Research Article An Assessment of Alternative Low Level...

Research ArticleAn Assessment of Alternative Low Level Calculation Methods forthe Initial Selection of Conformers of Diastereomeric Esters

Andrus Metsala1 Sven Tamp1 Kady Danilas1 Uumllo Lille1 Ly Villo1 Sirje Vija2

Totildenis Pehk2 and Omar Parve1

1 Department of Chemistry Tallinn University of Technology Ehitajate Tee 5 19086 Tallinn Estonia2National Institute of Chemical Physics and Biophysics Akadeemia Tee 23 12618 Tallinn Estonia

Correspondence should be addressed to Andrus Metsala metsalachemnetee

Received 21 January 2014 Revised 25 May 2014 Accepted 27 May 2014 Published 23 June 2014

Academic Editor Qingfeng Ge

Copyright copy 2014 Andrus Metsala et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Critical assessment of performance of alternative molecular modeling methods depending on a specific object and goal of theinvestigation is a question of continuous interest This prompted us to demonstrate the origin of the guidelines we have usedfor a rational choice and use of a proper low level calculation method (LLM) for an initial geometry optimization of generatedconformers with the aim of selecting a set for further optimizationWhat was performed herein was a comparison of LLMs MM3MM+ UFF Dreiding AM1 PM3 and PM6 on the optimization of conformersrsquo geometry of 120572-methoxyphenylacetic acid (MPA)2-butyl esters as a set of typical diastereomeric esters of a chiral derivatizing agent This set of esters calculated represents onlycompounds of this certain type in the current work The LLM conformer energies were correlated with benchmark energies foundby using higher level reference method B3LYP6-311++Glowastlowast on the geometries gained previously by optimization with LLMs Inan alternative treatment the energy range to be covered and corresponding number of LLM optimized conformers obligatory forsubmitting to further optimization using a high level optimization cascade were considered on the basis of determination of thecut-off conformer (COFC)

1 Introduction

Critical assessment of performance of different alternativemolecular modeling methods depending on the particularobjects and specific goals is a question of continuous interest[1ndash7] The aim of the current work is to demonstrate howthe guidelines are derived for a rational choice of a properlow level calculation method (LLM) for the initial geometryoptimization of generated conformers in the total confor-mational analysis of diastereomeric esters The LLM chosenshould allow selecting of a reliable set of conformers forfurther higher level optimizationHaving previously followedsuch guidelines in the total conformational analysis of severalesters with up to 11 dihedrals in their structure the initialoptimization of thousands of conformers all together haveafforded reliable sets of conformers The following higherlevel optimization of the selected conformers has led to theresults that in turn have allowed calculation of themolecular

shielding models in exceptional accordance with differentialshielding effects in the NMR spectra [8]

The properties of organic compounds are dependent ontheir three-dimensional structures Knowing the prevailingconformer [1] of certain compounds or population of reactiveconformers of molecules of another type is often a key tounderstanding their spectral properties or stereochemistryof the reactions under various experimental conditionsrespectively The most frequently used approach is to studythe conformersrsquo geometry and relative energy as well as theirbarriers to the rotational interconversion

The theoretical conformational analysis enables a reliableestimation of the geometrical structure and energy of eachconformer in a set of conformers and from such resultsvarious thermochemical parameters and spectral charac-teristics (NMR coupling constants and chemical shifts IRvibration modes etc) can be derived Density functionaltheory (DFT) [9] calculations have proved successful in

Hindawi Publishing CorporationJournal of eoretical ChemistryVolume 2014 Article ID 714164 10 pageshttpdxdoiorg1011552014714164

2 Journal of Theoretical Chemistry

numerous studies based on theoretical conformational anal-ysis [10] Although geometrical parameters such as bondlengths angles and dihedrals can be reasonably accuratelypredicted on molecular mechanical and semiempirical levelsof theory the electron correlation effects are important forquantitative considerations These effects significantly affectthe conformer energies as well as rotational barriers betweenvarious conformers and should therefore certainly be takeninto account in the total conformational analysis

DFT and the hybrid B3LYP functional have allowedaccurate computation of the geometries concerning the typeof molecules under study [8] This in turn has allowedcalculating NMR and IR spectral characteristics in very goodagreement with the experimental data [8 11 12] The DFmethod using the B3LYP hybrid functional has been provento give a good estimate of the electron correlation for somemolecules in particular in conformational studies when it isused with the 6-31Glowast or 6-311++Glowastlowast basis set [13 14]

Semiempirical methods (AM1 PM3) have been shown tooverestimate the number of minima on the potential energysurface (PES) and underestimate the internal rotationalbarriers for substituted hydrazines [13] Several force fieldshave been assessed by comparing calculated conformationalenergies in relation to MP2aug-cc-pVTZ level benchmarkenergies for compounds with varying polarity The qualityof the results degraded along with increasing polarity of themoleculeThis effect was attributed to insufficient descriptionof the electrostatic term by using fixed partial charges in forcefields [15]

The attempts to simplify conformational analysis arealways problematic In particular limiting the number ofconformations or setting certain geometrical constraints onthe molecules under study can give a poor description ofthe PES leading to erroneous results Therefore if the subjectmolecule is conformationally flexible and contains manydihedrals with low potential energy barriers a systematicsearch for conformers should be undertaken

Identification of and involving all low energy conformersis important in a sense that compoundsrsquo certain physico-chemical properties as a rule depend on the whole confor-mational ensemble not just on the conformer correspondingto the global minimum on the PES However investigationof only the energetically most favored conformer may givegood results in some cases [1] An example of this approachis reproducing NMR spectral parameters (chemical shiftscoupling constants) of flexible organic compounds at theDFTlevel using the Boltzmann distribution [16] A systematicsearch for conformers and also taking into account the Boltz-mann weighting of individual conformers have allowed thecalculation of the circular dichroism spectra of macrocycliclactones (by using the time dependent DFT method) in avery good correlation with experimental spectra [17] Thesame approach has allowed an accurate estimation of theyield of hydroxybenzophenones in the Fries rearrangementof hydroxyphenyl benzoates [14]

Usual procedure of conformational analysis involves thegeneration of conformers by automated means using aconformational search algorithm (stochastic Monte Carlosimulated annealing genetic algorithm etc) followed by

the initial optimization of the geometry of the generatedstructures with the help of molecular mechanical or asemiempiricalmethodThe further refinement of conformersis carried out on higher theoretical levels at the same timediscarding higher energy conformers After optimization ofall structures at a certain level of theory a geometrical analogycomparison is used to identify duplicates This is carried outby RMS values of geometrical deviation of the positions ofthe atoms of one conformer in relation to other conformers[18] The cascade of calculations is usually finalized by usinga higher level DFT method

