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1800 Journal of Chemical Education • Vol. 82 No. 12 December 2005 • www.JCE.DivCHED.org

The torsional potential energy surface of a chemical com-pound, the accessible conformations at a specified tempera-ture and the transition states that connect these conformations,establishes many chemical properties such as dynamic behav-ior, reactivity, and biological activity. The relative populationof a conformation at a specified temperature depends on itsstatistical weight, which is influenced by the enthalpy and bythe entropy. As a consequence, the global minimum at con-stant temperature and pressure might not correspond to thestructure with the minimum global enthalpy, but to the mini-mum Gibbs free energy (1). In many situations, the confor-mation of interest does not correspond to the most populatedone, as in the case of an interaction of a compound with bio-logical macromolecules when only one conformation isbioactive (1, 2) or in the case of the reactivity of chemicalcompounds. However, for a molecule with several degrees offreedom there is no guarantee to find the global minimumand all accessible local minima at a specified temperature (3,4). Owing to the importance of determining the accessibleconformations and to study their properties (5), advanced un-dergraduate and graduate chemistry students can benefit fromperforming computational practices to better understand theconcepts involved in such topics.

n-Pentane has been chosen as a model molecule for thecomputational experiments to explore the torsional poten-tial surface. Students can classify the stability of the n-pen-tane conformers using qualitative concepts and test theirpredictions using molecular modeling software. This moleculehas two torsional degrees of freedom and nine apparent con-formational states, CSs, where four of them are unique. Also,there are experimental and computational data for this com-pound in the literature using different approaches, allowingfor comparison. The energy differences for some conformersof n-pentane have been determined by infrared or Ramanspectroscopy (6–8). Benchmark calculations of the confor-mational equilibrium of n-pentane using confocal analysishave been published (9). Simulation methods were employedto assess the conformational analysis of n-pentane in the liq-uid state (10, 11). The conformational analysis of n-pentaneusing molecular mechanics and molecular dynamics has beenpublished in this Journal to demonstrate some aspects of thesetechniques (12).

In this article, a computational experiment is proposedto explore the torsional potential energy surface of n-pen-tane. Using molecular models, the students could find all nineapparent CSs and were able to identify the four unique con-formers (UCs). Using qualitative arguments founded mainlyin steric repulsions, the students determined the relative sta-bility of these UCs. The nine CSs were built using a mo-lecular graphics program and their geometry was minimized

by molecular mechanics methods to define the UCs. Start-ing with any UC simulated annealing method allowed thelocalization of global minimum. The relative populations ofeach conformer and the coupling constants of vicinal pro-tons could easily be determined. In addition, computationaltests could be performed to verify the influence of differentforce fields on the relative energies of UCs. The results ob-tained by this computational experiment were compared withresults reported by Salam and Deleuze (9), which used con-focal analysis.

Computational Methods

The conformers were built and analyzed after minimi-zation and vibrational analysis using the Molden moleculargraphics software (13). All calculations were performed us-ing the Tinker 4.0 suite of programs (14) and MM3 forcefield (15–17). MM2 was also tested (18). The geometry op-timization and vibrational frequency calculations were madeby OPTIMIZE and VIBRATE programs of the Tinker suite,respectively. The OPTIMIZE program performs a minimi-zation of an input structure over Cartesian coordinates us-ing an algorithm developed by William Davidson. TheVIBRATE program performs the vibrational analysis by di-agonalizing the full Hessian matrix for an input structure.

The conformational search was performed with theSCAN program. This program performs the conformationalsearch for an entire potential energy surface via basin hopsobtained by activations along normal modes. The ANNEALprogram was used to attain the global minimum by the simu-lated annealing method.

The vicinal proton coupling constants 3JHH were calcu-lated using the Karplus equation (19),

3HH

2 ΦcosJ A= + BB CcosΦ + (1)

where A = 7.76, B = �1.0, C = 1.40, and Φ is the dihedralangle.

Additionally, other force fields such MM2* (20), AM-BER* (21), or MMFF (22) can be tested if Maestro (23) andMacromodel 7.0 (23) are available. The conformational analy-sis can be performed by MCMM (24), SUMM (25), or low-mode-search (26) methods.

