA) displaying different intramolecular hydrogen bonds.

In Figure 2 it can be seen that the carbamate molecules tend to form intramolecular

hydrogen bonds between alcohol-group hydrogen atoms and CO2-group oxygens. For

the amines themselves we found intramolecular hydrogen bonding between the

amine-groups and the alcohol-groups.

In the present work we assumed that these conformers with intramolecular

hydrogen bonds also dominate in solution. It is however clear that in solution this

11

intramolecular hydrogen bonding competes with hydrogen bonding to the solution

water-molecules.

Modeling32 and experimental work33, 34 for ethanolamine suggest that in the

liquid form or aqueous solution the conformers change compared to the gas phase, the

geometry changes to allow greater formation of intermolecular hydrogen bonds. The

results do however also suggest that intramolecular hydrogen bonding remains. Work

on 2-(methylamino)ethanol12 (MMEA) suggest that this molecule also has some

degree of intramolecular hydrogen bonding in solution. The same work also finds

intramolecular hydrogen bonds in solution for the carbamate species. This is

consistent with the present model results for MPA. In summary this would suggest

some degree of conformer change for neutral amines in aqueous solution compared to

the gas phase, less so for the carbamate species. Using conformers identified as the

most stable in the gas phase is therefore an approximation, but since the conformers

are likely to be close in energy this should not have a too large effect on calculated

energies.

In Table 2 are shown the results for gas phase reaction energies ( cgG∆ )

calculated at B3LYP and MP2 level. Considerable differences can be seen MP2 and

B3LYP gas phase results. The differences are however comparable to what we found

using the same levels of theory in our work on base-strength.9 As noted in the

Methods Section we believe the B3LYP results to be the more accurate.

12

Table 2. Calculated Gas Phase Reaction Energies

No. Name Gcg

MP2a B3LYPb

1 MEA -7.79 -6.26

2 MPA(1)c -8.50 -5.83

MPA(2)c -2.98 -0.90

MPA(3)c 6.19 3.31

3 DGA -5.60 -3.55

4 EDA -2.60 0.28

5 MIPA -7.99 -5.11

6 AEEA(p) -8.12 -4.56

AEEA(s) -13.41 -6.87

7 AMP -4.09 -1.13

8 AMPD -12.18 -8.39

9 AEPD -13.13 -8.54

10 DEA -19.66 -12.99

11 DIPA -20.55 -13.10

12 MMEA -9.14 -5.46

13 Morpholine -4.52 -2.26

14 Piperazine -3.20 -0.53

15 Piperidine -2.26 2.14

a: MP2/6-31G(d) with thermal correction and zero-point energy at HF/3-21G(d) level. b: B3LYP/6-

311++G(d,p) level with thermal correction and zero-point energy at HF/3-21G(d) level. c: With

different carbamate conformers as shown in Figure 3.

In Table 3 are shown the solvation energies calculated with free energy

perturbations and the continuum models. The continuum and free energy perturbation

solvation energies are mostly in reasonable agreement, but do differ significantly in

some cases. Finally in Table 4 is shown the solvation phase energy for equation 1 and

equation 4. The energies are based on the B3LYP gas phase energies and separate sets

of results are shown based on the different solvation models. To calculate the energy

for Kc2 (equation 1) experimental pKa data were used together with model data for

equation 2 (given in the supporting information).

13


No. Name FEPa PCMb SMc

Am AmCO2- Am AmCO2

- Am AmCO2-

1 MEA -8.9 -67.8 -8.9 -67.8 -9.0 -72.3

2 MPA(1)d -8.7 -64.1 -8.6 -66.8 -9.2 -70.7

MPA(2)d -63.0 -68.0 -71.8

MPA(3)d -70.5 -75.9 -78.1

3 DGA -12.9 -68.9 -10.5 -63.9 -11.3 -68.9

4 EDA -11.8 -85.7 -9.1 -69.2 -9.3 -74.3

5 MIPA -10.2 -68.9 -8.1 -66.0 -8.4 -70.7

6 AEEA(p) -10.3 -46.3 -11.5 -64.4 -11.0 -71.4

AEEA(s) -54.0 -62.3 -67.4

7 AMP -6.8 -65.0 -7.3 -64.4 -6.8 -69.1

8 AMPD -7.7 -59.9 -8.7 -62.5 -9.9 -68.3

9 AEPD -6.9 -58.4 -7.7 -60.9 -9.3 -67.2

10 DEA -11.2 -60.6 -9.8 -60.0 -12.9 -66.0

11 DIPA -8.1 -58.3 -10.5 -57.3 -10.6 -64.0

12 MMEA -5.7 -68.8 -8.1 -64.3 -7.4 -69.6

13 Morpholine -4.4 -76.7 -9.1 -70.2 -7.2 -72.3

14 Piperazine -5.7 -86.4 -11.0 -72.7 -9.1 -75.3

15 Piperidine -2.7 -81.8 -5.4 -68.5 -4.3 -71.4

a: Free Energy Perturbations with CM2 charges on B3LYP/6-311++G(d,p) geometry. b:

IEFPCM/MP2/6-31G(d)//MP2/6-31G(d). c: SM 5.42R/HF/6-31G(d)// HF/6-31G(d). d: With different

carbamate conformers as shown in Figure 3.

14

Table 4. Free Energies of Reaction in solution (All Results in kcal/mol)

No. Name csG∆ a, b

2csG∆ a, c, d

FEP PCM SM FEP PCM SM

1 MEA 1.9 1.9 -2.5 13.6 13.6 9.2

2 MPA(1)e 5.9 3.1 -0.2 17.0 14.2 10.9

MPA(2)e 11.9 6.9 3.6 23.0 18.0 14.7

MPA(3)e 8.7 3.2 1.4 19.8 14.3 12.5

3 DGA 7.5 10.2 6.0 19.3 21.9 17.8

4 EDA -6.5 7.3 2.4 4.7 18.5 13.5

5 MIPA 3.3 4.0 -0.3 15.1 15.8 11.5

6 AEEA(p) 26.5 9.7 2.1 37.8 21.0 13.4

AEEA(s) 16.5 9.4 3.8 27.8 27.6 22.0

7 AMP 7.8 8.8 3.6 19.3 20.2 15.0

8 AMPD 6.6 4.8 -2.3 19.2 17.5 10.4

9 AEPD 7.1 5.4 0.7 19.7 18.1 13.4

10 DEA 4.7 3.9 1.0 17.1 16.4 13.5

11 DIPA 3.8 7.3 0.6 16.4 19.8 13.2

12 MMEA -1.4 5.5 -0.6 9.9 16.8 10.8

13 Morpholine -7.5 3.7 -0.2 5.6 16.8 12.9

14 Piperazine -12.5 4.8 0.3 -1.2 16.1 11.6

15 Piperidine -11.4 6.1 2.2 -1.9 15.7 11.7

a: Gas phase energies are B3LYP/6-311++G(d,p) level with thermal correction and zero-point energy

at HF/3-21G(d) level. b: Reaction energy for eq 4. c: Reaction energy for eq 1. d: Experimental pKa

data used in calculation. e: With different carbamate conformers as shown in Figure 3.

AEEA is special among the amines in present study in having two non-equivalent

amine-functionalities. In Table 4 equilibrium constants are calculated based on

bonding to both amine functionalities. It can be seen from the table that while the free

energy perturbation results suggest that CO2 bonded to the secondary amine

functionality produces the more stable carbamate form, the SM results suggest that

primary carbamate is more stable. All the models suggest that AEEA has a lower

equilibrium constant for carbamate formation than MEA. The models do however

differ on how great this difference is.

15

It can also be seen from Table 4 that different solvation models give different

relative energies for many of the other amines. The assessments of the accuracy of the

different models will be based on comparison with experimental data.

Before turning to comparison with experimental data some general comments

should be made on the quality of the quantum mechanical calculations and solvation

energies. In our study of amine pKa values9 we obtained results that can perhaps best

be summarized as semi-quantitative. In the present study the method used is almost

identical. The carbamate formation reaction is however between an anionic species

and a neutral species, while the pKa study involved cationic molecules. There are

some reasons to believe that the carbamate stability calculations will be at least as

accurate as the pKa calculations: the CO2-group does not vary that much in nature

between the different carbamate molecules, and the intramolecular hydrogen bonds

seem to play a lesser role than is the case for the protonated amines in the pKa study.

It should be noted that we do not believe the absolute energies calculated to be

reliable, the present level of modeling should however be sufficient to reasonably

predict the relative stability of carbamates formed from different amines.

Comparison with Experimental Data

While tertiary amines are not included in the present study, some calculations were

performed on the stability of carbamate-like species from the tertiary amines

triethanolamine and MDEA. No stable species involving CO2 bonding to the amine

functionality were found in these calculations. This is in agreement with the

established knowledge that tertiary amines do not form carbamate species.8

The calculations were performed on single solute molecules with solvation

models that produce results corresponding to infinite dilution in aqueous solution.

As noted in the introduction the carbamate is in fact only formed at detectable levels

in systems where several other species are also present in significant concentrations,

and most experimental measurements are performed in conditions far from infinite

dilution. In comparing the calculated results with experimental data we will be

ignoring concentration effects, this is an approximation that should be kept in mind

when studying the results.

As already noted, NMR-experiments offer the only direct route to finding

carbamate stabilities. Sartori and Savage6 reported the following order for Kc: MEA <

diethanolamine (DEA)< AMP. The results with free energy perturbations in Table 4

16

reproduce this trend and so do the continuum models. Suda et al.8 gave the following

order in Kc2: MEA<MMEA< MDEA. The results with free energy perturbations give

MMEA<MEA<MDEA, while both the continuum models produce the same trend as

the experimental data.

Data from Yoon and Lee7 give the following order in Kc2: MEA<2-amino-2-

methyl-1,3-propanediol (AMPD)<2-amino-2-ethyl-1,3-propanediol (AEPD) <AMP.

The free energy perturbation data in Table 4 give the following order:

MEA<AMP≈ AMPD<AEPD. The continuum models produce results in full

agreement with the experimental trend.

In summary it can be observed that the continuum model based results give

the same relative carbamate stabilities as the NMR-data, while the free energy

perturbations errs in some cases.

While the NMR-methods offer the only direct method for estimating

carbamate stability there are other ways to infer carbamate stability from experimental

data. Carbamate formation (eq 1) is a much faster reaction than bicarbonate

formation, high reaction-rates is therefore evidence of carbamate formation, and it

would seem reasonable to expect a correlation between the reaction-rate and the

stability of the carbamate formed (i.e. the reaction energy). Available kinetic data are

from experiments on a single amine species in aqueous solution. In this case eq 1

represents the reaction that takes place. For molecules that undergo the same reaction

we can assume that there is a linear relation between the logarithm of the rate of

reaction and the reaction energy. In Figure 4 calculated 2csG∆ from Table 4 is plotted

against the logarithm of experimental kinetic parameters for second order reaction (k2

, m3mol-1s-1). Experimental data are from the references given in Table 1 and the

chosen values are given in the Supporting Information. The data are at 25°C, where

several values are available the most representative values have been chosen. It

should be noted that there are inconsistencies and uncertainties in experimental

kinetics data, but these should not affect the overall trends in the results. The

experimental value for AMPD was very low and was considered to be relatively

uncertain, this value was therefore omitted from the plot.

17

Figure 4. Plot of logarithm of experimental reaction rate versus calculated energies. Stippled lines

indicate the set of results for a molecule.

Figure 4 shows good overall correlation between calculated reaction energies with

free energy perturbation solvation energies and the kinetic data, the trend line might

however overstate the relative energy differences. The outlying points in the free

energy perturbation based plot in Figure 4 are for MPA and diglycolamine (DGA).

The results with the continuum solvation models in this case show somewhat poorer

correlation with experimental data. It would appear that both the continuum models

underestimate the solvation energy of the carbamate-forms of the cyclical amines.

This suggests that while the continuum models are more reliable for molecules with

similar structures they are not as good as the free energy perturbations in predicting

the relative solvation energies of species with different structures.

In general the calculations appear to be in reasonable good agreement with

trends in experimental data. It is however clear that the models are not completely

accurate, and the solvation energies appear to be the main source of uncertainty.

18

A final possibility to extract information on relative carbamate stability from

experimental data is to look at the amount of CO2 absorbed in the system. This is

usually measured as the loading: mol CO2/mol amine in solution. Carbamate

formation consumes amine and CO2 at a stoichiometry of 2:1, while bicarbonate

formation has a stoichiometry of 1:1. Systems where carbamate formation dominate

will therefore have loadings not much higher then 0.5, while systems with only

bicarbonate formation can have loadings close to 1. Such an analysis can however be

ambiguous as a low loading can indicate either carbamate formation or a low overall

equilibrium. While comparison which such data is not included in the present work, it

is an option for systems where other experimental data is not available.

Contributions to Carbamate Stability

Some efforts have been made to rationalize observed trends in carbamate stability. It

is of interest to see if the results from the present work validate such rationalizations

or if any new general correlations can be identified.