The purpose of the present study is to show how thechoice of the initial low level optimization method and thedetails of its use can influence the outcome of the total con-formational analysis consisting of a cascade of optimizationsincluding relatively high-level calculations at the final stageMore specifically the aim is to elucidate which initial methodpermits reducing most efficiently the number of conformersnecessary to be optimized at the higher level Another aim isto provide certain criteria that could be relied on in order toguarantee obtaining reliable results along with an optimizedfeasibility of calculations In this regard the key feature is theestimation of the conformer energy range for a certain initialcalculationmethodmarking the conformers to be selected forfurther calculations This should guarantee that the analyzerdoes not miss any important conformer at the initial stage ofoptimization

As to the contents this paper will firstly tackle the ques-tion ofmain correlational parameters such as slope interceptand the coefficient of correlation between the results of testedLLMs and the benchmark energies calculated using higherlevel reference method (RefM1) A satisfactory correlationis obligatory for an LLM to be used in the initial stageof conformational analysis However these correlationalparameters are still by themselves insufficient for a correctevaluation of the prospective quality of calculation results tobe obtained just by using the LLM Secondly the estimation ofthe energy ranges for the initially LLM-optimized conformersto be selected for further optimization is considered

In addition a critical consideration is given to theapproach within the systematic theoretical conformationalanalysis according to which decisive conclusions about therelative energies and corresponding distribution of con-formers are drawn on the basis of results obtained usingmerely an LLM The accuracy of the LLMs for calculationof conformational energies as compared to the benchmarkvalues has been assessed

For the current research 120572-methoxyphenylacetic acid(MPA) 2-butyl esters (Figure 1) were chosen as subject com-pounds They are diastereomeric esters of the well-knownchiral derivatizing agent for NMR spectroscopic analysis [819ndash21] In the current work they are mere model compoundsfor calculation (Figure 1)TheMPA esters are not too elemen-tary in conformational sense yet the optimization of theirconformers is possible by using higher level methods suchas B3LYP6-311++Glowastlowast included into the cascade protocol foroptimization (RefM2) in the current work

The calculations have been performed in gas phase Thisis justified by very good accordance achieved in between

Journal of Theoretical Chemistry 3

OMeO

HO

H

CH3C H2

CH3

Figure 1 2-Butyl esters of MPA

the shielding models calculated in this environment and theNMR data measured in the CDCl

3[8]

2 Theoretical Approach

21 Abbreviations

PES Potential energy surfaceMPA 120572-Methoxyphenylacetic acidLLM Low level calculation methodRefM1 The first reference method is ldquothe single pointcalculation of conformer energy using B3LYP6-311++Glowastlowast methodrdquo (Step 3 Figure 2) this is thesingle point calculation of conformer energy for theconformersrsquo geometries optimized with LLMs (Steps1 and 2 Figure 2)RefM2 The second reference method is ldquothe highlevel conformational analysis using cascade pro-cedure for optimization of conformersrdquo (Step 4Figure 2)RefM3 B97D Grimmersquos functional including disper-sion the basis set is the same as RefM2 (6-311++Glowastlowast)COFC ldquoCut-off conformerrdquo this is a conformercharacterized by the highest conformer energy in aseries of LLM optimized conformers selected for fur-ther calculation (Steps 1 and 2 Figure 2) these con-formers have been selected as corresponding to thelower energy conformers (up to 100 kcalmol) thatwere found by optimization of all conformers usingthe high level RefM2 (Step 4 Figure 2) The COFCenergy determines an energy range for conformersof an LLM potentially involving all lower energyconformers to be submitted for further optimization

22 Computational Strategy In order to achieve the goals ofthe research the following five-step computational procedurewas performed (Figure 2)

(1) The initial task was to find all the local minima overall configurations of the stereocenters of the MPA diastere-omeric esters (Figure 1)The conformational landscape of thePES has been explored using the program Tinker (Figure 2)[22] (module SCAN) This program performs a generalconformational search for the entire PES by using a basinhopping algorithm [23] which is able to overcome poten-tial energy barriers The basin hopping algorithm exploresthe PES along various normal modes from the initial local

minimum When all minima on the search list have beensubjected to the normal mode activation without locatingadditional new minima the program terminates Thus thescanning time for this program is not unlimited and it alsominimizes the energy of each conformer after it has beengeneratedTheMM3 force field chosen for this minimizationis known to be well parameterized for many organic com-pounds [24]

(2) All the conformers generated by the Tinker programwere optimized withMM3 (Step 1 Figure 2)The conformersobtained were further optimized also with all the other LLMsunder test molecular mechanical MM+ UFF Dreiding andsemiempirical methods AM1 PM3 PM6 (Step 2 Figure 2)The initial optimization of the conformers in this workwith MM3 may in principle bias the results towards thismethod This is because conformations may be lost in thisfirst reminimization step which would be included if separateconformation searches were done with each force fieldHowever this assumption is not valid It has been proven byexceptional accordance of experimental NMR shielding data[8] with the results of the theoretical calculations performedignoring the matter of the above assumption Consequentlythe MM3 conformer energies might be comparable withoutrestrictionswith the conformer energies obtained using otherLLMs

(3) The quality of the LLMs was initially evaluated (theconformer energies correlated) on the basis of single pointDFT B3LYP6-311++Glowastlowast calculation of conformer energies(RefM1) (Step 3 Figure 2) on the previously optimized forcefield and semiempirical (LLM) geometries

(4) The conformers resulting from the above conforma-tional search (from Step 1 Figure 2) were further geometryoptimized in a sequential treatment (Step 4 Figure 2) withthe help of the Gaussian 09 program [25] The initial com-putational level used was the Hartree-Fock method with anSTO-3G basis set These 119886119887 119894119899119894119905119894119900 calculated structures wereused as input structures for the density functional methodusing the hybrid B3LYP exchange correlation functional and3-21G basis set (ie B3LYP3-21G) Similarly the output ofthe latter method was used as an input for the B3LYP6-31G method The optimization cascade was finalized atthe B3LYP6-311++Glowastlowast level This cascade methodology forconformational analysis is referred to in the current text asRefM2

Every optimization step was followed by a geometricalcomparison of conformers with the aim of extracting uniquestructures based on a geometrical RMS criterion (lt20 A)Progressing towards higher levels of calculation some of theconformers converge on each other resulting in substantiallyreduced number of conformers to be optimized at the highestlevel