Experiment Description

Unique ConformationsIn the classroom the students verified that CSs are de-

termined by rotations of C2�C3 and C3�C4 bonds andonly a, g+, and g− conformations are obtained by rotations

A New Exploration of the Torsional Energy Surfaceof n-Pentane Using Molecular Modelsand Molecular Modeling Software WSérgio E. Galembeck,* Giovanni F. Caramori, and José Ricardo RomeroDepartamento de Química, Universidade de São Paulo, Av. Bandeirantes, 3900, 14040-901 Ribeirão Preto, São Paulo,Brazil; *segalemb@usp.br

In the Classroom

www.JCE.DivCHED.org • Vol. 82 No. 12 December 2005 • Journal of Chemical Education 1801

around these bonds, corresponding to dihedral anglesC1�C2�C3�C4 and C2�C3�C4�C5 of 180�, 60�, and�60�, respectively. The nomenclature a, g+, and g− is used togive the complete description of structure through of thespecification of torsion angle, ω. According with the valuesof ω, the following designations are used: the designation

gauche, g, for ω ≈ 60� and anti, a, for ω ≈ 180�. The tor-sional angle for gauche conformation can be approximately+60� (g+) or �60� (g−). The n-pentane can be split into twosegments: A and B, according Figure 1. The rotation of thesegroups in appropriate directions produces nine staggered con-formations that are described using the above nomenclature.Using molecular models the nine CSs were built, the degen-erate conformers were found (12) (Figure 1), and the fourUCs were identified (Figure 2). The pairs ag− and ag+, g+aand g−a, g−g− and g+g+, g−g+ and g+g− are mirror images butnot enantiomers (12) since they are superimposable. The CSsag−, ag+, g+a, and g−a are the UCs. Taking into account stericrepulsion between hydrogen atoms, the relative stability ofthe UCs were determined as aa > g+a > g+g+ >> g+g−. Thetotal anti conformer, aa, would be the most stable (the me-thyl groups are anti), the conformer g+g− the least stable (me-thyl groups are eclipsed), and the conformers g+a and g+g+

have an intermediate stability (the methyl groups are gauche).Furthermore, the students could conclude that the steric re-pulsion between methyl groups in UC g+g− is so high thatthis conformer presents a small influence on the n-pentaneproperties in solution.

The four UCs showed in Figure 2 were built using theMolden program. The students built the n-pentane moleculeand adjusted the C2�C3and C3�C4 torsional angles to gen-erate each UC. Each conformer was saved in the Tinker for-mat. The g+a and g+g+ structures have a gauche conformationfrom the point of view of the methyl groups and if we tookinto account only the UCs shown in Figure 2 it is very hardto see that they are different conformers. However if we re-turn to Figure 1 it is possible to see that the atoms 1 and 2,taken together as a segment of the molecule, have a relation-ship that is gauche with respect to the segment defined byatoms 3 and 4, and this relationship of the same segmentsfor the conformer g+g+ is anti. With the file generated byMolden each geometry was optimized, using MM3 param-eter file. The optimized geometry file is used for the calcula-tion of vibrational frequency analysis. An input and outputfile for optimization of geometry and vibrational analysis forthe aa UC is found in the Supplemental Material.W

Analysis of the UCs resulted in positive frequencies in-dicating that the UCs are minima on the potential energysurface (Table 1). Relative energies were obtained from stericenergies. Comparing these results with those obtained by con-focal analysis (27), it can be observed that the relative stabil-ity obtained with the MM3 force field was qualitativelycorrect, but overestimated. The results obtained using MM2are similar to those obtained using MM3 force field. Fur-thermore, the students could compare the dihedral angles,which characterize the UC before and after geometry opti-mizations (Table 1 and Figure 2). All the optimized dihe-drals were close to their initial values, except for one angle ofthe g+g− UC, which was 30� larger than expected, probablydue to an improper description of 1,3-methyl–methyl repul-sion. This can indicate some problems with van der Waalsinteractions or charges in the nonbonded terms in the MM3force field.