Versteeg et al.4 observed a correlation between the pKa and the reaction rate

for a series of amines. A similar plot for the molecules in Figure 4 is given in the

Supporting Information. Little overall correlation is found in this plot. The correlation

observed by Versteeg et al.4 can be seen for a group of nine molecules, the data for

piperidine, morpholine and AMP do however not fit with this correlation. That the

previously observed correlation does not hold for all primary and secondary

molecules is not at all surprising. The base strength and carbamate stability are two

separate equilibrium constants representing the stability ratio between different

chemical species, and it is not at all a priori evident, but rather surprising, that there

should be any such correlation at all. While the correlation observed by Versteeg et

al.4 is of interest it would therefore not appear likely that it has predictive value. We

see no apparent explanation for the correlation observed for some amines. It might be

that some molecular characteristics is favorable both to the formation of anionic and

cationic species.

Sartori and Savage6 showed that a series of amines with substituent groups on

the carbon bonded to the amine functionality formed carbamate to a lesser extent than

other primary and secondary amines. They referred to these amines as “sterically

hindered”. While these amines do have some degree of steric hindrance, we would

19

caution that the name conveys an overly simple physical interpretation of carbamate

stability.

The effect of a substituent group on the stability of a species can take several

forms. There are the effects of donating or withdrawing electrons through bonds, there

can be energetically favorable or unfavorable interactions to groups to which the

substituent is not directly bonded. Steric hinderance refer to the latter of these

interactions. In addition a substituent group can also affect the accessibility of the

solvent to various parts of the molecular surface, thereby changing the solvation

energy.

Looking at the geometry of AMP-carbamate (Figure 1 and Supporting

Information) it can be seen that there is some steric interaction between a methyl

substituent and the CO2 carbon. In particular the N-C-C(OH) angle tightens from

114.53 in MEA-carbamate to 111.38 in AMP-carbamate, suggesting that the nitrogen

atom together with the carbamate functionality is forced away from one of the methyl

groups. While this effect is significant for AMP it will however not always

necessarily be the dominant factor. When estimating the reactivity of an amine all of

these effects must be considered together, AMPD and AEPD are for example clearly

no less sterically hindered than AMP but nevertheless the experimental results

strongly suggest that they have more stable carbamate forms.

One group of amines that stand out in terms of rate of carbamate formation is

the cyclical amines. There would appear to be two factors that can account for these

amines having a strong tendency to form carbamate species. The carbamate group on

the cyclical molecules are completely accessible to solvent, leading to high solvation

energies for the carbamate form. The solvation energy of the neutral amines

themselves is also relatively low, these two solvent effects together contributes to the

carbamate formation being favored. These effects will however vary with the

structure of the cyclical amine, and this should not be thought of as some form of

general rule.

It would therefore not appear that the carbamate stability can be explained in

terms of single molecular property. While steric effects do play a role, other factors

such as intramolecular hydrogen bonding and variations in solvation energy can

dominate.

20

Temperature Effects

In the earlier work on pKa calculations9 it was found that entropies from quantum

mechanical calculations together with pKa values can be used to predict changes in

pKa with temperature. The equation presented for pKa in that work can be written in a

more general form:

( ) ( )ln / / ln /reactiond K dT S R K T= ∆ − (12)

With this equation it should also be possible to estimate how the carbamate stability

changes over temperature. The lack of accurate carbamate equilibrium constants even

at room temperature means that the same level of accuracy in prediction can not be

achieved. There is also very little experimental data for carbamate to validate model

results.

Solvation Energy

In this work free energies of solvation has been used to calculate equilibrium

constants, but they are also of intrinsic interest. The free energy of solvation

represents the partitioning of a species between the gas and liquid phase and it is

directly related to the partial pressure of a component in the gas phase.35 Negative

values indicate a preference for the solute to stay in the liquid phase. For the amines

used in aqueous solution it is preferable if they are soluble in large quantities and do

not evaporate. The solubility is one of the factors that must be considered when

selecting solvents for industrial application. High solubility is perhaps the main reason

why alkanolamines are usually chosen for CO2 absorption processes.

The solvation models used in this work can give indications of which amines

have high solubility. Looking at the data for neutral amines in Table 3 it can be seen

that piperidine has low solubility and that AMP has relatively low solubility. This is

consistent with what is known about these amines experimentally. New solvents for

this process should ideally have solvation energies comparable to MEA (Table 3).

Conclusions

In the present work the carbamate stability of a series of amines have been calculated

with quantum mechanical gas phase energies and various solvation models. The

results are in good overall agreement with trends in available experimental data.

21

This shows that carbamate stability can be predicted with a reasonable

accuracy. Together with similar models for calculating amine basicity the present

work can be utilized to predict the chemistry and overall performance of different

amine solvents in CO2 absorption.

Different solvent models produced results in reasonable overall agreement.

The results obtained from different models did however vary and none of the models

are completely accurate.

The carbamate species appear to form hydrogen bonds between alcohol groups

and carbamate functionality oxygen atoms.

The model results suggest that steric hinderance is only one of several effects

contributing to relative carbamate stability. The high carbamate stability of some

cyclical amines appears to be caused by the high solubility of the carbamate

functionality.

Acknowledgement

This work has received support from the Research Council of Norway through a grant

of computing time.

Supporting Information Available:

Underlying values for data in Table 2, conformers of amine molecules, details of

MEA and AMP carbamate geometry, rate constants for Figure 4 and a plot of

experimental pKa versus reaction rate.

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1

Supporting Information for: Study of the Carbamate Stability of Amines Using ab Initio Methods and

Free Energy Perturbations

Eirik F. da Silva and Hallvard F. Svendsen

Supporting Information is 6 pages.

Tables:

S1. Key B3LYP/6-311++G(d,p) geometry values of MEA carbamate

S2. Key B3LYP/6-311++G(d,p) geometry values of AMP carbamate

S4. Energy data for Table 2 in Manuscript

S5. Energy Data to Calculate Reaction Energy for Eq 2 in Manuscript

S6. Rate constants for various amines at 25ºC

Figures:

S3. Amine molecule conformers

S7. Plot of experimental pKa versus logarithm of experimental reaction rate

2

S1. Key B3LYP/6-311++G(d,p) Geometry Values of MEA Carbamate

Ethanolamine

Bond lengths [Å] N-C 1.459 C-C 1.535 C-O 1.409 N-C(CO2) 1.444 H1(N)-N 1.010 H(O)-O 1.000 O1(CO2)-C(CO2) 1.267 O2(CO2)-C(CO2) 1.245 Angles N-C-C 114.53 C-C-O 113.99 H(N)-N-C 114.33 C(CO2)-N-C 121.49 H(O)-O-C 105.52 O1(CO2)-C(CO2)-N 115.65 O2(CO2)-C(CO2)-N 115.50 Dihedral angles N-C-C-O -75.63 H(N)-N-C-C -144.87 H(O)-O-C-C 32.11 C(CO2)-N-C-C 79.56 O1(CO2)-C(CO2)-N-C -27.43 O2(CO2)-C(CO2)-N-C 153.65 Hydrogen Bonds [Å] H(O)-O1(CO2) 1.650

3

S2. Key B3LYP/6-311++G(d,p) Geometry Values of AMP Carbamate

Ethanolamine

Bond lengths [Å] N-C1 1.473 C1-C2 1.555 C2-O 1.406 N-C(CO2) 1.445 H1(N)-N 1.011 H(O)-O 1.004 O1(CO2)-C(CO2) 1.267 O2(CO2)-C(CO2) 1.246 C3-C1 1.544 C4-C1 1.539 Angles N-C1-C2 111.38 N-C1-C3 112.25 N-C1-C4 106.08 C1-C2-O 115.50 C2-O-H(O) 104.76 H(N)-N-C1 113.08 C(CO2)-N-C1 125.37 O1(CO2)-C(CO2)-N 116.91 O2(CO2)-C(CO2)-N 114.86 Dihedral angles N-C1-C2-O 76.91 H(N)-N-C1-C2 153.24 H(O)-O-C2-C1 -44.22 C(CO2)-N-C1-C2 -70.07 O1(CO2)-C(CO2)-N-C1 28.46 O2(CO2)-C(CO2)-N-C1 -153.06 C3-C1-C2-O -48.49 C4-C1-C2-O -167.66 Hydrogen Bonds [Å] H(O)-O1(CO2) 1.608

C1 is bonded to Nitrogen. C2 is bonded to C1 and alcohol-group oxygen. C3 and C4 are methyl group carbons bonded to C1.

4

S3. Amine molecule conformers. Stippled lines indicate hydrogen bonds.

5

S4. Energy Data for Table 2 in Manuscript (Data in Atomic Units)

No. Name MP2/6-31G(d) B3LYP/ 6-311++G(d,p)

Thermal correction and ZPE

Am AmCO2- Am AmCO2

- Am AmCO2-

1 MEA -209.704 -397.257 -210.464 -398.567 0.07819 0.07652

2 MPA -248.872 -436.427 -249.790 -437.893 0.10779 0.10689

3 DGA -363.057 -550.608 -364.342 -552.442 0.14041 0.14061

4 EDA -189.858 -377.403 -190.588 -378.68 0.09103 0.08933

5 MIPA -248.877 -436.431 -249.794 -437.896 0.10621 0.10508

6 AEEA(p) -343.215 -530.771 -344.473 -532.575 0.15237 0.15303

AEEA(s) -530.779 -532.578 0.15191

7 AMP -288.048 -475.601 -289.118 -477.218 0.13059 0.13449

8 AMPD -363.076 -550.638 -364.358 -552.467 0.14008 0.14042

9 AEPD -402.24 -589.804 -403.679 -591.788 0.16889 0.16954

10 DEA -363.056 -550.630 -364.346 -552.462 0.13860 0.13889

11 DIPA -441.402 -628.978 -443.004 -631.12 0.19498 0.19564

12 MMEA -248.862 -436.417 -249.779 -437.88 0.10629 0.10476

13 Morpholine -286.854 -474.4 -287.882 -475.977 0.11660 0.11346

14 Piperazine -267.012 -454.557 -268.011 -456.104 0.12959 0.12674

15 Piperidine -251.003 -438.546 -251.979 -440.067 0.14202 0.13866

S5. Energy Data to Calculate Reaction Energy for Eq 2 in Manuscript

[Data in Atomic Units].

Species B3LYP/ 6-311++G(d,p) a

sG∆ b Thermal correction and ZPE c

H2O -76.4585 -0.01027 0.004129 HCO3

- -264.551 -0.1172 0.002176 CO2 -188.647 0.001066 -0.00882 H3O+ -76.7295 -0.16665 0.017562

a: Gas phase energy. b: Solvation energy (IEFPCM/ MP2/6-31G(d)// MP2/6-31G(d). c: Calculated at HF/3-21G(d) level.

6

S6. Rate Constants for Various Amines at 25ºC. k2 [m3mol-1s-1] Reference Ethanolamine 8 54004.4 10 exp

T⎛ ⎞⎟⎜× − ⎟⎜ ⎟⎜⎝ ⎠

a

3-Amino-1-Propanol 9 56051.3 10 expT

⎛ ⎞⎟⎜× − ⎟⎜ ⎟⎜⎝ ⎠

a

2-(2-aminoethoxy)ethanol 3.99 a

Ethylendiamine 15.1 b

1-Amino-2-Propanol 7 50339.11 10 expT

⎛ ⎞⎟⎜× ⎟⎜ ⎟⎜⎝ ⎠

a

2-amino-2-methylpropanol 1.05 b

2-Amino-2-methyl-1,3-propanediold 0.04 b

Diethanolamine 3.24 a

Diisopropanolamine 2.70 a

2-(methylamino)ethanol 5 35329.63 10 expT

⎛ ⎞⎟⎜× − ⎟⎜ ⎟⎜⎝ ⎠

a

Morpholine 20.0 b

Diethylenediamine 53.7 c

Piperidine 60.3 b

a: Versteeg, G. F.; van Dijck, L.A.J.; van Swaaij, W.P.M. On the kinetics between CO2 and

alkanolamines both in aqueous and non-aqueous solutions. An overview. Chem. Eng. Comm.

1996, 144, 113. b: Sharma, M. M., Kinetics of Reactions of Carbonyl Sulphide and Carbon

Dioxide with Amines. Trans. Faraday Soc., 1965, 61, 681. c: Bishnoi, S. Dissertation,

University of Texas, 2000. d: Not utilized in plot as number would seem relatively uncertain.

7

S7. Plot of experimental pKa versus logarithm of experimental reaction rate. a

Versteeg, G. F.; van Dijck, L.A.J.; van Swaaij, W.P.M. On the kinetics between CO2

and alkanolamines both in aqueous and non-aqueous solutions. An overview. Chem.

Eng. Comm. 1996, 144, 113.

Paper VI

Molecular Dynamics Study of Ethanolamine as a Pure Liquid and in

Aqueous Solution

Eirik Falck da Silva, Tatyana Kuznetsova and Bjørn Kvamme

2005

1

Molecular Dynamics Study of Ethanolamine as a Pure

Liquid and in Aqueous Solution

Eirik F. da Silva,*a Tatyana Kuznetsovab and Bjørn Kvammeb

aDepartment of Chemical Engineering, Norwegian University of Science and Technology, N-7491

Trondheim, Norway.

bDepartment of Physics, University of Bergen, N-5007 Bergen, Norway.