Additionally the frequency analysis was performed atthe highest optimization level This was done in order toverify that every optimized conformer corresponds to a localminimum on the PES that is to a stationary point with noimaginary frequencies

(5) All the conformers obtained by means of the aboveoptimization cascade (Step 4 Figure 2) that fall into energyrange of 0ndash100 kcalmol were subjected to the optimization


Step 3

Step 1Step 2

Step 4

Step 5

DFT

DFT

DFT

DFT DFT

DFT

DFT

PM3

AM1

PM3

AM1

UFF

UFF

TinkerMM3

MM3

PM6

PM6

MM+ MM+

Dreiding Dreiding

HFSTO-3G

B3LYP

B3LYP

B3LYP

3-21G

6-31G

6-311++Glowastlowast

AM1

PM3

MM3

HFSTO-3G PM6

MM+

UFF

Dreiding

Figure 2 Flow chart of the calculations (Step 1 generation of conformers followed by the initial optimization using MM3 method Step 2optimization of the conformers by using LLMs Step 3 single-point calculation of the conformer energies by using the reference methodDFT B3LYP6-311++Glowastlowast (RefM1) Step 4 the sequential optimization cascade of conformational analysis (RefM2) Step 5 optimization ofthe refined conformers for their identification by using the LLMs) performed

with all the LLMs under study (Step 5 Figure 2) It shouldbe emphasized that Step 5 is necessary for identification ofthe conformers optimized in Steps 1 and 2 among geometriesobtained finally in Step 4

(6) In order to explore the accuracy of themethodologicaltreatment presented on scheme (Figure 2) with respect toother high level reference methods an additional methodsuch as B97D (Grimmersquos functional including dispersion)[26] is added using the same basis set (6-311++Glowastlowast) as inRefM2 B97D method uses density functional constructedwith a long-range dispersion correction We label the latterreference method as RefM3 in our text

For low level calculation using semiempirical methods[27] AM1 [28 29] PM3 [30] and PM6 [31] molecularmechanical methods UFF [32] (UFF uses charges calculatedby the method of charge equilibration [33]) and Dreiding[34] the Gaussian 09 program [25] was used while for theMM+method [35] the Hyperchem program [36] and for theMM3 the Tinker Program [22] were used instead

3 Results

Steps 1 and 2 The test set of conformers of MPA 2-butylesters (including both the RR and RS diastereomers) were

generated and initially optimizedwithMM3method by usingthe Tinker program (Step 1 Figure 2) The MM3 optimizedconformers (geometries) were firstly further subjected tooptimization with other LLMs under test (Step 2 Figure 2)

Step 3 and Correlation of the Conformer Energies LLMs areassessed by correlating their conformer energies (from Steps1 and 2 Figure 2) with the energy values resulting from singlepoint DFT B3LYP6-31lowast calculations (Step 3 Figure 2) onthe same LLM optimized geometries (Table 1 Figures 3 45 6 7 and 8) In this case the MM3 method yields thebest correlation and also correctly predicts the lowest energyconformer

Step 4 The results of the optimization cascade (Step 4Figure 2) and the energies of the low energy conformersin the energy range of 0 to 100 kcalmol are summarizedin Table 2 along with conformer energies calculated for thesame conformers by optimization with LLMs (Steps 1 and2 Figure 2) and the HFSTO-3G method (Step 4 the firstlevel Figure 2)

The energies of the low energy conformers from all ofthe test set of conformers (of MPA 2-butyl esters includingboth the RR and RS diastereomers) were found by using


Table 1 Correlation of conformer energies resulted from minimization with LLMs (Steps 1 and 2 Figure 2) with single point energiescalculated for the geometries optimized with LLMs by using high level RefM1 (Step 3 Figure 2)

Parametera UFFb Dreidingb AM1b PM3b PM6 MM3b MM+b

1198772 076 014 060 004 0436 089 065

RMS (kcalmol) 417 538 380 731 354 278 332Slope 117 024 046 004 049 112 056Intercept 038 231 049 164 191 minus015 142a1198772-correlation coefficient

RMS-root mean square deviation of the energy valuesSlope and intercept characterized systematic deviation of the correlated energy valuesIdeally they should be 100 and 000 respectivelybCorrelation diagrams are presented in Figures 3ndash8

Table 2 Determination of the cut-off conformer (COFC) energya (given in bold typeface) within a series of optimized with LLMs andHFSTO-3G conformers (Steps 1 and 2 and Step 4 (the first level) resp Figure 2)

Conformer RefM2 RefM3 HF UFF Dreiding AM1 PM3 PM6 MM3 MM+a 000 040 009 080 099 143 035 337 003 042b 009 000 009 060 064 131 156 324 000 032c 056 041 027 113 095 140 060 429 305 044d 057 057 089 236 187 143 148 327 090 109e 059 073 086 213 203 139 148 316 089 091f 060 052 024 131 144 126 150 418 309 078g 067 091 091 220 216 145 145 316 099 068h 069 100 088 232 223 135 144 327 096 058i 072 074 001 029 106 211a 156 481 299 020j 082 087 000 000 000 200 122 413 029 088k 085 057 003 089 065 200 125 412 032 121RMSb 000 020 046 109 101 094 079 344 130 031aThe COFC energy is the highest conformer energy in the series of conformers optimized with an LLM and selected as corresponding to more populatedconformers in the energy range of 0ndash100 kcalmol found by optimization with the cascade optimization method RefM2 The COFC energy determines theconformer energy range that potentially involves all the set of significant LLM conformers to be subjected to optimization at higher levels of theorybThe RMS values indicate deviations of LLM energies from the energies calculated by using the RefM2

02468

101214161820

0 5 10 15 20 25RefM1

MM

3

Figure 3 Correlation between energies (kcalmol) of MM3 opti-mized conformers (Step 1 Figure 2) and energies calculated withRefM1 (Step 3 Figure 2) for the same geometries

the cascade of calculations (RefM2 Step 4 Figure 2) and areshown in Figure 9 in comparison with the energies resultingfromoptimization of just the same conformerswith the LLMs

02468

101214161820

0 5 10 15 20 25RefM1

MM+

Figure 4 Correlation between energies (kcalmol) of MM+ opti-mized conformers (Step 2 Figure 2) and energies calculated withRefM1 (Step 3 Figure 2) for the same geometries

under test (Steps 1 and 2 Figure 2) and also with HFSTO-3G (Step 4 the first level Figure 2) The latter method isincluded in the RefM2 as the first level of calculations thus