Force Field CalculationsThe effect of different force fields calculations on the

relative stabilities of UCs was examined (Table 2). MMFF

Figure 1. Nine conformational states of n-pentane.

Figure 2. Unique conformations of n-pentane.

Me Me

H(a)H

H HH(b) H(c)

H(b) Me

H(a)H

Me HH H(c)

H(a) H

H(a)H

Me H(c)H Me

H(b) H(c)

H(a)H

Me MeH H

aa g�a

g�g� g�g�

,ciretS.1elbaT Es ,seigrenEciretSevitaleRdna, ∆Es,foCUehtrofselgnAslardehiDdna n enatneP-

CU Es/lomlack( �1)

∆Es/lomlack( �1)

ged/elgnAlardehiD

)a(H-C-C-)b(H )c(H-C-C-)a(H

aa 41.4 00.0 0.081 0.081g+a 00.5 68.0 9.771 1.46g+g+ 67.5 26.1 8.06 3.06g+g− 64.7 23.3 � 8.78 1.16

,seigrenEciretSevitaleR.2elbaT ∆Es sCUrof,fo -n sdleiFecroFtnereffiDgnisUdetaluclaCenatneP

ecroFdleiF

∆Es lomlack(/ �1)

aa g+a g+g+ g+g−

FFMM 00.0 38.0 54.1 83.41*2MM 00.0 09.0 26.1 46.31

3MM 00.0 68.0 26.1 0 26.4*REBMA 00.0 54.0 48.0 0 27.3

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1802 Journal of Chemical Education • Vol. 82 No. 12 December 2005 • www.JCE.DivCHED.org

force field produced relative energies closer to MM3 andMM2 than to AMBER, which produced underestimated val-ues. These observations provided interesting discussions aboutpotentialities and limitations of various force fields in the pre-diction of properties in solution, as for example the require-ment of tests before the use of a force field to an unknownproblem. If the results do not agree with the experimental orhigh-level calculations, it is necessary to calculate atomiccharges and to reparameterize some terms of the force field,specially the dihedral angles (2, 28). The difficulties with thecalculations of thermochemical data, which were close to theexperimental results (chemical accuracy within 1 kcal�mol;ref 5 ), can also be explored and the instructor can present ageneral overview of quantum chemical methods of compu-tational thermochemistry.

A conformational search was performed using one of theUCs. As a result, four CSs were obtained, each of them be-longed to a different UC. If the conformational analysis wasrepeated for each of the three other UCs, again four CSs wereobtained, each one representing a UC. However, in each con-formational analysis, a different CS was obtained for eachUC. These results strengthen the observation that each UCcomprises several degenerate CSs. Starting with any UC theglobal minimum was located, the geometry was optimized,and the vibrational frequencies were calculated, thus allow-ing the students to verify the possibility of localization of glo-bal minimum in favorable cases. The instructor can explorethe difficulties of conformational analysis and the localiza-tion of global minimum in systems with many torsional de-grees of freedom, in contrast with the ease of localization oflocal minima. The output of the SCAN program for perform-ing the conformational analysis is available in the Supple-mental Material.W

As an addendum for the experiment, the conformationalanalysis can also be made with Macromodel software. It isimportant to note that the SUMM method produces five con-formers in any force field, in contrast with other methodsthat produce only four UCs obtained in other conformationalanalysis (12, 27). The extra conformer has dihedral angles of0� and 180�, and an anti, eclipsed conformation. This con-former is approximately 5.0 kcal mol�1 less stable than theaa, using any force field.

Frequently, the students ask about the possibility of de-termining transition states for the interchange between UCs.Tests can be made using SADDLE, which is included inthe Tinker package. This program allows the localization oftransition states beginning with the structures of reagentsand products. For some transition states the dihedral angleswere not between those of reactants and products and forsome others the geometry optimization and frequency cal-culations resulted in none or two imaginary frequencies.These facts allow the discussion of the difficulties involvedin the use of force fields for calculations of transition states,which is a more challenging problem than the study ofminima (5). It should be noted that force fields were devel-oped to analyze structures on the minima of the potentialenergy surface. The instructor can present the methods andparameterizations of force fields specific to the study of tran-sition states (29).