[email protected]

Molecular dynamics simulations have been carried out for ethanolamine as a pure liquid and in aqueous

solution at 298.15K and 333K. Two force field representations were utilized for ethanolamine. Results

are presented for density, enthalpy of vaporization, radial distribution functions and conformer

distributions. The results strongly suggest that the main (O-C-C-N) dihedral tends to stay in its gauche

conformers in solution and that the ethanolamine molecules populate conformers with a considerable

degree of intramolecular hydrogen bonds. Aqueous ethanolamine shows a preference to be solvated by

water molecules, resulting in a liquid structure that is fairly homogeneous at the molecular level. A

simulation was also carried out with a CO2 molecule in an aqueous ethanolamine system, the results

suggesting that CO2 is almost equally attracted to ethanolamine and water.

Introduction

Mixtures of Alkanolamines and water are commonly used to absorb carbon dioxide from natural gas

and exhaust gases.1 This is currently one of the most viable among the available technologies to capture

2

carbon dioxide.2 While alkanolamine based CO2 capture has received considerable experimental

attention little work has been done on the understanding of these systems at the molecular level.

Ethanolamine is the simplest of the alkanolamine molecules and some simulation work has been done in

recent years to ascertain its liquid structure and properties as well as its behavior in aqueous mixtures.3 -7

Besides being important in gas sweetening and other industrial processes, ethanolamine and other

alkanolamines are also of interest for other reasons. Together with 1-2 ethanediol, ethanolamine

represents one of the simplest molecules able to form intramolecular hydrogen bonds. Both in pure

liquids and aqueous solutions intramolecular hydrogen bonds will compete with the formation of

intermolecular hydrogen bonds. This potential for hydrogen bonding also raises questions about the

structure of ethanolamine both as a pure liquid and in aqueous solution. The modeling of such small

organic molecules is clearly also of relevance to the modeling of more complex biomolecules.

In the parameterization of molecular force fields, ethanolamine and other alkanolamines present an

interesting challenge. Two main approaches for parameterization of force fields exist in the open

literature. For water and small organic molecules, such as methanol, a number of specially fitted force

fields have been presented (Guillot8 and Walser et al.9 and references therein). These are typically based

on reproducing certain experimental properties, such as density, radial distribution functions and

enthalpy of vaporization, and each parameter in the force field is often fine-tuned. This approach to

force field fitting is not viable in case of larger organic molecules with many atomic sites. For such

molecules general transferable force fields such as OPLS10 have been developed. Ethanolamine is a

relatively small molecule, but the number of parameters in a force field will tend to be much higher than

for water, and the molecule has not been as rigorously studied experimentally as water or the simple

mono-alcohols. There would however appear to be room for more detailed force field parameterization

than usually seen for biomolecules.

The intention of the present work has been to look in greater detail at force field parameterization,

conformer distribution and other aspects of the system of particular relevance to the gas absorption

3

process. We were especially interested in understanding the carbamate formation mechanism, which

according to da Silva and Svendsen11 can be written in the following way:

2 1 2 1 2CO R R NH B R R NCOO BH− ++ (1)

Where B is a base molecule (usually a second ethanolamine molecule) and 1 2R R NH is an

ethanolamine molecule. The stippled line indicates a hydrogen bond.

Force Field

Two force field representations of ethanolamine were studied in the present work. One is a somewhat

adjusted version of the force field presented by Alejandro et al.4 while the second force field was based

on our own parameterization and analysis. A united atom approach in which methyl group hydrogens

are not explicitly represented is utilized for both representations of ethanolamine.

Bond angles are handled by harmonic type potentials:

( ) ( )20U kθθ = θ−θ (2)

where θ is the bond angle and the subscript 0 denotes the equilbrium value. kθ is the spring constant.

Dihedral angle energies around bonds are given by:

( ) ( )5

1

cos ii

i

U C=

φ = φ∑ (3)

where φ is the dihedral angle and the iC are constants. In this potential 0φ= corresponds to the trans

form and 180φ= to the cis form. The potential energy is given by the standard combination of

Lennard-Jones and Coulomb potentials:

( )12 6

4 i jij

ij ij ij

q qU r

r r r

⎡ ⎤⎛ ⎞ ⎛ ⎞σ σ⎢ ⎥⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜= ε − +⎢ ⎥⎟ ⎟⎜ ⎜⎟ ⎟⎟ ⎟⎜ ⎜⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦ (4)

where q are atomic charges, σ and ε are the Lennard-Jones parameters and i and j are any atomic

sites. Only intermolecular potential energy is calculated in both the force fields, the intramolecular

4

potential is represented solely by the dihedral and bond energies. Standard Lorenz-Berthelot mixing

rules were applied.

The new representation was based on quantum mechanical calculations to determine geometry and

intramolecular potential together with standard Lennard-Jones parameters from the united12 and all

atom10, 13 OPLS force field. Atomic charges were fitted to the electrostatic potential from quantum

mechanical calculations. The choice of parameters was also guided by our desire to reproduce the

experimental enthalpy of vaporization and density. This parameterization combines elements of the

approach taken by Jorgensen and coworkers10 and Cornell and coworkers14 in their respective force field

development.

Conformer notation has been adopted from work by Vorobyov et al.15 A conformer is represented as

xYz. Where x designates the C-C-N- lpN dihedral angle, Y is the O-C-C-N dihedral angle, and z the C-

C-O-H dihedral angle. lpN denotes the lone pair on the nitrogen atom. G or g indicates gauche(+), G’ or

g’ indicates gauche(-) and T or t indicates trans.

Vorobyov et al.15 have published results of quantum mechanical calculations on the ethanolamine

geometry more advanced than those presented by Alejandro et al.4 In the present work we have replaced

the force field geometry presented by Alejandro et al.4 with the B3LYP/6-311++G(2d,2p) g’Gg’

geometry from this new paper.15 The resulting force field will be referred to as MEAa, MEA

(monoethanolamine) being the common acronym for ethanolamine in chemical engineering.

Gubskaya and Kusilik6 observed that the Alejandro et al.4 force field has a enthalpy of vaporization

significantly lower than the experimental value. In the present work we will use a parametrization

procedure similar to that utilized by Alejandro et al.4, but making sure that the experimental heat of

vaporization is reproduced reasonably well. One of the purposes of the present work is to study the

conformer distribution of ethanolamine in greater detail, and for this purpose we performed a more

detailed analysis of the intramolecular potential.

For the new force field we again chose geometry from recent quantum mechanical calculations15 and

OPLS Lennard Jones parameters similar to the ones selected by Alejandro et al.4 The bond angle

5

potential was adopted from Alejandro et al.4 The approach of deriving the atomic charges from the

electrostatic potential taken by Alejandro et al.4 seems to us a sensible one, but as their model produces

to low heat of vaporization we carried out more detailed analysis of the atomic charges. To calculate the

atomic charges from the electrostatic potential the Merz-Kollman16 (MK) scheme implemented in

Gaussian 9817 was utilized. Calculation on a single molecule in gas-phase will yield only gas-phase

charges, while molecules in solution are polarized by the environment and tend to have higher charges.

Calculations with a continuum solvent model were carried out to obtain solution phase charges.

Different conformer geometries were optimized at the B3LYP/6-311++G(d,p) level and continuum

model calculations were carried out as single-point IEFPCM18 calculations (IEFPCM-B3LYP/6-

311++G(d,p)// B3LYP/6-311++G(d,p)). The methyl group charges were added together, and the total

charge of these groups were distributed evenly between the two carbon atoms. The amine group

hydrogen atom charges were also averaged.

A modified version of the EMP2 model19 has been utilized to simulate CO2. The modification consists

of adding a flexible bond angle. The spring constant was determined by use of ab initio calculation.

B3LYP/6-311++G(d,p) calculations were carried out for unconstrained CO2 and CO2 with the bond

angle set to 150º. The energy difference between these forms was determined to be 81 kJ/mole, and the

spring constant was set to reproduce this energy difference. The model details are given in the

supporting information.

Intramolecular Potential

Some simple spread-sheet calculations were performed to study the intramolecular potential for

different conformers. The intramolecular distances can be determined from the geometry data for

different conformers15 and the energy of a conformer can be calculated directly for a given force field.

The angle energies were neglected in these calculations. Energies were calculated both with ab initio

dihedral angles and dihedral values found to be optimal in simulations. Such approximate spread-sheet

calculations can provide an immediate picture of relative conformer energies.

6

Simulations Details

The SPC model20 was chosen to represent water. Simulations were carried out using the constant-

temperature, constant-pressure algorithm (nPT) in the MdynaMix package written by Lyubartsev and

Laaksonen.21 Long-range electrostatic interactions were handled by means of Ewald summation.

Lennard-Jones forces and real-space electrostatics were cut off at 11.5Å. A dual time step algorithm

was used, with all the forces in the system divided into fast and slow ones. Fast forces included

interactions arising from bonds, constrained angles and dihedral angles, as well as Lennard-Jones and

real-space electrostatic forces within a cutoff of 5Å. They were recalculated each short time step (0.05

fs), with the rest of the forces recalculated once every 10 short steps. Simulations were carried out with

512 molecules at 298.15 K and 333K and 1 atmosphere of pressure. Two different compositions were

studied, one with pure ethanolamine and one with 461 water molecules and 51 ethanolamine molecules.

The latter corresponds to 10 mol percent ethanolamine, representative of the composition often used in

industrial applications. For comparison purposes simulations we also carried out pure water simulation.

Each system was equilibrated over at least 200000 steps (100ps), and sampling was done over 100000

steps (50ps).

The single-molecule simulations (gas-phase) were run for over 20 million steps (20 ns). For these

simulations, we followed the approach of Jellinek and Li22 and modified the original MdynaMix

package to implement separate temperature controls for each kinetic mode (translation, rotation, and

internal).

7

Results

The relative conformer energies of the MEAa force field are shown together with the relative energies

from quantum mechanical calculations in Table 1. Energies for all 14 nonequivalent conformers are

shown.15 The force field results are presented both for quantum mechanical dihedral angles determined

by Vorobyov et al.15 and for the average dihedral angles for each conformer determined from liquid-

phase simulations. These were estimated to be 77 for O-C-C-N gauche and 180 for trans, 45 for C-C-

O-H gauche and 182 for trans and finally 58 for C-C-N- lpN gauche and 180 for trans.

The most stable gas-phase conformer (g’Gg’) is shown in Figure 1.

Table 1. Relative conformer energies. Values in [kJ/mole].

B3LYPa MEAab MEAac

g'Gg' 0 0 0.0

gGg' 5.5 8.5 0.0

gGt 5.3 5.0 2.6

tGt 5.7 17.0 5.3

tGg 6.6 11.5 2.7

gGg 6.9 -1.4 0.0

tGg’ 8.0 9.2 2.7

tTt 9.5 18.2 6.2

tTg 9.7 9.6 3.6

gTt 10.0 9.1 3.5

gTg 10.5 0.5 0.9

g’Tg 10.6 -0.1 0.9

g’Gt 16.2 6.9 2.6

g’Gg No minima -1.7 0.0

a: Sum of electronic and zero-point energies at B3LYP/6-311++G(2d,2p) level from Vorbyov et al.15 b: Conformer energies calculated with dihedral angles determined from ab initio calculations. c: Conformer energies calculated with optimal dihedral angles for force field.

8

Figure 1. g’Gg’ conformer of ethanolamine

The MEAa force field can be seen from the data in Table 1 to be in mostly reasonable agreement with

the quantum mechanical results. Some conformers that are not equivalent in the ab initio calculations do

however become equivalent in the force field. This is a direct consequence of using a force field with an

intramolecular energy only represented by uncoupled dihedral energies. Thus g'Gg', gGg', gGg and g'Gg

become equivalent in terms of energy, the same holds for the g'Gt and gGt pair and gTg and g’Tg as

well.

A number of different force fields of ethanolamine were studied in a recent paper by Gubskaya and

Kusalik.6 They apparently treated the intramolecular potential as a parameter to be set in the overall

fitting of liquid properties. It is not clear from their paper if the representations chosen reproduce

relative conformer energy differences from quantum mechanical calculations. We believe a more

realistic solvent representation is obtained by determining the intramolecular potential from quantum

mechanical potential, and that this part of the potential should not be arbitrarily fitted to experimental

data. In this we follow the approach taken by Jorgensen et al.10

Gubskaya and Kusalik6 observed, as previously noted, that the MEAa force field had a too low

enthalpy of vaporization. Results from our own calculations shown in Table 2 are in agreement with

that observation. It should be noted that our density for MEAa is higher than reported by Alejandro et

al.4 The discrepancy is most probably caused by different ensambles utilized and that, unlike Alejandro

et al.4, we did not shift or truncate the Lennard-Jones potential.