0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35RefM1

UFF

Figure 5 Correlation between energies (kcalmol) of UFF opti-mized conformers (Step 2 Figure 2) and energies calculated withRefM1 (Step 3 Figure 2) for the same geometries

02468

101214

0 2 4 6 8 10 12 14 16RefM1

Dre

idin

g

Figure 6 Correlation between energies (kcalmol) of the Dreidingoptimized conformers (Step 2 Figure 2) and energies calculatedwith RefM1 (Step 3 Figure 2) for the same geometries

the separated results for this method allow estimating theimpact of the higher levels to the final result

As noted several initial conformers with different ener-gies are converging to one certain conformer upon thesequential high level optimization procedureThe total num-ber of conformers resulting from generation and initialoptimization by using the Tinker program (Step 1 Figure 2)was 262 The further geometry optimization on subsequenthigher levels reduces this number for example performingan HFSTO-3G step after the Tinker calculations (Figure 2)reduces it to 187This tendency is observed for all higher levelmethods used

The numbers of conformers obtained by using differentLLMs (Steps 1 and 2 Figure 2) and HFSTO-3G (Step 4 firstlevel) belonging to certain energy ranges in comparison withRefM2 are presented in Table 3

In the case of semiempirical methods (AM1 PM3 andPM6) the number of conformers in the lower energy region islarger than that found using the other methods For instanceby optimization with MM3 11 conformers within the energyrange from 0 to 100 kcalmol have been identified whereasAM1 and PM3 yielded 32 and 41 conformers respectively

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14RefM1

AM

1

Figure 7 Correlation between energies (kcalmol) of AM1 opti-mized conformers (Step 2 Figure 2) and energies calculated withRefM1 (Step 3 Figure 2) for the same geometries

012345678

0 5 10 15 20RefM1

PM3

Figure 8 Correlation between energies (kcalmol) of PM3 opti-mized conformers (Step 2 Figure 2) and energies calculated withRefM1 (Step 3 Figure 2) for the same geometries

The semiempirical methods tend to overestimate the numberof conformers

Step 5 After performing the calculations of Step 5 (Figure 2)it is possible to directly compare the conformational energiesof identified conformers (Figure 9) that is of conformersoptimized by the LLMs and HFSTO-3G with these min-imized by RefM2 (Table 2) The energy level of the lowestenergy conformer is set to 0 kcalmol as usual It has beennoticed that quite a good similarity between energies of theentire RefM2 and HFSTO-3G occurs (Figure 10)

4 Discussion

It is an unavoidable problem in the conformational analysis ingeneral that the number of conformers initially generated istoo high and its quality too low for justified optimization of allof them on time-consuming higher calculation levels A sig-nificant part of conformers initially generated turn out to behigh energy ones or saddle points on a PESThis shortcominghas to be overcome by using an initial optimization procedurewith a less accurate but also less resource consuming LLM


Table 3The number of conformers found by optimization with LLMs and HFSTO-3G (Steps 1 and 2 Step 4 (the first level) resp Figure 2)as well as with the RefM2 (entire Step 4 Figure 2) within certain energy ranges

Energy range from 000 to119883 [kcalmol] RefM2 HF UFF Dreiding AM1 PM3 PM6 MM3 MM+COFC energya 11 11 35 97 87 94 76 55 37250 46 54 35 111 109 159 28 39 71200 43 42 23 81 78 132 27 29 64150 33 42 10 49 60 89 14 26 51100 11 11 6 17 32 41 10 11 26075 9 4 4 13 18 26 10 4 16aThe COFC energy values for LLMs are given in Table 2

02468

101214

0 5 10 15 20RefM1

PM6


0

05

1

15

2

25

a b c d e f g h i j kConformer

Ener

gy (k

calm

ol)

RefM2HFUFFDRE

AM1PM3MM+

Figure 10 The LLM and HF conformer energies (Steps 1 2 and 4(the first level) resp Figure 2) compared to the energies refined bythe RefM2 (entire Step 4 Figure 2)

The rational choice of a LLM for this purpose is an importantquestion for refining the generated conformers in orderto select a reliable set for further optimization using anab initio or density functional method The failure at theinitial stage of systematic conformational analysis would leadto erroneous results that cannot usually be corrected insubsequent steps by using better methods A common way tominimize the number of conformers for further optimization

is neglecting the high energy conformers However this kindof simplification of the process may be unjustified if thechoice of an LLM for the initial optimization aswell as (or) thechoice of the corresponding cut-off conformer is not rightStill it has been difficult to guarantee that conformers whichlater upon optimization with RefM2 will turn out to be lowenergy conformers are not discarded

In order to investigate the approach none of the higherenergy conformers has been discarded at any of the calcula-tion steps (Figure 2) in the current work

In sum there are two requirements to the use of a LLMat the initial stage to guarantee obtaining high computationalefficiency along with reliable results Both of them depend onthe quality of the LLM as well as on a rational protocol forperforming the selection

The LLMs that correlate with the RefM1 regarding theconformer energies are suitable for the initial stage of aconformational analysis The suitable LLM should also becharacterized by low (preferably the lowest) cut-off con-former energy

In addition the situation where the LLM results in a lowenergy conformer but a high levelmethod gives a high energyvalue for the same conformer is not disastrous (ie it does notbring upon erroneous results) but rather makes the LLM lessselective and therefore the number of the conformers to beoptimized still remains too high which is just unpractical Apreferable situation would be if a low and a high level methodwould correlate to a satisfactory extent

The quality of the conformer energies minimized withdifferent LLMs (Steps 1 and 2 Figure 2) is evaluated on thebasis of single point DFT B3LYP6-311++Glowastlowast calculation(RefM1 Step 3 Figure 2) of energies corresponding to themolecular geometries optimized with LLMs under test (Steps1 and 2 Figure 2) (correlation diagrams are presented inFigures 3ndash8) Table 1 presents correlation parameters betweenthese two types of energy values

The conformer energies are best reproduced with MM3force field followed by UFF (1198772 values of 089 and 076resp) though both of them tend to slightly overestimateconformational energies given by the slope value above10 of the least square fit line The MM+ force field withan RMS value of 33 kcalmol tends to underestimate theconformational energies In the series of LLMs under testthe Dreiding force field proved to be rather problematic


with its very poor correlation and severe underestimation ofconformational energies