Gibbs Free EnergiesThe relative Gibbs free energies were calculated for each

UC using steric energies, which were obtained from confor-mational analysis and relative entropies. These entropies werecalculated using internal and external symmetry numbers (30)because the calculations using standard statistical mechanicsexpressions are laborious and have many approximations,such as calculations involving free rotations. From ∆(∆G ) itwas possible to estimate the relative populations and, withthe use of the Karplus equation (eq 1), the coupling con-stants between vicinal protons (3JHH) could be determined.The entropies, free energies, and populations are presentedin Table 3. The relative population of each conformer wascalculated according to

N

Nj

GRT

j∆

=

−

e

t

−( )∑ e∆G

RT

i

i (2)

where Nj is the population of the conformer, Nt is the totalpopulation of all conformers, ∆G is given by ∆G = ∆H –T∆S, R is 8.3145 J K�1 mol�1, and T is in units of K. Therelative enthalpy, ∆H, is considered equal to the relative stericenergy, ∆Es. For the calculation of relative entropy, only theentropy of symmetry was taking into account as a first ap-proximation, owing to difficulties described above. Hence,the entropy of symmetry of each conformer was determinedaccording to

= −sym, i i iS R nln( )σ (3)

where ni and σi are the internal and external symmetry num-bers, respectively.

From Table 3 it is possible to compare the relative en-tropies estimated by eq 3 with those calculated by Salam us-ing rigid rotor and harmonic oscillator approximations. Theresults indicate a qualitative disagreement of symmetry en-tropies from those calculated with a more sophisticated treat-ment. Unlike quantum mechanics methods that makecalculations of entropy and Gibbs free energy at the end of avibrational analysis, molecular mechanics programs do notinclude this possibility. The different order of ∆S comparedwith ∆Es does not change the relative stability, as determinedby ∆G, for MM2 force field. MM3 and MMFF present aaand g+a isomers as degenerate and AMBER presents g+a asthe most stable conformer, despite its gauche conformationcompared with the anti for the g+g+.

The average coupling constants are shown in Table 4. Itis interesting to note that each force field presents a differentdistribution of conformers and none of these is similar tothe results obtained by confocal analysis. Average couplingconstants exemplify this result. Whereas MM2 and MM3methods presented values of 3Jab in agreement with resultscalculated using Salam and Mencarelli data, the best valuesof 3Jac were obtained by AMBER and MMFF approach.These results indicate the difficulty in performing calcula-tions of average properties for flexible molecules owing tothe weakness of van der Waals interactions and Pauli forces,which are responsible for the conformational preferences.

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www.JCE.DivCHED.org • Vol. 82 No. 12 December 2005 • Journal of Chemical Education 1803

,seigrenEciretS.3elbaT Es ,seigrenEciretSevitaleR, ∆Es ,seiportnEevitaleR, ∆S ,seigrenEeerFevitaleR, ∆G,tN/iNsnoitalupoPevitaleRdna

CU Es/lomlack( �1)

∆Es/lomlack( �1)

ρi puorGtnioP σ ∆S/lomlac( �1 K�1)

∆G/lomlack( �1)