9

Table 2. Densities and Heats of Vaporization for ethanolamine.

MEAa MEAb Experimental

( )298.15Kρ a 1.032 1.060 1.012d, 1.008e

( )333Kρ a 1.003 1.037 0.984d,0.984e

(298.15 )liqU K a -43.04 -62.34

(298.15 )gasU K a 1.90 -1.97

(298.15 )vapH K∆ b 47.7 63.13

(333 )liqU K a -37.45 -55.34

(333 )gasU K a 2.59 -1.32

(333 )vapH K∆ b 42.8 56.80 57.7d

a Density in g/cm3. b Energy in kJ/mole. c Enthalpy of vaporization in kJ/mole. d Data from da Silva5

and references therein. e Data from Cheng et al.27

Alejandro et al.4 reported a single set of atomic charges for the fitting of charges to the electrostatic

potential. Such procedures to fit charges are however known to be ambiguous,23 and the charges may

depend on the conformer form of the molecule.24 In Table 3 results of fitting of the charges to the

electrostatic potential in a solvent field (IEFPCM model) for a number of conformer forms are shown.

10

Table 3. Dipole Moments and Atomic Charges from Fitting the Electrostatic potential.a

g’Gg’ tGt gGt tTt gTt

Dipole Moment: 4.110 2.360 1.329 3.607 0.998

N -1.035 -1.162 -1.163 -1.224 -1.256

H1(N) 0.397 0.423 0.415 0.427 0.436

H2(N) 0.399 0.423 0.436 0.425 0.450

C(N) 0.274 0.402 0.367 0.490 0.448

H1(C(N)) -0.036 -0.016 0.003 -0.008 0.014

H2(C(N)) 0.048 0.026 -0.016 -0.004 -0.043

C(O) 0.189 0.161 0.238 0.317 0.312

H1(C(O)) 0.021 -0.011 -0.027 -0.028 -0.011

H2(C(O)) 0.046 0.034 0.026 -0.030 0.009

O -0.705 -0.767 -0.756 -0.891 -0.864

H(O) 0.402 0.484 0.477 0.526 0.504

a MK charges at IEFPCM-B3LYP/6-311++G(d,p)//B3LYP/6-311++G(d,p) level.

It can be seen from Table 3 that there are significant differences in the charges calculated for different

conformers. Both the magnitude of charges and (to a lesser extent) their relative distribution between

the hydroxyl functional group and the amino functional group vary. The present charges calculated in a

solvent field for the g’Gg’ conformer are as might be expected higher than the gas-phase charges

utilized by Alejandro et al.4 It can also be noted that the g’Gg’ conformer has the lowest charges of all

these conformers. Alejandro et al.4 suggested that their choice of charges was validated by the

agreement with experimentally-determined dipole moment. The experimental dipole moment is

however an average over the conformer population, and as the data in Table 3 suggest that the

conformers have widely varying dipole moments, it becomes apparent that this comparison with the

experimental value is inconclusive.

We looked at which set of charges that would produce best agreement with the experimental heat of

vaporization. A force field based on the g’Gg’ charges gave good agreement with the experimental heat

11

of vaporization and these charges have been adopted. This agreement must be viewed as fortuitous and

can not be used to draw conclusions regarding the conformers in solution.

While there is some ambiguity in which charges to choose, the MEAa and MEAb representation are

in reasonable qualitative agreement and do not differ too much from the values for ethanolamine in the

semi-empirical OPLS force field.3, 5

The MEAb model utilized the same intramolecular potential as in MEAa. In our work we did attempt

to apply different intramolecular potentials to get the best possible agreement with the relative

conformer energies determined from quantum mechanical calculations. The presence of intramolecular

hydrogen bonds in some conformers does mean that the energy dependency of the different dihedral

angles is strongly coupled. We have looked into adding intramolecular Coulomb and Lennard-Jones

forces interactions as a means to capture this coupling. In such representations there was unfortunately a

tendency for the strength of the hydrogen bonds to be overestimated and we were unable to come up

with a set of parameters that produced a representation better than the MEAa force field.

The MEAb charges are higher than those used by Alejandro et al.4, combined with an otherwise

identical force field, this results in increased density. To keep the density from deviating too much from

the experimental values, we looked at the possible changes that could be made to the parameters

without deviating from geometries derived from quantum mechanical calculations. Alejandro et al.4

used the g’Gg’ conformer to determine the bond lengths and angles. It is however not clear if this is the

best choice when representing a liquid phase were a number of conformer forms are populated.

Conformer geometries reported by Vorobyov et al.15 show that while most bond-lengths change little

with conformer, most conformer have a C-O bond of around 1.43Å, longer than for the g’Gg’

conformer (1.42 Å). For MEAb the value of 1.43 Å is therefore chosen. The g’Gg’ values are clearly

not representative for some of the angles either. We set the C-O-H(O) angle to 108.7 in MEAb, while

both the C-C-N and C-C-O angles were set to 112. We also chose to increase the Lennard-Jones σ for

Nitrogen to 3.3Å, which is the standard in the all atom OPLS force field.13 The MEAb force field

parameters are shown in Table 4, the MEAa parameters are given in the Supporting Information.

12

Table 4. Potential Parameters of MEAb

Bond 0r [Å]

N-H 1.012

N-C 1.471

C-C 1.524

C-O 1.43

O-H 0.966

Angle 0θ kθ [J/mole]

H-N-H 107.4 269.39

H-N-C 111.4 316.65

N-C-C 112 506.21

C-C-O 112 546.91

C-O-H 108.8 298.79

Dihedral C1a C2

a C3 a C4

a C5 a

H-N-C-C -11.05 -2.37 25.30 0.43 -2.02

O-C-C-N -17.78 23.60 36.81 -16.64 -13.32

C-C-O-H -19.15 -2.79 13.61 -0.12 1.55

Site σ [Å] ε [KJ/mole] q

H(N) 0 0 0.40

N 3.3 0.7108 -1.035

CH2 3.905 0.494 0.27

O 3.07 0.7108 -0.705

H(O) 0 0 0.40

a In kJ/mole.

The density and heat of vaporization of MEAb is shown in Table 1. The ethanolamine force field has

a large number of parameters and one could certainly refine the parameters to improve the fit with

experimental data. It is however not clear to us at present what kind of parameter adjustment is the most

13

reasonable, and we have chosen not to deviate from the quantum mechanical representation of the

molecule.

The simulated and experimental densities of both MEAa and MEAb as pure component and in

mixture with water at 298.15K and 333K are given in Table 5. MEAa reproduces the experimental

values quite well, the deviation from experimental values being small and fairly constant. The MEAb is

in somewhat worse, but still reasonable, agreement with experimental data. The densities are in general

somewhat high, even for SPC water, this would appear to be a result of the type of ensemble and

simulation algorithm employed.

Table 5. Densities of ethanolamine-water systems

MEA 10% MEAb H2O

( )298.15Kρ a-Exp. 1.008 1.009 0.997

( )298.15Kρ a-MEAa 1.032 1.040 1.015

( )298.15Kρ a-MEAb 1.060 1.045

( )333Kρ a-Exp. 0.984 0.992 0.983

( )333Kρ a-MEAa 1.003 1.011 0.994

( )333Kρ a-MEAb 1.037 1.019

a Density in g/cm3, experimental data are from Cheng et al.27 b 10 mol percent ethanolamine.

Some of the intermolecular radial distributions for pure ethanolamine at 298.15K and 333K are

presented in Figure 2. The MEAa results are mostly in good agreement with those presented by

Alejandro et al.4 The O-H(N) curve does however show a significantly higher peak in the present

calculations. Despite the differences in the force fields utilized most of the radial distribution functions

are also in good agreement with results obtained by Gubskaya and Kusilik.6

14

Figure 2. Radial distribution functions for pure ethanolamine. Gray lines are MEAa and black lines are

MEAb. Solid lines are for 298.15K while dashed lines are for 333K.

MEAb produces somewhat higher peaks in the radial functions than MEAa, this is consistent with

MEAb being the force field with higher atomic charges. The force fields do however appear to produce

very similar liquid structures, suggesting that results can be viewed with a high degree of confidence.

The results suggest that the strongest bonding takes place between hydroxyl-groups. The second

strongest feature is bonding between hydroxyl-group oxygen atoms and amino-group hydrogens.

Bonding between the amino groups appear to be somewhat weaker. Both the N-H(O) and N-H(N)

curves have second peaks that are higher then first, these reflect bonding taking place at the hydroxyl-

functionality of the molecule. The liquid ethanolamine structure is clearly dominated by the hydrogen

bonding features. Neither radial distribution functions nor visual inspection of the ensemble suggested

any ordered structure.

15

At 333K the radial distribution functions become somewhat less pronounced, a trend which is

common and expected in most liquids. The changes in structure do however appear to be quite small for

the temperature range studied.

Radial distribution functions for 10 mol percent MEAa and MEAb in aqueous solution are presented

in Figures 3 and 4. Once again we have chosen to display the radial distribution functions that convey

information about the hydrogen bonding. In Figure 3 the same ethanolamine-ethanolamine radial

distributions as plotted for pure ethanolamine (Figure 2) are shown. All the peaks are lower than in the

pure liquid suggesting that ethanolamine molecules have a preference to be surrounded by water

molecules, bonding between ethanolamine molecules does however persist. The amino-amino bonding

becomes significantly less frequent in the aqueous solution, while the hydroxyl-group interactions

change less in their relative prevalence. A fairly homogeneous and random molecular-level structure is

suggested by the radial distribution functions and visual inspection of the structure.

16

Figure 3. Radial distribution functions for 10 mol percent ethanolamine in water. Gray lines are MEAa

and black lines are MEAb. Solid lines are for 298.15K while dashed lines are for 333K.

17

Figure 4. Radial distribution functions for 10 mol percent ethanolamine in water. Gray lines are MEAa

and black lines are MEAb. Solid lines are for 298.15K while dashed lines are for 333K.

Radial distributions for the water molecules are shown in Figure 5. The results are for 10 mole

percent aqueous ethanolamine and pure water. While the changes are quite small it can be observed that

first peaks in the radial distribution functions become somewhat higher in the aqueous ethanolamine

system.

18

Figure 5. Water-water radial distribution functions at 333K. Stippled lines are from 10 mole percent

mixture with MEAb, while solid lines are from pure water simulation.

It has been suggested that ethanolamine forms dimers in aqueous solution.25 The liquid structure and

the nature of the bonding in the simulated system is however such that stable dimers would seem

unlikely to be formed. The force fields in the present work have however not been parameterized to

reproduce dimer formation energies, and more careful studies would be required to draw confident

conclusions on this point.

The populations of the various conformers for pure ethanolamine and 10 mol percent aqueous

solution of ethanolamine are shown in Table 6. Most of the data pertains to 333K, pure MEAa and

MEAb data at 298K are also included.

19

Table 6. Conformer Populations.

Maa

333K

Maa, c

333K

Maa

298K

Maa, c

298K

Mbb

333K

Mbb, c

333K

Mbb,

298K

Mbb, c

298K

aH2Od

333K

aH2Od,

c

333K

bH2Oe

333K

bH2Oe,

c

333K

g'Gg' 3.3 13 3.4 11 1.2 1 1.2 9 3.9 27 1 12

gGg' 34.0 43 35.6 37 21 6 22.6 54 22.7 28 14.4 54

gGt 0.1 0 0.1 4 0 0 0 0 0.1 0 0 0

tGt 0.0 0 0.0 0 0 0 0 0 0.0 0 0 0

tGg 0.1 4 0.3 0 1.3 8 0 0 0.0 0 0 0

gGg 40.0 16 37.3 12 16.7 1 16.9 13 55.7 22 20 23

tGg’ 0.7 11 1.4 20 16.4 63 0.4 13 0.0 0 0 0

tTt 0.0 0 0.0 0 0 0 0 0 0.0 0 0 0

tTg 0.1 0 0.2 5 2.3 20 0.2 0 0.0 0 0 0

gTt 0.0 0 0.1 0 0.0 0 0 0 0.0 0 0 0

gTg 5.7 3 5.4 2 3.1 0 3 3 3.5 2 0.8 1

g’Tg 13.8 7 13.7 6 6 1 7.4 7 0.1 0 2 3

g’Gt 2.3 3 2.5 3 0.5 0 0.3 1 14.1 21 1.5 7

g’Gg 0.0 0 0.0 11 0 0 0 0 0.0 0 0 0

a MEAa.b MEAb. c Values corrected for errors in relative conformer energies of force field. d10 weight percent MEAa in water. e10 weight percent MEAb in water.

We have analyzed the relative conformer populations of both liquid and aqueous MEA at the two

temperatures. The dihedral angle distributions for MEAa at 298K are plotted in Figure 6, with the data

for the other systems given in the supporting information section. The peaks of MEAa dihedral

distributions are located at 77 (gauche) and 180 (trans) in case of the O-C-C-N torsional, 45 (gauche)

and 180 (trans) for the C-C-O-H torsional, and finally 58 (gauche) and 180 (trans) for C-C-N-lpN

angle. A molecule was classified as a given conformer if its dihedral angles lay within 40 degrees (45

for MEA-water systems) of the corresponding dihedral peaks. Varying the 40 degrees limit did not

20

significantly alter the relative conformer populations. With this kind of definition a part of the

molecules will not be counted as occupying any conformer form, this fraction amounted to between 30

and 60 percent of the ethanolamine molecules. The statistics was worse in case of aqueous solutions,

resulting in significantly larger uncertainty in the relative conformer populations.