AM1 systematically underestimates the energies that aremore pronounced in the middle-range DFT energy valuesAlthough the AM1 method gives a fairly good regression fit(1198772 = 06) PM3 shows no correlation with DFT relativeenergy values Besides the slope value close to zero indicatesan underestimation of conformer energies However regard-ing energy differences herein the PM3 method has correctlyidentified the energetically most favorable conformer thatis a very valuable result In particular the use of thesemiempirical methods for the conformational analysis ofcomplex compounds may give valuable information Forinstance AM1 has been used for the conformational analysisof prostaglandins providing results (based on identification ofthe prevailing conformers) that qualitatively correlated withexperimental characteristics [28]

Based on the above reasoning the MM force fieldscan thus be suggested as quick preliminary methods forenergy minimization yielding satisfactory semiqualitativeresults regarding the energies of conformers In addition theexamination of the results of conformational analysis withentire RefM2 indicates that molecular mechanics MM3 forcefield is able (as PM3did) to predict correctly the lowest energyconformers (Figure 3 conformers a and b) obtained by thishigher level procedure

The semiempirical methods usually give less accurateresults This is because they are parameterized near thelocal minimum of the PES At more prominent distancesfrom these minima the semiempirical methods are notable to reproduce correct energy values Thus optimizingthe structure from this region of a PES might result in anincorrect optimized structure

TheCOFCenergieswere found as follows Table 2 lists thelow energy (lt100 kcalmol) conformers obtained with a highlevelmethodRefM2These conformer energies are comparedwith energies found for the same conformers by optimizationwith various LLMs For instance the COFC found withMM3 has energy of 309 kcalmol which corresponds to aconformer labeled with min this paper (Table 2) In the sameway the UFF method yields the COFC namely n with theenergy of 236 kcalmol Repeating this procedure for the restof the methods yielded all the COFCs for the methods testedherein and the results are presented in Table 2 (the COFCenergies are in bold typeface)

The number of significant LLM conformers appeared tobe different in case of different LLMsThe question related tocomputational efficiency in an attempt to find all significantlow energy conformers (000ndash100 kcalmol) is the followingwhich initial LLM gives a minimum number of conformersnecessary to be optimized with a high level method Thenumbers of conformers corresponding to the energy rangesare given in Table 3 All the conformers in a series withinenergy range up to COFCrsquos energy value (which are includedin Table 3) have to be considered On the basis of the resultsprovided in Table 3 it can be concluded that themost efficientLLM is the UFF which permits to limit the amount of con-formers to 35 The MM+ and MM3 methods select 37 and 55

conformers respectively Semiempirical methods AM1 PM3and PM6 yield 87 94 and 76 conformers respectively whileDreiding force field selects 97 conformers to be subjectedto further calculation with a high level method Replacingthe high level reference method from RefM2 to RefM3 andperforming a similar cascade like optimization scheme asperformed in case of RefM2 (Figure 2 Step 4) no significantchanges occur as can be seen fromTable 4TheUFF selects 39conformers the other low level methods collect the numberswhich are approximately at the same line as compared toRefM2

Special attention should be paid to the (low level ab initio)Hartree-Fock HFSTO-3G method It could be positioned inbetween the low and high level computational methods Inthis work HFSTO-3G is included into RefM2 as the first stepof the cascade of higher level calculations (Step 4 Figure 2)and therefore comparison of the results of RefM2 withthese of HFSTO-3G can only be illustrative The accordancebetween the HFSTO-3G method and the entire RefM2 ispretty good the energy of the corresponding COFC is thelowest found for LLMs only 107 kcalmol As mentionedHFSTO-3G is assumed to belong to LLMs in some respectand corresponding characteristics have been included in theTables 1 and 2 This method yields only 11 conformers in theenergy range up to the COFC energy

In addition to evaluation of the quality of an LLMfor the calculation of conformer energy it is important tocreate and follow criteria for the use of an LLM In thisregard it is reasonable to pick up the RefM2 optimizedconformers appearing within an energy range for exam-ple lt100 kcalmol (Figure 3) Approximately this range isjustified because of the Boltzmann law according to whichthe higher energy conformers are less significant due tolow populations Among these selected conformers oneshould identify the conformer showing the highest LLMenergy (Table 2) Herein we label this conformer as a cut-offconformer (COFC) for this LLM and its energy defines theenergy range involving the LLM conformers that have to besubjected to further consideration

In order to assess the LLMs we have to determine theCOFCs and corresponding energies for all of the methodsunder test The best LLM in this respect is characterized bythe lowest COFC energy valueThus the LLMs can be rankedaccording to the COFC energies However this rankingshould be very critically evaluated taking into account alsothe conformer energy correlation results (Table 1) and thenumber of conformers to be submitted to optimization on thehigher levels of theory

In sum it is assumed that the following guidelines shouldbe taken into account in assessing the suitability of the LLM

(1) Conformer energies found by using the high and lowlevel method should correlate

(2) A COFC of an LLM selected for use should becharacterized by the low energy in the manifold ofLLMs indicating probably amore preferable methodThe COFC energy should be taken as a cut-off valuewhen discarding high energy conformers after initialoptimization of conformers generated


Table 4The same as Table 3 but the high level referencemethod is replaced fromB3LYP6-311++Glowastlowast (RefM2) to B97D6-311++Glowastlowast (RefM3)

Energy range from 000 to119883 [kcalmol] RefM3 HF UFF Dreiding AM1 PM3 PM6 MM3 MM+COFC energy 15 36 39 84 73 112 84 44 55250 61 52 42 68 76 110 27 39 76200 47 43 32 47 49 93 26 29 61150 38 43 13 21 39 59 13 26 37100 11 33 10 6 22 23 9 11 16075 9 8 7 3 13 17 9 4 13

(3) It would be preferable if the lowest energy conformercalculatedwith a high levelmethodwould also appearas the lowest energy conformer obtained by using thechosen LLM

(4) The selectivity of the LLM should be sufficient thatis the number of conformers remaining for theoptimization on higher levels should be acceptable (ascompared with other LLMs)

5 Summary

A comparative demonstration of the LLMsrsquo performancebased on optimization of conformer geometries of the 2-butyl esters of MPA was carried out Special focus was onthe rational selection of the LLM for the initial optimizationof generated conformers in total conformational analysisof esters The methods assessed were MM3 MM+ UFFDreiding AM1 PM3 and PM6 The performance of the lowlevel ab initio calculation method HFSTO-3G was studiedin the role of a lower step of the optimization cascade Thesingle point calculation of the conformer benchmark energiesfor the LLM optimized geometries with DFT B3LYP6-311++Glowastlowast was performedThe LLM conformer energies werecorrelated with the higher level benchmark single pointenergies corresponding diagrams along with the correlationparameters are presented In this approach the MM3 forcefield appeared to yield the best correlation values