Figure 6. Dihedral angle distribution for pure MEAa at 298K.

The ethanolamine force fields do not fully reproduce the relative conformer energies from ab initio

calculations (Table 1). We have therefore done calculations to attempt to correct for this error and give

a picture of what the conformer populations would have been if the force field intramolecular potential

had accurately reproduced the ab initio energies. The conformer populations were first converted to

relative energies. The relative energies were then corrected by the difference between ab initio and force

field energies (data in Table 1, second and fourth column). The relative energies were then finally

converted back to conformer populations. The results with these corrections provide an approximate

estimate of what the conformer population would have been for a more accurate intramolecular

potential. Such a correction will however produce uncertain results in case of sparsely populated

conformers, therefore no correction was applied and the corrected population values were set to 0 for

conformers accounting for less than 0.5 percent of all molecules.

21

The g’Gg’ conformer has a small population in solution, despite being the most stable in the gas-

phase. This conclusion holds for both force fields and in aqueous solution as well as in the pure liquid.

It can also be seen that the total population for O-C-C-N trans conformers is quite small. While the

corrected values for MEAb in aqueous solution in one case shows a significant trans conformer

population, the correction was in this case being made to a very small population number and is highly

uncertain. Several of the trans conformers in the force field have intramolecular energy differences

relative to the g’Gg’ conformer that are equal or smaller to the ab initio differences. This would suggest

that the force fields overestimate the trans populations, and the total trans (O-C-C-N) population would

therefore in general seem to be less than 20 percent. These conclusions are in good agreement with

those drawn from experimental work on pure ethanolamine.26 These results strongly suggest that

ethanolamine forms a significant amount of intramolecular hydrogen bonds in solution.

In the case of pure ethanolamine the most populated conformers are for MEAa gGg’ and gGg, and

tGg’, gGg’ and tTg’ for MEAb. Looking at the values corrected for the intramolecular potential there

can however be seen to be significant changes. There are also some significant difference between the

two force fields. An interesting feature of the MEAb force field is the high tGg’ populations for pure

component at 333K, at 298K and in aqueous solution this conformer has a much smaller population.

The MEAa force field has a very small population for the same conformer. Conformers with the C-C-N-

lpN dihedral in a trans form can more readily form intermolecular hydrogen bonds to nitrogen atom.

Stronger hydrogen bonds to the nitrogen atom in the MEAb force field are therefore the most likely

explanation for the high tGg’population.

Silva et al.26 reported the gGt and tGt conformers to be the most common for pure ethanolamine

solution. The main difference between their findings and the simulation results would appear to be in

the C-C-O-H dihedral angle. All the simulation results (see Figure 6, supporting information and Table

5) suggest that this dihedral remains mainly in the gauche conformers. This might suggest that the

atomic charge on the hydroxyl-group hydrogen atom is too low, thereby underestimating the strength of

22

intermolecular hydrogen bonds formed with the hydroxyl-group hydrogen atom. This observation could

perhaps in future work be utilized for further refinement of the force field.

Radial distribution functions for system of a CO2 molecule in a 10 mole percent ethanolamine

(MEAb) in aqueous solution at 333K are shown in Figure 7. The radial distributions shown are for the

interactions that are expected to dominate the bonding of CO2. The results suggest that the CO2

molecule is somewhat more attracted to the ethanolamine amino-functionality than to the hydroxyl

group. This interaction with the amino group is however somewhat less favored than with the water

molecules.

Figure 7. CO2-ethanolamine-H2O radial distribution functions at 333K for 10 mol percent

ethanolamine (MEAb) in water. Lines in left plot: Solid line is C(CO2)-N(MEA), dashed line is C(CO2)-

O(MEA) and dotted line is C(CO2)-O(H2O). Lines in right plot: Solid line is O(CO2)-H(N)(MEA),

dashed line is O(CO2)-H(O)(MEA) and dotted line is O(CO2)-H(H2O).

CO2 is known to react with ethanolamine according to equation 1 in an aqueous alkanolamine system.

da Silva and Svendsen10 concluded that the reaction mechanism had no intrinsic barrier. They also

suggested that the barrier could either arise from the CO2 molecule needing to displace the water

molecules around the amino group before reacting or from the need for two amine molecules to

23

approach each other sufficiently for a proton transfer to take place. Such a reaction can not readily be

studied with the classical simulations in the present work. The picture of the liquid structure from the

present work can nevertheless further the understanding of the reaction mechanism. Since the CO2

molecule bonds readily to the amino group it would appear that there is not a significant barrier to the

approach of the ethanolamine amino group and CO2. The low degree of direct interaction between

amino-functionalities on different molecules would on the other hand suggest that the low likelihood of

such interactions may be a significant barrier to reaction.

Conclusions

Two different force fields were used to perform simulations of ethanolamine. The general agreement

in results between the two parameterization suggest that the results can be viewed with a high degree of

confidence. The results suggest that the ethanolamine O-C-C-N dihedral tends to stay in a gauche

conformer and that there is a significant degree of intramolecular hydrogen bonding. These findings

holds for ethanolamine as a pure liquid as well as in aqueous solution. While the simulation results are

in broad general agreement with conclusions drawn from experimental work on conformer populations,

it would appear that the force fields are not sufficiently accurate to predict relative conformer energies

in solution. In aqueous solution ethanolamine is preferentially solvated by water molecules, producing

an aqueous solution that is homogeneous on the molecular level.

Simulations in aqueous solution suggest that CO2 has a comparable level of affinity to ethanolamine

molecules and water.

Supporting Information Available: Force field paramaters for MEAa and CO2 and dihedral angle

distribution figures.

24

REFERENCES

(1) Versteeg, G. F.; Van Dijck, L. A. J.; Van Swaaij, W. P. M. Chem. Eng. Comm. 1996, 144, 113.

(2) Rao, A. B.; Rubin, E. S. Environ. Sci. Technol. 2002, 36, 4467.

(3) Button, J. K.; Gubbins, K. E.; Tanaka, H.; Nakanishi, K. Fluid Phase Equilib. 1996, 116, 320.

(4) Alejandro, J.; Rivera, J. L.; Mora, M. A.; de la Garza, V. J. Phys. Chem. B 2000, 104, 1332.

(5) da Silva, E. F. Fluid Phase Equilib. 2004, 220, 239.

(6) Gubskaya, A. V.; Kusilik, P. G. J. Phys. Chem. A 2004, 108, 7151.

(7) Gubskaya, A. V.; Kusilik, P. G. J. Phys. Chem. A 2004, 108, 7165.

(8) Guillot, B. J. Mol. Liq. 2002, 101, 219.

(9) Walser, R.; Mark, A. E.; van Gunsteren, W. F. J. Chem. Phys. 2000, 112, 10450.

(10) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225.

(11) da Silva, E. F.; Svendsen, H. F. Ind. Eng. Chem. Res. 2004, 43, 3413.

(12) Jorgensen, W. L.; Tirado-Rives, J. J. Am. Chem. Soc. 1988, 110, 1657.

(13) Jorgensen, W. L.; Rizzo, R. C. J. Am. Chem. Soc. 1999, 121, 4827.

(14) Cornell, W. L.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M.; Ferguson, D. M.;

Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117,

5179.

(15) Vorobyov, I.; Yappert, M. C.; DuPre, D. B. J. Phys. Chem. A, 2002, 106, 668.

(16) Singh, U. C.; Kollman, P. A. J. Comp. Chem. 1984, 5, 129.

25

(17) M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R.

Cheeseman, V. G. Zakrzewski, J. A. Montgomery, Jr., R. E. Stratmann, J. C. Burant, S.

Dapprich, J. M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V.

Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.

A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K. Raghavachari,

J. B. Foresman, J. Cioslowski, J. V. Ortiz, A. G. Baboul, B. B. Stefanov, G. Liu, A. Liashenko,

P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y.

Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J.

L. Andres, C. Gonzalez, M. Head-Gordon, E. S. Replogle, and J. A. Pople, Gaussian 98,

Revision A.9, Gaussian, Inc., Pittsburgh PA, 1998.

(18) Cances, M. T.; Mennucci, V.; Tomasi, J. Chem. Phys. 1997, 107, 3032.

(19) Harris, J. G.; Yung, K. H.; J. Phys. Chem. 1995, 99, 12021.

(20) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, Klein, M. L. J. Chem. Phys.

1983, 79, 926.

(21) Lyubartsev, A. P.; Laaksonen, A. Comput. Phys. Commun. 2000, 128, 565.

(22) Jellinek, J.; Li, D. H. Phys. Rev. Let. 1989, 62, 241.

(23) Franckl, M. M.; Chirlian, L. In Reviews in Computational Chemistry Lipkowitz, K. B.;

Boyd, D. B.; Ed.; Volume 14, Wiley-VCH, 2000, 1-31.

(24) Bayly, C. I.; Cieplak, P.; Cornell, W. D.; Kollman, P. A. J. Phys. Chem. 1993, 97, 10269.

(25) Mate-Divo, M.; Barcza, L. Zeit. Physicalische Chemie 1995, 190, 223.

(26) Silva, C. F. P.; Duarte, M. L. T. S.; Fausto, R. J. Mol. Struct. 1999, 482-483, 591.

(27) Cheng, S.; Meisen, A., Chakma, A. Hydrocarbon Processing, 1996, February, 81.

Supporting Information for: Molecular Dynamics Study of Ethanolamine as a Pure Liquid and in Aqueous

Solution Eirik F. da Silva, Tatyana Kuznetsova and Bjørn Kvamme

Potential Parameters of MEAa

Bond 0r [Å]

N-H 1.012

N-C 1.471

C-C 1.524

C-O 1.419

O-H 0.966


H-N-H 107.4 269.39

H-N-C 111.4 316.65

N-C-C 109 506.21

C-C-O 111.4 546.91

C-O-H 105.8 298.79

Dihedral C1a C2

a C3 a C4

a C5 a

H-N-C-C -11.05 -2.37 25.30 0.43 -2.02

N-C-C-O -17.78 23.60 36.81 -16.64 -13.32

C-C-O-H -19.15 -2.79 13.61 -0.12 1.55

Site σ [Å] ε [J/mole] q

H(N) 0 0 0.347

N 3.25 0.7108 -0.938

CH2 3.905 0.494 0.257

O 3.07 0.7108 -0.644

H(O) 0 0 0.374

a In KJ/mole.

Potential Parameters of CO2

Bond 0r [Å]

C-O 1.149


O-C-O 180 236.3

Site σ [Å] ε [J/mole] q

C 2.757 0.2334 0.6512

O 3.033 0.6694 -0.3256

a In kJ/mole.

Dihedral angle distribution for pure MEAa at 333K.

Dihedral angle distribution for pure MEAb at 333K.

Dihedral angle distribution for pure MEAb at 298K.

Dihedral angle distribution for 10 mol percent MEAa in aqueous solution at 333K.

Dihedral angle distribution for 10 mol percent MEAb in aqueous solution at 333K.

Paper VII

Comparison of Solvation Models in the Calculation of Amine Basicity

Eirik Falck da Silva, Takeshi Yamazaki and Fumio Hirata

2005

1

Theoretical Study of Amine Basicity in Solution with RISM-SCF Calculations and Free Energy

Perturbations

Eirik F. da Silva*, Takeshi Yamazaki and Fumio Hirata

Contribution from the Department of Chemical Engineering, Norwegian University of Science and

Technology, Trondheim, Norway and the Institute of Molecular Science, Okazaki, Japan

[email protected]

Abstract

The relative basicity of a series of 10 amines in aqueous solution was calculated with three separate sets

of solvation energies and gas phase basicities calculated at the B3LYP/6-311++G(d,p) level. The

solvation energies were calculated with RISM-SCF and two sets of Monte Carlo simulations. RISM-

SCF is a method combining ab initio solute description with the reference interaction site method in

statistical mechanics to describe solvation. The simulations were free energy perturbations with

classical force fields and charges derived from ab inito calculations. Two different types of charges

were studied. Both the RISM-SCF calculations and simulations produced results in reasonable

agreement with experimental data. The level of agreement between RISM-SCF and free energy

perturbations is consistent with the similarity in solute and solvent representation. Explicit solute

polarization, included in RISM-SCF but not simulations, did have a significant effect on relative

solvation energies. Solvation energies were found to be sensitive to the scheme utilized to determine

atomic charges.

2

Introduction

Many important chemical processes take place in solution and the effects of the solvent are often of

crucial importance. Solution phenomena are therefore of interest in many fields of chemistry, from

chemical engineering to biochemistry. Considerable effort has also gone into the study of solution

phenomena in computational chemistry, and while various methods in computational chemistry have

contributed to the understanding of solvation phenomena it is also clear that the modeling of solvation

effects remains challenging.