It is also shown that the above correlation parametersobligatory for the assessment of the quality of a LLMregarding the energy calculation are neither sufficient toassess fully the quality of a LLM nor do they provide exactcriteria for applying of a more proper LLM to the initialoptimization of geometry of conformers For the adequateassessment of an LLM in addition to the energy correlationquality the number of conformers that need to be fed tothe further optimization in order to obtain reliable resultsshould be determined and critically assessed in comparisonwith the other methods This is the number of conformersup to the cut-off conformer (COFC) energy value the lowerthese numbers are for a certain LLM the better its quality isAnd in reverse high number of such conformers is indicativeof poor selectivity of the LLM Various methods have yieldeddifferent thresholds for the energy ranges (the COFC ener-gies) and the number of conformers to be considered further

Taking into account the assessment criteria the MM3force field has been chosen for the initial optimization ofgenerated conformers in our investigations of esters [8]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors thank the Estonian Ministry of Education andScience (Grants no SF0140133s08 SF0690034s09 ETF8880and IUT19-32) and EU European Regional DevelopmentFund (32010108-0017) for the financial supportThe authorsare also grateful to Tallinn University of Technology for thefinancial support through Grant no B35

References

[1] R Aav T Pehk S Tamp et al ldquoTheoretical prediction andassignment of vicinal1H-1H coupling constants of diastere-omeric 3-alkoxy-67-epoxy-2-oxabicyclo[330]octanesrdquo Mag-netic Resonance in Chemistry vol 49 no 2 pp 76ndash82 2011

[2] K W Sattelmeyer J Tirado-Rives and W L JorgensenldquoComparison of SCC-DFTB and NDDO-based semiempiricalmolecular orbital methods for organic moleculesrdquo Journal ofPhysical Chemistry A vol 110 no 50 pp 13551ndash13559 2006

[3] K Gkionis J G Hill S P Oldfield and J A Platts ldquoPer-formance of Beckes half-and-half functional for non-covalentinteractions energetics geometries and electron densitiesrdquoJournal ofMolecularModeling vol 15 no 9 pp 1051ndash1060 2009

[4] R S Paton and J M Goodman ldquoHydrogen bonding and 120587-stacking how reliable are force fields A critical evaluation offorce field descriptions of nonbonded interactionsrdquo Journal ofChemical Information andModeling vol 49 no 4 pp 944ndash9552009

[5] G L Warren C W Andrews A-M Capelli et al ldquoA criticalassessment of docking programs and scoring functionsrdquo Journalof Medicinal Chemistry vol 49 no 20 pp 5912ndash5931 2006

[6] R Wang Y Lu and S Wang ldquoComparative evaluation of 11scoring functions for molecular dockingrdquo Journal of MedicinalChemistry vol 46 no 12 pp 2287ndash2303 2003

[7] T Cheng X Li Y Li Z Liu and R Wang ldquoComparativeassessment of scoring functions on a diverse test setrdquo Journalof Chemical Information and Modeling vol 49 no 4 pp 1079ndash1093 2009

[8] S Tamp K Danilas M Kreen et al ldquoA total conformationalanalysis of diastereomeric esters and calculation of their con-formational shielding modelsrdquo Journal of Molecular StructureTHEOCHEM vol 851 no 1ndash3 pp 84ndash91 2008


[9] R G Parr andW YangDensity-FunctionalTheory of Atoms andMolecules Oxford University Press Oxford UK 1989

[10] O Alver M F Kaya M Bilge and C Parlak ldquoVibrationalspectroscopic investigation and conformational analysis ofmethacrylamidoantipyrine a comparative density functionalstudyrdquo Journal of Theoretical Chemistry vol 2013 Article ID386247 10 pages 2013

[11] ZWeiqun L Baolong C Yang Z Yong and L L Y Xujie ldquoThestructure and conformation analysis of N-2-fluorobenzoyl-N1015840-2-methoxyphenylthioureardquo Journal of Molecular StructureTHEOCHEM vol 715 no 1ndash3 pp 117ndash124 2005

[12] MWHill K BWiberg H CastrejonW F Bailey J Ochterskiand J M Seminario Recent Developments and Applications ofModern Density FunctionalTheory Elsevier London UK 1996

[13] O Tsubrik P Burk T Pehk and U Maeorg ldquoConformationalanalysis of 1-acetyl-2-methylhydrazinerdquo Journal of MolecularStructure THEOCHEM vol 546 pp 119ndash125 2001

[14] A Metsala E Usin I Vallikivi L Villo T Pehk and OParve ldquoQuantum chemical evaluation of the yield of hydrox-ybenzophenones in the fries rearrangement of hydroxyphenylbenzoatesrdquo Journal of Molecular Structure THEOCHEM vol712 no 1ndash3 pp 215ndash221 2004

[15] T D Rasmussen and F Jensen ldquoForce field modelling ofconformational energiesrdquoMolecular Simulation vol 30 no 11-12 pp 801ndash806 2004

[16] M Stahl U Schopfer G Frenking and RW Hoffmann ldquoCon-formational analysis with carbon-carbon coupling constants Adensity functional and molecular mechanics studyrdquo Journal ofOrganic Chemistry vol 62 no 11 pp 3702ndash3704 1997

[17] E Voloshina J Fleischhauer and P Kraft ldquoConforma-tional analysis and CD calculations of methyl-substituted 13-tridecano-13-lactonesrdquo Helvetica Chimica Acta vol 88 no 2pp 194ndash209 2005

[18] A Leach Molecular Modeling Principles and ApplicationsPrentice Hall New York NY USA 2nd edition 2001

[19] B M Trost J L Belletire S Godleski et al ldquoOn the use of theO-methylmandelate ester for establishment of absolute configu-ration of secondary alcoholsrdquo Journal of Organic Chemistry vol51 no 12 pp 2370ndash2374 1986

[20] T Pehk E Lippmaa M Lopp A Paju B C Borer and RJ K Taylor ldquoDetermination of the absolute configuration ofchiral secondary alcohols new advances using carbon-13 and2D-NMR spectroscopyrdquo Tetrahedron Asymmetry vol 4 no 7pp 1527ndash1532 1993

[21] J M Seco E Quinoa and R Riguera ldquoThe assignment ofabsolute configuration byNMRrdquoChemical Reviews vol 104 no1 pp 17ndash117 2004

[22] J W Ponder Program TINKER (version 50) 2007httpdasherwustledutinker

[23] R V Pappu R K Hart and J W Ponder ldquoAnalysis andapplication of potential energy smoothing and search methodsfor global optimizationrdquo Journal of Physical Chemistry B vol102 no 48 pp 9725ndash9742 1998

[24] D C Young Computational Chemistry A Practical Guide forApplying Techniques to Real-World Problems John Wiley ampSons New York NY USA 2001

[25] M J Frisch G W Trucks H B Schlegel et al Gaussian 03(Revision E 01) Gaussian Inc Wallingford Conn USA 2009

[26] S Grimme ldquoSemiempirical GGA-type density functional con-structed with a long-range dispersion correctionrdquo Journal ofComputational Chemistry vol 27 no 15 pp 1787ndash1799 2006

[27] J J P Stewart ldquoOptimization of parameters for semiempiricalmethods II Applicationsrdquo Journal of Computational Chemistryvol 109 pp 221ndash264 1998

[28] M J S Dewar E G Zoebisch and E F Healy ldquoDevelopmentand use of quantum mechanical molecular models 76 AM1 anew general purpose quantum mechanical molecular modelrdquoJournal of the American Chemical Society vol 107 no 13 pp3902ndash3909 1985

[29] L P Davis R M Guidry J R Williams M J S Dewar andH S Rzepa ldquoMNDO calculations for compounds containingaluminum and boronrdquo Journal of Computational Chemistry vol2 pp 433ndash445 1981

[30] J J P Stewart ldquoOptimization of parameters for semiempiricalmethods I Methodrdquo Journal of Computational Chemistry vol10 pp 209ndash220 1989

[31] J J P Stewart ldquoOptimization of parameters for semiempiricalmethods V modification of NDDO approximations and appli-cation to 70 elementsrdquo Journal of Molecular Modeling vol 13no 12 pp 1173ndash1213 2007

[32] A K Rappe C J Casewit K S Colwell W A Goddard III andW M Skiff ldquoUFF a full periodic table force field for molecularmechanics and molecular dynamics simulationsrdquo Journal of theAmerican Chemical Society vol 114 no 25 pp 10024ndash100351992

[33] A K Rappe and W A Goddard III ldquoCharge equilibration formolecular dynamics simulationsrdquo Journal of Physical Chemistryvol 95 no 8 pp 3358ndash3363 1991

[34] S L Mayo B D Olafson andW A Goddard III ldquoDREIDINGa generic force field for molecular simulationsrdquo Journal ofPhysical Chemistry vol 94 no 26 pp 8897ndash8909 1990

[35] Hyperchem manual[36] HYPERCHEM ver 7 Hypercube Inc httpwwwhypercom

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


numerous studies based on theoretical conformational anal-ysis [10] Although geometrical parameters such as bondlengths angles and dihedrals can be reasonably accuratelypredicted on molecular mechanical and semiempirical levelsof theory the electron correlation effects are important forquantitative considerations These effects significantly affectthe conformer energies as well as rotational barriers betweenvarious conformers and should therefore certainly be takeninto account in the total conformational analysis

DFT and the hybrid B3LYP functional have allowedaccurate computation of the geometries concerning the typeof molecules under study [8] This in turn has allowedcalculating NMR and IR spectral characteristics in very goodagreement with the experimental data [8 11 12] The DFmethod using the B3LYP hybrid functional has been provento give a good estimate of the electron correlation for somemolecules in particular in conformational studies when it isused with the 6-31Glowast or 6-311++Glowastlowast basis set [13 14]

Semiempirical methods (AM1 PM3) have been shown tooverestimate the number of minima on the potential energysurface (PES) and underestimate the internal rotationalbarriers for substituted hydrazines [13] Several force fieldshave been assessed by comparing calculated conformationalenergies in relation to MP2aug-cc-pVTZ level benchmarkenergies for compounds with varying polarity The qualityof the results degraded along with increasing polarity of themoleculeThis effect was attributed to insufficient descriptionof the electrostatic term by using fixed partial charges in forcefields [15]

The attempts to simplify conformational analysis arealways problematic In particular limiting the number ofconformations or setting certain geometrical constraints onthe molecules under study can give a poor description ofthe PES leading to erroneous results Therefore if the subjectmolecule is conformationally flexible and contains manydihedrals with low potential energy barriers a systematicsearch for conformers should be undertaken

Identification of and involving all low energy conformersis important in a sense that compoundsrsquo certain physico-chemical properties as a rule depend on the whole confor-mational ensemble not just on the conformer correspondingto the global minimum on the PES However investigationof only the energetically most favored conformer may givegood results in some cases [1] An example of this approachis reproducing NMR spectral parameters (chemical shiftscoupling constants) of flexible organic compounds at theDFTlevel using the Boltzmann distribution [16] A systematicsearch for conformers and also taking into account the Boltz-mann weighting of individual conformers have allowed thecalculation of the circular dichroism spectra of macrocycliclactones (by using the time dependent DFT method) in avery good correlation with experimental spectra [17] Thesame approach has allowed an accurate estimation of theyield of hydroxybenzophenones in the Fries rearrangementof hydroxyphenyl benzoates [14]

Usual procedure of conformational analysis involves thegeneration of conformers by automated means using aconformational search algorithm (stochastic Monte Carlosimulated annealing genetic algorithm etc) followed by

the initial optimization of the geometry of the generatedstructures with the help of molecular mechanical or asemiempiricalmethodThe further refinement of conformersis carried out on higher theoretical levels at the same timediscarding higher energy conformers After optimization ofall structures at a certain level of theory a geometrical analogycomparison is used to identify duplicates This is carried outby RMS values of geometrical deviation of the positions ofthe atoms of one conformer in relation to other conformers[18] The cascade of calculations is usually finalized by usinga higher level DFT method

The purpose of the present study is to show how thechoice of the initial low level optimization method and thedetails of its use can influence the outcome of the total con-formational analysis consisting of a cascade of optimizationsincluding relatively high-level calculations at the final stageMore specifically the aim is to elucidate which initial methodpermits reducing most efficiently the number of conformersnecessary to be optimized at the higher level Another aim isto provide certain criteria that could be relied on in order toguarantee obtaining reliable results along with an optimizedfeasibility of calculations In this regard the key feature is theestimation of the conformer energy range for a certain initialcalculationmethodmarking the conformers to be selected forfurther calculations This should guarantee that the analyzerdoes not miss any important conformer at the initial stage ofoptimization