One of the solvation properties of greatest interest is the free energy of solvation. It is key both to

modeling chemical equilibrium in the solution and vapor-gas equilibrium. A fairly large number of

schemes have been developed to calculate the free energy of solvation. The most common forms of

solvation models in the context of computational chemistry are simulations and continuum models.

Some reviews offer general coverage of most schemes1-4 while others focus on continuum models. 5-6

In the present work the RISM-SCF method and simulations were used for the calculation of solvation

energy. RISM-SCF7-8 is a method developed from the statistical mechanics of molecular liquids. While

various forms of RISM have successfully been applied to a number of issues in the modeling of liquids9

it has still not received much attention as a general solvation model. The simulations were Monte Carlo

free energy perturbations (FEP). The RISM-SCF calculations and FEP were carried out with similar,

but different, solute and solvent representation. Comparison of the results serves to validate the

methodologies, and at the same time this can give insight into what effect differences in solute and

solvent representation have on calculated solvation energies.

The solvation energies obtained from RISM-SCF and simulations were used to calculate basicities of

a series of amine molecules. While estimates of free energy of solution can be made directly from

experimental data for neutral species, this is much more difficult for ionic species. Calculation of base,

or acid, strength offers an indirect route to testing the ability of a method to calculate the energy of both

3

neutral and ionic species. For base strength fairly accurate experimental data are available for a large

number of molecules.

It should be noted that both RISM-SCF and simulations can be used to acquire a microscopic picture

of solvation effects, for example in terms of radial distribution functions. In the present work we will

however focus on solvation energies and solute atomic charges.

The dissociation of the conjugate base of a molecule can be written as

2 3BH H O B H O+ ++ + (1)

assuming the molfraction based activity of water to be 1 and writing H3O+ as H+ the following

equilibrium constant is obtained:

B Ha

BH

a aK

a+

+

= (2)

The definition of pKa is:

loga apK K=− (3)

The free energy of protonation in aqueous solution ( psG∆ ) is related to Ka by the following equation:

2.303 logps aG RT K∆ =− (4)

This gives us the relation between pKa and psG∆ .

12.303a pspK G

RT= ∆ (5)

4

Model predictions for psG∆ should therefore give a linear correlation with the pKa.

The general approach for calculating psG∆ is to use a thermodynamic cycle:10

where pgG∆ is the gas phase basicity and the sG∆ ’s are the solvation energies of the different species

involved.

In the present work the relative basicity in solution, will be studied. The relative basicity is defined as:

( ) ( )refps g gG G B G B∆∆ =∆ −∆ (6)

Ammonia will be used as reference base ( refB ). The energy of the proton itself (H+) is not needed to

determine relative basicity and is not included in the calculations. Based on the thermodynamic cycle,

psG∆∆ can be divided into the relative gas phase basicity ( pgG∆∆ ) and contributions from solvation:

( )3 4( ) ( ) ( )pg g g g gG G B G NH G BH G NH+ +⎡ ⎤⎡ ⎤∆ = − − −⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ (7)

and

( ) [ ]3 4( ) ( ) ( ) ( )ps pg s s s sG G B G B G NH G BH G NH+ +⎡ ⎤∆∆ =∆∆ + ∆ −∆ − ∆ −∆⎢ ⎥⎣ ⎦ (8)

This can be written as:

( ) ( ) ( )ps pg s sG G B G B G BH +∆∆ =∆∆ +∆∆ −∆∆ (9)

Given a reasonably accurate model for the calculation of relative gas phase basicity the challenge is

reduced to calculating the relative solvation energies.

5

Methods

Gas Phase Basicity

The theoretical basicity of a series of amines at B3LYP/6-311++G(d,p) level with thermal

corrections to the free energy and the zero point energies (ZPE) calculated at HF/6-31G(d) level have

recently been published.11 It was in the same publication shown that basicities calculated at this level are

in good agreement with experimental values. For 2,2,6,6-Tetramethyl-4-piperidinol (TMP) we have

performed calculations at the same theoretical level as these published values. Gas phase energy

calculations were performed with Gaussian 98.12

Solvent Phase Geometry

Amine geometries were optimized in gas phase and the same geometries were used for all

calculations in solution. The RISM-SCF calculations were performed on gas phase HF/6-31G(d,p)

geometry, similar to what was utilized in a previous study.13 Simulations were carried out on HF/6-

31G(d) gas phase geometries. The RISM-SCF calculations were performed without optimization of

solute geometry. Optimization of solute geometry is in general expected to have a limited effect on

calculated energies, 14,15 something that should hold true for the fairly rigid molecules studied in the

present work. We have chosen to carry out calculations on a widely used and not particularly large

basis set. In this work we chose to calculate gas phase energies and geometry at a different level from

the solution phase calculations. While it might seem more consistent to use the same level of theory for

calculations in gas phase and in solution, it must be noted that the relationship between level of theory

and quality of results is not the same in the two phases. In gas phase a level of theory that is accurate in

calculating basicities is desired. For the solvation energy calculations partial atomic charges and

geometry are required as input, and the level of theory should be selected keeping these properties in

mind.

6

RISM-SCF

The Reference Interaction Site Model (RISM) is a method originally developed by Chandler and

Anderson16 in statistical mechanics for the description of interactions in molecular liquids. RISM-SCF7,8,

17 (Self-Consistent Field) is an extension that allows the simultaneous calculation of distribution of

solvent molecules and the electronic structure of the solute molecule. For the calculation of free energy

of solvation, the equation derived by Singer and Chandler is employed.18 In the present work the focus

will be on the molecular representation, for description of theory and method we refer the reader to

previous work.9

In the RISM-SCF framework, the solute molecule is described by ab initio electronic structure theory

and the solvent is represented by a classical force field. The interaction between the solute and solvent

is described as a sum of classical Coulomb and Lennard-Jones potentials. The Coulomb potential is the

potential between the partial charges of the solvent and partial charges of solute sites derived from the

electronic wave function of the solute molecule. In the present RISM-SCF calculations Hartree-Fock

theory is utilized. The contribution of the solvent reaction-field is introduced in the Fock operator of the

solute:8, 17

solv vacuumi i i

u

F F f V bλ λλ∈

= − ∑ (9)

where vacuumiF is the Fock operator in vacuum, if is the occupation number of orbital i and bλ is the

population operator that determines the partial charge on site λ in the solute molecule (subscript u ).

Vλ is obtained as the electrostatic potential on site λ in the solute molecule generated by the atomic

charges on the solvent molecules (subscript v ):

2

0

( )4uv

h rV q r drr

∞λα

λ∈ αα∈

= ρ π∑ ∫ (10)

7

where hλα is the pair correlation function between site λ on the solute molecule and siteα on the

solvent molecule. The pair correlation function is determined from the RISM equations.19 The solvent

effect is in this calculation represented by the microscopic distribution of the charges on the solvent

molecules. A RISM-SCF calculation begins with deriving solute partial atomic charges from the gas

phase electronic structure in a quantum mechanical calculation. From these partial atomic charges the

solute-solvent interactions are tabulated. The solvent structure around the solute is then calculated using

the RISM equation. The solute electronic structure and partial atomic charges are then recalculated from

the solvated Fock operator. These calculations proceed in an iterative cycle until the electronic structure

of the solute and solvent distribution converge.

Atomic charges are in the present RISM-SCF calculations represented with MK* charges described in

the following section. The solute Lennard-Jones parameters are from the all-atom OPLS force field.20,21

The choice was made to use the same Lennard-Jones parameters for the neutral and protonated forms of

the amines. The solvent was represented with the TIP3P22 water model. Hydrogen atom sites with zero

Lennard-Jones parameters in the OPLS force field are augmented with a small core to facilitate the

RISM calculations.8 Calculations were performed at 298.15K and a density of 0.997 g/cm3 (0.03334

molecules/Å). To improve convergence the modified-DIIS method for RISM was utilized.23 In the

present work the RISM equations were solved with the hyper-netted chain (HNC) approximation. 24 It

should be noted that the use of RISM with the HNC closure produces results that are known to

overestimate the effect of solute size on solvation energy.25 In the present work where the focus is on

calculating the relative solvation energies this effect is expected to cancel out.

Simulations

Monte Carlo FEP simulations were carried out in a NPT ensemble at 298.15K and 1 atmosphere

pressure. These calculations were performed with BOSS version 4.126 using procedures developed by

Jorgensen et al.20, 27 A single solute molecule was placed in a periodic cube with 267 TIP4P22 water

molecules. Periodic boundary conditions were applied. A number of water molecules corresponding to

8

the number (n) of non-hydrogen atoms in the amine molecule were removed, giving 267 - n water

molecules. The perturbations were carried out over 10 windows of double-wide sampling giving 20 free

energy increments that are summed up to give the total change in the free energy of solvation. Each

window had 500000 steps for equilibration and another 500000 for sampling. FEPs were used to

calculate the relative free energies between neutral species and in a separate series the relative free

energies of the protonated forms. Simulations were carried out between the amines closest in size.

The Lennard-Jones potential parameters from the all-atom OPLS force field20,21 ( same as used for the

RISM-SCF calculations) were utilized. These were used together with two different types of charges

derived from quantum mechanical calculations. The description of the charges is given in the following

section. These simulations are very similar in form to what has been presented by Wiberg et al.,28 the

main difference being the choice of routines to calculate the atomic charges.

The simulations, unlike the RISM-SCF calculations, are not deterministic and each perturbation has a

statistical uncertainty. This was by the batch means procedure20 determined to be between 0.1 to 0.5

kcal/mol for each simulation. While this uncertainty is significant it will be seen in the results that

energy differences are in general larger than these uncertainties.

In the present study the focus is on the description of solute partial atomic charges. The main

difference between the RISM-SCF and simulations lies in the schemes to calculate the atomic charges

and the use of a polarizable solute representation, in which the energy to polarize the solute is also

accounted for, in the RISM-SCF calculations.

Atomic Charges

In the RISM-SCF and the simulations atomic charges are used together with a Lennard-Jones

potential both in the solute and solvent representation. Intermolecular energies between molecules a and

b are then written in the following well-known form:

9

12 62on a on b

4i j ij ijab ij

i j ij ij ij

q q eE

r r r

⎧ ⎫⎡ ⎤⎪ ⎪⎛ ⎞ ⎛ ⎞σ σ⎪ ⎪⎢ ⎥⎟ ⎟⎜ ⎜⎪ ⎪⎟ ⎟⎜ ⎜∆ = + ε −⎨ ⎬⎢ ⎥⎟ ⎟⎜ ⎜⎟ ⎟⎪ ⎪⎟ ⎟⎜ ⎜⎢ ⎥⎝ ⎠ ⎝ ⎠⎪ ⎪⎣ ⎦⎪ ⎪⎩ ⎭∑∑ (11)

Where q is the atomic charge, ε and σ are the Lennard-Jones potential parameters. In both RISM-

SCF calculations and simulation, solute partial atomic charges derived from quantum mechanical

calculations were utilized. Atomic charges are not uniquely defined and a number of different schemes

for their calculation have been proposed. These are often based on reproducing some form of

observable quantities or properties from quantum mechanical calculations. One of the more common

schemes is to reproduce the electrostatic potential around the solute. Even for this approach there are

however a number of different implementations. 29-33 Singh and Kollmann29 developed a procedure based

on reproducing the electrostatic potential on gridpoints distributed spherically around each solute atom

center, outside the van der Waals volume of the solute. This scheme will in the present work be referred

to by its common acronym MK. In the RISM-SCF calculations a procedure similar to the one proposed

by Singh and Kollmann is utilized. A grid was set up with nine spherical layers around each atom

center. Layers with equal thickness were utilized, the inner having a radius of 1.5 Å and the outer a

radius of 2.4 Å. For each layer 36 gridpoints were evenly distributed. Any gridpoints within the van der

Waals radii of the solute atoms were disregarded. The atomic charges were then fitted to optimize the

agreement, as measured by the mean square error, with the electrostatic potential at these gridpoints.

Charges calculated by this procedure will be referred to as MK*. In the first cycle of the RISM-SCF

calculation the gas phase charges are calculated, the (converged) solution phase charges are obtained in

the final step of the iterative loop.

It has been observed by Besler, Merz and Kollman 34 that the Hartree-Fock 6-31G(d) procedure

overestimate gas phase dipole moments by 10-20%. The same authors suggest that charges calculated at

this level therefore implicitly account for solvation effects. This approach has later been implemented

by Cornell et al. 35 in a simulation force field. In the RISM-SCF calculation polarization is added to such

charges, and there might be a risk of overestimation of polarization in solution.

10

Simulations were carried out with charges derived from two different schemes. One scheme is

reproduction of the electrostatic potential in the gas phase. Here the standard Gaussian 9811 version of

the MK29 scheme was utilized. Charges were calculated at the HF/6-31G(d) level. Here gas phase values

were chosen. As noted above gas phase Hartree-Fock level charges are believed to be inherently high,

and we adopt the approach suggested by Besler et al. 34 of using these gas phase charges without

modification in solution. Free energy perturbations carried out with the combination of these charges

and the OPLS force field will be referred to as FEP-MK.

The second type of charges utilized in the simulations is CM236 charges calculated at the HF/6-31G(d)

level. While this model is also based on the quantum mechanical description of the solute, it involves

semi-empirical corrections to reproduce experimental gas phase dipole moments. With the CM2 charges

there is no implicit polarization present, and the charges should be adjusted to the levels one would

expect in solution. Here we chose to do the calculations with a continuum solvent model to obtain

solution phase charges. CM2 charges were therefore calculated with the SM 5.42R solvent field model37

in Gamesol.38 Free energy perturbations carried out with the combination of these charges and the OPLS

force field will be referred to as FEP-CM2.

While atomic charges are not uniquely defined some criteria have been presented for when they can

be considered reasonable. 32, 33 In the present work the purpose is to calculate solvation energies and in

this context we argue that the best charges are those that produce free energies of solvation closest to

experimental values. Charges should also take on values that are not unreasonably large and should

reflect molecular symmetry.

Molecules

In Figure 1 are shown the amine molecules studied. The purpose of the present study was to look at

how RISM-SCF and simulations perform in general prediction of solvation energies. The set of amines

was therefore chosen to include varied forms of molecular geometry. A second consideration in

selecting the amines has been to use molecules for which experimental gas phase and solution phase

11

basicity data are available. No gas phase value has however been reported for 2,2,6,6-Tetramethyl-4-

piperidinol (TMP). Finally the set has been limited to molecules with no conformers or known

conformers (piperazine). For piperazine calculations have been done on the chair-conformer.

Figure 1. Amine molecules studied.

Results

In Table 1 calculated and experimental gas phase basicity for the amines are shown. All data are

given relative to ammonia, a convention that will be used for all basicity results presented. While

neither experimental nor calculated gas phase basicites are likely to be completely accurate, the

agreement between the data offers a level of mutual validation. While no experimental data is available

for TMP, the agreement between theoretical and experimental results for the other molecules would

suggest that the level of theory is adequate for this molecule too. It should be noted that the present

values differ significantly from what have been used in previous studies13,14 on ammonia, methylamine,

dimethylamine and trimethylamine. The present values are in better agreement with currently accepted

experimental values (Table 1) and are likely to be the more accurate.

12

Table 1. Relative Gas Phase Protonation Energies. Data in [kcal/mol].

Molecule Theoreticala Experimentalb

Ammonia 0.0 0.0

Methylamine 10.2 10.9

Ethylamine 14.3 14.1

Dimethylamine 17.9 18.5

Trimethylamine 22.2 23.7

Piperidine 24.2 24.4

Piperazine 23.3 22.9

Morpholine 17.0 17.3

Pyrrolidine 23.6 23.0

2,2,6,6-Tetramethyl-4-piperidinol (TMP) 29.7

a B3LYP/6-311++G(d,p) energy with thermal correction and ZPE calculated at HF/6-31G(d), TMP data are from present work, other data from da Silva.11 b Data from Hunter and Lias.39

In Table 2 the atomic charges of the amine functionalities for the neutral amines are given and in

Table 3 data for the protonated forms are given. MK* charges are given both for gas phase and solution

(from RISM-SCF calculation). MK charges are in gas phase and CM2 charges are in solution (SM

5.42R solvation model). These are the same form of the charges as utilized in the energy calculations.

The MK* gas phase charges are however only used as a starting point for the RISM-SCF calculations.

13

Table 2. Partial Atomic Charges of Neutral Amines.

Molecule MK*

gas phase

MK*

solutiona

MK

gas phase

CM2

solutionb

N Hc N Hc N Hc N Hc

Ammonia -1.02 0.34 -1.28 0.43 -1.11 0.37 -0.86 0.29

Methylamine -1.01 0.35 -1.18 0.45 -1.03 0.38 -0.75 0.33

Ethylamine -1.02 0.35 -1.33 0.46 -1.06 0.37 -0.72 0.32

Dimethylamine -0.75 0.35 -0.96 0.44 -0.72 0.38 -0.55 0.28

Trimethylamine -0.41 ---- -0.55 ---- -0.23 ---- -0.41 ----

Piperidine -0.83 0.37 -1.17 0.52 -0.80 0.36 -0.54 0.28

Piperazine(1) -0.73 0.34 -0.94 0.43 -0.74 0.37 -0.53 0.27

Piperazine(2) -0.80 0.36 -1.07 0.47 -0.75 0.39 -0.54 0.28

Morpholine -0.82 0.38 -1.16 0.53 -0.77 0.37 -0.54 0.28

Pyrrolidine -0.81 0.30 -0.98 0.45 -0.75 0.35 -0.53 0.33

TMP -1.14 0.37 -1.67 0.52 -1.06 0.38 -0.52 0.35

a RISM-SCF method.b SM 5.42R solvation model. c Amine functionality hydrogen atoms, average value for amine group with more than one hydrogen atom.

14

Table 3. Partial Atomic Charges of Protonated Amines.

Molecule MK*

gas phase

MK*

solutiona

MK

gas phase

CM2

solutionb

N Hc N Hc N Hc N Hc

Ammonia -0.78 0.44 -0.81 0.45 -0.87 0.47 -0.52 0.38

Methylamine -0.21 0.31 -0.26 0.33 -0.30 0.32 -0.44 0.37

Ethylamine -0.65 0.39 -0.72 0.43 -0.69 0.40 -0.69 0.40

Dimethylamine -0.05 0.29 -0.06 0.33 -0.05 0.30 -0.34 0.35

Trimethylamine 0.17 0.31 0.14 0.37 0.08 0.34 -0.25 0.34

Piperidine -0.25 0.31 -0.29 0.35 -0.28 0.32 -0.32 0.35

Piperazine(1)d -0.23 0.33 -0.32 0.39 -0.22 0.33 -0.32 0.35

Piperazine(2) -0.83 0.42 -1.09 0.52 -0.81 0.42 -0.53 0.29

Morpholine -0.24 0.32 -0.33 0.38 -0.32 0.36 -0.32 0.36

Pyrrolidine -0.23 0.30 -0.28 0.35 -0.34 0.33 -0.53 0.33

TMP -0.13 0.22 -0.31 0.31 -0.93 0.45 -0.34 0.34

a RISM-SCF method.b SM 5.42R solvation model. c Amine functionality hydrogen atoms, average value for amine group with more than one hydrogen atom.d Protonated site.

It can be observed that in the RISM-SCF results polarization is significantly higher for the neutral

(unprotonated) amines than for the protonated forms. For the neutral species charges on the amine

functionalities can be seen to increase with 20-40% over the gas phase values, while the increase for the

protonated forms are around 10-20%.The same observation was made in previous RISM-SCF work.13 It

was in that work suggested that this was caused by the (uncharged) amines producing an anisotropic

field in the solvent, which again causes an anisotropic reaction field on the solute giving additional

electrical polarization. The protonated amines will on the other hand produce a more isotropic field and

the same effect will not be seen. Most of the amines show comparable level of increases in charges in

soultion, but particularly large increases can be observed for neutral (uncharged) TMP, piperidine and

morpholine. For TMP the value would appear to be greater than what can be considered physically

reasonable.

15

The amine functionalities and their representation are expected to be the most important in

determining the solvation behavior of the molecules. Some observations will however be made on the

other charges, the full set of data is given in the supporting information.

In most cases neutral amine gas phase MK* and MK were in reasonable agreement. Carbon charges

were mostly in a range between 0 to 0.4, while hydrogen charges were close to zero. For trimethylamine

the average MK carbon charge was however –0.29 while the average MK* value was 0.07. In some

cases MK and MK* charges took on unreasonable high values. For TMP the MK carbon charges varied

between 0.87 and –0.53, while the MK* charges varied between 0.88 and -0.41. In most cases MK and

MK* charges were quite similar for atoms in symmetrically equivalent positions. Both MK and MK*

charges were however somewhat different for carbons in equivalent positions in morpholine.

The CM2 charges for the alkane functionalities were much more stable, reflecting the different nature

of the model. Carbon charges stayed mostly in a range of 0 to –0.3 for neutral amines. Alkane-

hydrogens mostly had charges around 0.1. The CM2 charges did in general display values that would

appear not to be unreasonable in terms of the dimension of the charges.

In summary it can be observed that MK* and MK charges are quite similar, which is reassuring since

they are only variations of fittings to the same electrostatic potential. The trends in charges for different

molecules would seem to be similar for the MK and CM2 charges. The CM2 charges are however

systematically lower than the MK charges, despite the fact that CM2 charges have been scaled up from

their gas phase values with the use of a continuum model. The MK/MK* charges also tend to fluctuate

more than the CM2 charges, this being particularly true for sp3 carbon atoms.

In Table 4 the relative solvation energies are shown, while in Table 5 the experimental pKa values and

relative basicity in solution calculated from these are shown together with the basicity in solution

derived from RISM-SCF and simulations.

16

Table 4. Total Relative Solvation Energy Contribution. Data in [kcal/mol].

( ) ( )s sG B G BH +∆∆ −∆∆ Molecule

RISM-SCF FEP-MK FEP-CM2

Ammonia 0 0.0 0.0

Methylamine -8.7 -10.4 -8.2

Ethylamine -9.3 -12.0 -9.1

Dimethylamine -14.0 -14.6 -14.8

Trimethylamine -17.4 -18.3 -22.4

Piperidine -23.7 -23.0 -17.9

Piperazine -19.3 -21.6 -17.2

Morpholine -19.3 -15.2 -14.4

Pyrrolidine -18.5 -18.4 -20.9

TMP -33.2 -21.1 -24.0

Table 5. Relative Basicity in solution. Data in [kcal/mol].

Molecule exptl pKa

psG∆∆ a

exptl RISM-SCF FEP-MK FEP-CM2

Ammonia 9.24b 0.00 0.0 0.0 0.0

Methylamine 10.65b 1.92 1.5 -0.2 2.1

Ethylamine 10.78b 2.10 5.0 2.3 5.3

Dimethylamine 10.8b 2.13 3.9 3.3 3.1

Trimethylamine 9.80b 0.90 4.8 3.9 -0.2

Piperidine 11.12c 2.56 0.5 1.2 6.3

Piperazine 9.83c 0.80 4.0 1.7 6.1

Morpholine 8.49c -1.02 -2.3 1.7 2.6

Pyrrolidine 11.30c 2.81 5.1 5.2 2.7

TMP 10.05c 1.10 -3.5 8.6 5.7

a Energies relative to ammonia. b Data from Jones and Arnett.10 c Data from Perrin.40

17

In Figure 2 the calculated gas phase basicities are plotted against the experimental pKa of the amines,

the low correlation in this plot shows how important the solvation energies are in determining basicity

in solution. In Figure 3 the relative pKa values calculated from RISM-SCF and FEP-MK are plotted

against the experimental pKa. In Figure 4 the pKa values determined from FEP-MK and FEP-CM2 are

plotted against experimental pKa. The stippled line in the figures indicates the theoretical ratio between

pKa and protonation energy from equation 5. All data are relative to ammonia.

Figure 2. Calculated gas phase basicity versus experimental pKa. The stippled line indicates the

theoretical trend relative to ammonia.

18

Figure 3. Calculated pKa versus experimental pKa. Crosshairs are RISM-SCF and Open circles are FEP-

MK. The stippled line indicates the theoretical trend relative to ammonia.

Figure 4. Calculated pKa versus experimental pKa. Open circles are FEP-MK and black circles are FEP-

CM2. The stippled line indicates the theoretical trend relative to ammonia.

19

In Figure 5 the contributions to the RISM-SCF solvation energy are shown together with the FEP-MK

solvation energies. The contributions to the RISM-SCF solvation energy are the solute polarization and

excess chemical potential from interactions with the solvent. The plot shows the solute polarization to

have a relatively small, but significant, effect on relative solvation energies. The figure also illustrates

the good overall agreement between RISM-SCF and FEP-MK solvation energies.

Figure 5. Contributions to RISM-SCF solvation energies. RISM-SCF (Electronic) refers to the solute

polarization energy. RISM-SCF (Excess) refers to the excess chemical potential from interactions with

the solvent.

20

Discussion

Basicity

Looking at Figures 3 and 4 it can be seen that neither RISM-SCF nor simulations produce full

quantitative agreement with experimental data. Comparing the solvation models results with the gas

phase energies in Figure 2 it can however be seen that the large gap between relative energies in the gas

phase and solution is closed. It must also be kept in mind that this set of amines contains large

variations in geometry and that the experimental energy differences to be reproduced are relatively

small.

The RISM-SCF results are mostly in reasonable agreement with the experimental data. The largest

error was for TMP. As noted in the Results section the MK* charges for this molecule were very high.

These charges are most likely the cause of the inaccurate solvation energies.

The present results differ somewhat from previous RISM-SCF results13 for ammonia, methylamine,

dimethylamine and trimethylamine. This is due to changes in the scheme to calculate atomic charges,

illustrating the sensitivity of the results to the choice of scheme.