As to the contents this paper will firstly tackle the ques-tion ofmain correlational parameters such as slope interceptand the coefficient of correlation between the results of testedLLMs and the benchmark energies calculated using higherlevel reference method (RefM1) A satisfactory correlationis obligatory for an LLM to be used in the initial stageof conformational analysis However these correlationalparameters are still by themselves insufficient for a correctevaluation of the prospective quality of calculation results tobe obtained just by using the LLM Secondly the estimation ofthe energy ranges for the initially LLM-optimized conformersto be selected for further optimization is considered

In addition a critical consideration is given to theapproach within the systematic theoretical conformationalanalysis according to which decisive conclusions about therelative energies and corresponding distribution of con-formers are drawn on the basis of results obtained usingmerely an LLM The accuracy of the LLMs for calculationof conformational energies as compared to the benchmarkvalues has been assessed

For the current research 120572-methoxyphenylacetic acid(MPA) 2-butyl esters (Figure 1) were chosen as subject com-pounds They are diastereomeric esters of the well-knownchiral derivatizing agent for NMR spectroscopic analysis [819ndash21] In the current work they are mere model compoundsfor calculation (Figure 1)TheMPA esters are not too elemen-tary in conformational sense yet the optimization of theirconformers is possible by using higher level methods suchas B3LYP6-311++Glowastlowast included into the cascade protocol foroptimization (RefM2) in the current work

The calculations have been performed in gas phase Thisis justified by very good accordance achieved in between


OMeO

HO

H

CH3C H2

CH3



3[8]


21 Abbreviations












Step 3

Step 1Step 2

Step 4

Step 5

DFT

DFT

DFT

DFT DFT

DFT

DFT

PM3

AM1

PM3

AM1

UFF

UFF

TinkerMM3

MM3

PM6

PM6

MM+ MM+

Dreiding Dreiding

HFSTO-3G

B3LYP

B3LYP

B3LYP

3-21G

6-31G


AM1

PM3

MM3

HFSTO-3G PM6

MM+

UFF

Dreiding





3 Results









1198772 076 014 060 004 0436 089 065





02468

101214161820

0 5 10 15 20 25RefM1

MM

3



02468

101214161820

0 5 10 15 20 25RefM1

MM+




0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35RefM1

UFF


02468

101214

0 2 4 6 8 10 12 14 16RefM1

Dre

idin

g






0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14RefM1

AM

1


012345678

0 5 10 15 20RefM1

PM3




4 Discussion





02468

101214

0 5 10 15 20RefM1

PM6


0

05

1

15

2

25


Ener

gy (k

calm

ol)

RefM2HFUFFDRE

AM1PM3MM+





























5 Summary






Acknowledgments


References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


OMeO

HO

H

CH3C H2

CH3



3[8]


21 Abbreviations












Step 3

Step 1Step 2

Step 4

Step 5

DFT

DFT

DFT

DFT DFT

DFT

DFT

PM3

AM1

PM3

AM1

UFF

UFF

TinkerMM3

MM3

PM6

PM6

MM+ MM+

Dreiding Dreiding

HFSTO-3G

B3LYP

B3LYP

B3LYP

3-21G

6-31G


AM1

PM3

MM3

HFSTO-3G PM6

MM+

UFF

Dreiding





3 Results









1198772 076 014 060 004 0436 089 065





02468

101214161820

0 5 10 15 20 25RefM1

MM

3



02468

101214161820

0 5 10 15 20 25RefM1

MM+




0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35RefM1

UFF


02468

101214

0 2 4 6 8 10 12 14 16RefM1

Dre

idin

g






0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14RefM1

AM

1


012345678

0 5 10 15 20RefM1

PM3




4 Discussion





02468

101214

0 5 10 15 20RefM1

PM6


0

05

1

15

2

25


Ener

gy (k

calm

ol)

RefM2HFUFFDRE

AM1PM3MM+





























5 Summary






Acknowledgments


References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Step 3

Step 1Step 2

Step 4

Step 5

DFT

DFT

DFT

DFT DFT

DFT

DFT

PM3

AM1

PM3

AM1

UFF

UFF

TinkerMM3

MM3

PM6

PM6

MM+ MM+

Dreiding Dreiding

HFSTO-3G

B3LYP

B3LYP

B3LYP

3-21G

6-31G


AM1

PM3

MM3

HFSTO-3G PM6

MM+

UFF

Dreiding





3 Results









1198772 076 014 060 004 0436 089 065





02468

101214161820

0 5 10 15 20 25RefM1

MM

3



02468

101214161820

0 5 10 15 20 25RefM1

MM+




0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35RefM1

UFF


02468

101214

0 2 4 6 8 10 12 14 16RefM1

Dre

idin

g






0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14RefM1

AM

1


012345678

0 5 10 15 20RefM1

PM3




4 Discussion





02468

101214

0 5 10 15 20RefM1

PM6


0

05

1

15

2

25


Ener

gy (k

calm

ol)

RefM2HFUFFDRE

AM1PM3MM+





























5 Summary






Acknowledgments


References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




1198772 076 014 060 004 0436 089 065





02468

101214161820

0 5 10 15 20 25RefM1

MM

3



02468

101214161820

0 5 10 15 20 25RefM1

MM+




0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35RefM1

UFF


02468

101214

0 2 4 6 8 10 12 14 16RefM1

Dre

idin

g






0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14RefM1

AM

1


012345678

0 5 10 15 20RefM1

PM3




4 Discussion





02468

101214

0 5 10 15 20RefM1

PM6


0

05

1

15

2

25


Ener

gy (k

calm

ol)

RefM2HFUFFDRE

AM1PM3MM+





























5 Summary






Acknowledgments


References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35RefM1

UFF


02468

101214

0 2 4 6 8 10 12 14 16RefM1

Dre

idin

g






0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14RefM1

AM

1


012345678

0 5 10 15 20RefM1

PM3




4 Discussion





02468

101214

0 5 10 15 20RefM1

PM6


0

05

1

15

2

25


Ener

gy (k

calm

ol)

RefM2HFUFFDRE

AM1PM3MM+





























5 Summary






Acknowledgments


References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




02468

101214

0 5 10 15 20RefM1

PM6


0

05

1

15

2

25


Ener

gy (k

calm

ol)

RefM2HFUFFDRE

AM1PM3MM+





























5 Summary






Acknowledgments


References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




















5 Summary






Acknowledgments


References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of






































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

Research Article An Assessment of Alternative Low Level...

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