The FEP-MK simulations and RISM-SCF calculations utilize similar charges, same Lennard-Jones

potential and similar solvent representation (TIP4P and TIP3P respectively). The agreement between

the results (Figure 3 and Figure 5) is consistent with the underlying similarities in solute and solvent

representation. For TMP the FEP-MK results and RISM-SCF results differ strongly from each other and

neither is close to the experimental value. In this case the MK and MK* charges were quite different,

both taking on unreasonable values. For morpholine the RISM-SCF result was in better agreement with

the experimental data than the FEP-MK result. This difference is probably due to the increase of solute

charges from solvent polarization in the RISM-SCF model. In this particular case this contribution

would appear to be necessary to predict the basicity relative to ammonia.

The FEP-MK and FEP-CM2 simulations only differ in the scheme to calculate atomic charges.

Comparing the two sets of results in Figure 4 one can see that the choice of scheme for calculating

atomic charges has a considerable effect on the solvation energies.

21

Some previous studies13,14 have looked at the irregular trend in basicity for the series ammonia,

methylamine, dimethylamine and trimethylamine. Both the RISM-SCF and simulations give a

decreasing trend in solvation energy of the protonated forms of these amines and stable values for the

neutral forms. If this trend in the solvation energies is taken together with the increasing trend in gas

phase basicities the irregular order in basicity is readily accounted for. The models can therefore be said

to capture this in a qualitative sense. At a quantitative level none of the models is however accurate

enough to confidently reproduce the small energy differences involved.

Atomic Charges

It can clearly be seen from the results, both for RISM-SCF and simulations, that the free energies are

sensitive to the scheme for calculating atomic charges. Some examples are also seen in the present study

of MK and MK* charges taking on unphysical values resulting in unreasonable solvation energies. This

is related to a known issue41 with fitting charges to the electrostatic potential: if an atomic center is far

away from the grid points in the fitting its value becomes ill-determined and the charges can fluctuate

dramatically without significantly altering the quality of the fit. This is often the case for sp3-carbons, in

the fitting they can become buried behind the atoms they are bonded to. In the present work the problem

was particularly large for TMP. This is not surprising given the structure of the molecule. Because of

the methyl substituents there are few gridpoints close to the amine functionality. Several atoms are

almost completely buried. This can result in charges that fluctuate widely. In the RISM-SCF

calculations polarization effects are added and ill-determined charges can fluctuate even more.

It has been suggested that this problem can be handled by adding constraints on the fitting. In the

RESP41 procedure the carbon-charges are constrained. This approach should resolve some of the

problems seen in the present work, but further work is perhaps needed to determine what are the best

constraining conditions for free energy calculations. A hybridization between fitting to the electrostatic

potential and semi-empirical corrections to reproduce different properties has also been proposed.42

Another modification that might improve the fitting is to include Boltzmann-weighting of the points

22

being fitted.32 It is clear that fitting atomic charges to the electrostatic potential is difficult and with the

scheme used in the present work not entirely reliable. The proposals to improve the fitting schemes do

however suggest that this approach to determine atomic charges can be developed further.

As noted in the Methods section the addition of solvent polarization to already high Hartree-Fock

level charges in the RISM-SCF calculations might result in too high charges. In future work the RISM-

SCF calculations should perhaps be performed at another level of theory or with some form of scaling

of charges to correct for the overestimation.

RISM-SCF

Improvement of the schemes to calculate the atomic charges are likely to lead to a more accurate

RISM-SCF model. Work has also been done on directly calculating the interaction between solvent

molecules and the electrostatic field of the solute,42 an approach that eliminates the task of determining

atomic charges.

One important approximation in the present work, and most simulations, is the use of a solvent model

with fixed charges. It has been suggested44 that introduction of polarizable solvent models have a

significant effect on solvation energies. This is an issue that should be explored further.

All together this would suggest that there is room for further refinement of the RISM-SCF method to

produce a general and accurate solvation model. It should also be noted that the present implementation

of RISM-SCF is fairly robust in terms of convergence.

Simulations

As with the RISM-SCF calculations the main issue with the simulations is the calculation of atomic

charges. In the simulations it is however less clear how polarization effects should be incorporated. In

the present work a continuum model and inherently high Hartree-Fock level charges have been used to

obtain charges in solution. In the literature other schemes can also be found such as scaling up gas phase

values and calculating the polarization from the average electrostatic potential of the solvent in

23

QM/MM simulations.45 Charges derived from RISM-SCF calculations could also be an interesting

option in simulations, particularly as they are derived in the context of the same solvent representation.

The choice of scheme to calculate charges is clearly of great importance and is likely to remain an area

of active research.

In RISM-SCF the charges include polarization effects and the energy to polarize the solute is included

when determining the solvation. It remains to be determined if and how this contribution should be

accounted for in simulations.

Conclusions

In the present work RISM-SCF and simulations have been used to calculate the relative basicity of a

series of 10 amine molecules. Results showed mostly reasonable agreement between experimental data

and calculated values. The results were however found to be sensitive to the scheme for calculation of

atomic charges. None of the methods used for determining charges in the present work were found to be

completely satisfactory. There would however appear to be a number of ways in which such schemes

can be improved upon. Comparison between results with (RISM-SCF) and without (simulations)

polarizable solute representation suggests that polarization can have a significant effect on relative

solvation energies.

Acknowledgment

Gratitude is expressed to the Japan-Norway Sasakawa foundation for supporting a visit by Eirik F. da

Silva to the Institute for Molecular Science.

24

Supporting Information Available:

Atomic charges for alkane and alcohol groups, Lennard-Jones force field parameters and data utlized

in Figure 5 are given in the supporting information. This material is available free of charge via the

Internet at http://pubs.acs.org.

25

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29

Appendix 1

OPLS Lennard Jones Parameters

[Å]

[kcal/mol]

q

electron units

N-Amine 3.3 0.17

N-Ammonia 3.42 0.17

H(N)-Amine 0.0 (1.0)a 0.0 (0.056) a

C-Carbon 3.5 0.066

H(C(N))-Hydrogen on carbon bonded to amine 2.5 0.015

H(C) Alkane 2.5 0.030

O-Alcohol 3.12 0.17

H(O) Alcohol 0.0 (1.0) a 0.0 (0.056) a

O-Morpholine 2.9 0.14

O-TIP3P 3.15061 0.1521 -0.834

H-TIP3P 0.0 (1.0) a 0.0 (0.015) a 0.417

O-TIP4P 3.15365 0.155 0.0

H-TIP4P 0.0 0.0 0.52

M-TIP4P 0.0 0.0 -1.040

a Parameters utilized in RISM-SCF calculations that differ from the standard values are given in parenthesis.

30

Appendix 2

Partial Atomic Charges of Alkane and Oxygen/Alcohol in Neutral Amines

Molecule sitea MK*

gas phase

MK*

solutionb

MK

gas phase

CM2

solutionc

C/Od Hd C/Od Hd C/Od Hd C/Od Hd

Methylamine-C 0.58 -0.09 0.69 -0.10 0.38 -0.04 -0.35 0.15

Ethylamine-C1 0.58 -0.07 0.69 -0.07 0.54 -0.06 -0.22 0.14

Ethylamine-C2 -0.27 0.07 -0.36 0.08 -0.33 0.08 -0.43 0.15

Dimethylamine-C 0.23 -0.02 0.26 0.00 0.05 0.04 -0.10 0.08

Trimethylamine-C 0.07 0.03 0.07 0.04 -0.29 0.12 -0.10 0.08

Piperidine-C1,C5 0.24 0.01 0.27 0.04 0.20 0.01 -0.01 0.09

Piperidine-C2, C4 -0.12 0.03 -0.23 0.07 -0.13 0.01 -0.16 0.09

Piperidine-C3 0.12 -0.01 0.13 0.00 0.11 0.02 -0.16 0.09

Piperazine-C2, C5 0.21 -0.02 0.23 0.00 0.00 0.06 -0.19 0.08

Piperazine-C3, C4 0.27 -0.03 0.35 -0.02 0.12 0.06 -0.20 0.08

Morpholine-C2 0.21 0.00 0.25 0.04 0.12 0.04 -0.02 0.08

Morpholine-C5 0.27 -0.01 0.33 0.02 0.20 0.02 -0.02 0.08

Morpholine- C3, C4 0.10 0.04 0.07 0.07 0.06 0.07 0.00 0.08

Morpholine-O -0.41 -0.52 -0.40 -0.33

Pyrrolidine-C1 0.26 -0.03 0.25 0.00 0.16 0.01 -0.20 0.14

Pyrrolidine-C4 0.26 -0.03 0.25 0.00 0.22 0.00 -0.20 0.14

Pyrrolidine-C2 0.03 -0.01 0.01 0.00 -0.04 0.03 -0.28 0.15

Pyrrolidine-C3 0.03 -0.01 0.01 0.00 -0.08 0.03 -0.28 0.15

TMP-C1,C5 0.88 1.15 0.82 0.13

TMP-C2,C4 -0.37 0.06 -0.39 0.05 -0.44 0.11 -0.16 0.08

TMP-C3 0.69 -0.13 0.72 -0.11 0.59 0.02 0.07 0.08

TMP-CH3 -0.41 0.08 -0.42 0.07 -0.53 0.11 -0.25 0.08

TMP-O -0.70 0.42 -0.90 0.51 -0.75 0.43 -0.49 0.27

a For symmetric sites average charges are given except when they diverge significantly. The carbon given the number 1 is bonded to the amine, the carbon bonded to C1 is given the number C2 and so on.

b RISM-SCF method. c SM 5.42R solvation model. d Average value in case of more than atom.

31

Partial Atomic Charges of Alkane and Oxygen/Alcohol in Protonated Amines

Moleculea MK*

gas phase

MK*

solutionb

MK

gas phase

CM2

solutionc

C/Od Hd C/Od Hd C/Od Hd C/Od Hd

Methylamine-C -0.14 0.14 -0.13 0.13 -0.02 0.11 -0.09 0.14

Ethylamine-C1 0.42 0.06 0.57 0.02 -0.22 0.26 -0.19 0.20

Ethylamine-C2 -0.84 0.26 -1.07 0.30 -0.52 0.22 -0.43 0.17

Dimethylamine-C -0.23 0.15 -0.23 0.14 -0.37 0.26 -0.09 0.20

Trimethylamine-C -0.32 0.17 -0.33 0.16 -0.35 0.25 -0.10 0.13

Piperidine-C1,C5 0.04 0.08 0.06 0.08 0.01 0.10 -0.01 0.11

Piperidine-C2, C4 -0.03 0.05 -0.03 0.04 -0.08 0.07 -0.01 0.11

Piperidine-C3 0.01 0.03 0.02 0.02 -0.04 0.06 -0.01 0.13

Piperazine-C2, C5 -0.12 0.13 -0.14 0.14 -0.13 0.14 -0.16 0.16

Piperazine-C3, C4 0.22 0.05 0.28 0.06 0.19 0.07 -0.15 0.15

Morpholine-C2 -0.07 0.12 -0.01 0.11 0.12 0.14 -0.02 0.14

Morpholine-C5 -0.07 0.12 -0.01 0.11 -0.11 0.10 -0.02 0.14

Morpholine-C3 0.19 0.07 0.22 0.07 -0.08 0.13 -0.01 0.10

Morpholine-C4 0.19 0.07 0.22 0.07 0.14 0.10 -0.01 0.10

Morpholine-O -0.41 -0.53 -0.41 -0.33

Pyrrolidine-C1,C4 0.06 0.08 0.09 0.08 0.08 0.08 -0.17 0.26

Pyrrolidine-C2,C3 -0.04 0.07 -0.07 0.06 -0.03 0.06 -0.27 0.23

TMP-C1,C5 0.45 0.61 0.66 0.14

TMP-C2,C4 -0.34 0.11 -0.39 0.11 -0.50 0.16 -0.16 0.10

TMP-C3 0.50 -0.04 0.61 -0.04 0.58 0.06 0.06 0.09

TMP-CH3 -0.44 0.13 -0.50 0.13 -0.56 0.16 -0.26 0.11

TMP-O -0.69 0.44 -0.85 0.51 -0.71 0.45 -0.48 0.35

a For symmetric sites average charges are given except when they diverge significantly. The carbon given the number 1 is bonded to the amine, the carbon bonded to C1 is given the number C2 and so on.

b RISM-SCF method. c SM 5.42R solvation model. d Average value in case of more than atom.

32

Appendix 3

RISM-SCF Relative Solvation Energy Contributions. Data in [kcal/mol].

excess chemical potential

solute polarization energy

Ammonia 0.00 0.00

Methylamine -8.46 -0.21

Ethylamine -7.94 -1.38

Dimethylamine -13.14 -0.85

Trimethylamine -15.53 -1.82

Piperidine -25.84 2.19

Piperazine -17.90 -1.39

Morpholine -19.29 -0.04

Pyrrolidine -17.65 -0.84

TMP -35.52 2.30

Doctor Thesis-Eirik Falck Da Silva

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