snoitalupoPleRNj/Nt

2MM

aa 28.2 00.0 1 C2v 2 00.0 00.0 25.0

g+a 27.3 98.0 4 C1 1 57.2 71.0 93.0

g+g+ 44.4 26.1 2 C2 2 83.1 12.1 60.0

g+g− 40.6 22.3 2 C1 1 57.2 04.2 00.0

3MM

aa 41.4 00.0 1 C2v 2 00.0 00.0 84.0

g+a 99.4 58.0 4 C1 1 57.2 30.0 54.0

g+g+ 67.5 26.1 2 C2 2 83.1 12.1 60.0

g+g− 64.7 13.3 2 C1 1 57.2 05.2 00.0

FFMM

aa 72.5- 00.0 1 C2v 2 00.0 00.0 14.0

g+a 44.4- 38.0 4 C1 1 57.2 00.0 14.0

g+g+ 58.3- 24.1 2 C2 2 83.1 10.1 51.0

g+g− 75.1- 07.3 2 C1 1 57.2 88.2 20.0

REBMA

aa 88.1 00.0 1 C2v 2 00.0 00.0 13.0

g+a 33.2 54.0 4 C1 1 57.2 � 73.0 44.0

g+g+ 27.2 38.0 2 C2 2 83.1 24.0 02.0

g+g− 05.4 26.2 2 C1 1 57.2 08.1 50.0

malaS a

aa --- 00.0 1 C2v 2 00.0 00.0 65.0

g+a --- 86.0 4 C1 1 42.1 05.0 43.0

g+g+ --- 24.1 2 C2 2 � 28.0 20.2 70.0

g+g− ---- 11.3 2 C1 1 62.1 01.3 30.0

illeracneM b

aa --- 00.0 1 C2v 2 00.0 00.0 94.0

g+a --- 09.0 4 C1 1 57.2 70.0 44.0

g+g+ --- 26.1 2 C2 2 83.1 12.1 60.0

g+g− ---- 22.3 2 C1 1 57.2 93.2 00.0a fermorfataD .9 b fermorfataD .21

)zH(stnatsnoCgnilpuoCegarevA.4elbaT

CU2MM 3MM FFMM REBMA malaS a ileracneM b

3J ba3J ca

3J ba3J ca

3J ba3J ca

3J ba3J ca

3J ba3J ca

3J ba3J ca

aa 82.5 82.5 88.4 88.4 53.3 53.3 35.2 35.2 48.2 48.2 99.4 99.4

g+a 59.3 89.0 65.4 01.1 61.4 49.0 44.4 30.1 97.6 35.1 74.4 52.1

g+g+ 81.0 91.0 71.0 71.0 24.0 24.0 75.0 75.0 70.0 80.0 71.0 71.0

g+g− 00.0 00.0 00.0 00.0 30.0 50.0 80.0 31.0 10.0 20.0 00.0 00.0

muS 24.9 54.6 16.9 41.6 69.7 67.4 26.7 62.4 37.9 84.4 26.9 04.6a fermorfataD .9 b fermorfataD .21

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1804 Journal of Chemical Education • Vol. 82 No. 12 December 2005 • www.JCE.DivCHED.org

Conclusions

A conformational search of n-pentane was presented us-ing a computational experiment designed for advanced un-dergraduate students and beginning graduate students. TheCSs for n-pentane were obtained using molecular models andfour UCs were determined. These UCs were displayed quali-tatively according to steric repulsions. After the students de-termined the four UCs, they built the structures of the UCsusing a molecular graphics program, minimized them, andcalculated the vibrational frequencies. The energies of theUCs were compared with the results obtained from high-levelcalculations available in the literature. The performance ofseveral force fields was compared. In addition, the UCs wereobtained by conformational search methods, as an illustra-tion of automatic conformational analysis. The global mini-mum was also found. The entropies were estimated usingsymmetry numbers. Free energies, relative populations, andcoupling constants between vicinal protons were determinedand the performance of several force fields was compared.

This work shows that it is possible to develop experi-ments in which not only computational tools but also mo-lecular models sets and some intuitive thinking are used toexplore the conformational behavior of substances. The ex-periment proposed in this article exposes the students to manyconcepts and techniques that are not usually broached intheoretical or experimental courses, such as the differencesbetween unique conformations and conformational states, theuse of computational software to obtain information aboutthe UCs, and how several conformations contribute to theobserved values of some property. The students demonstrateda better understanding of the concepts presented here afterthe experiment.

WSupplemental Material

An input and output file for optimization of geometryand vibrational analysis for the aa UC is available in this is-sue of JCE Online.

Acknowledgments

The authors thank LCCA-USP for generous allocationof its computational resources. GFC thanks Brazilian Foun-dation FAPESP for an undergraduate fellowship (grant No.99/08945-5). SEG thanks CNPq (research fellowship No.301957/88-6), FAPESP, and CAPES for financial support.The authors also thank Maria Lúcia Arruda de Moura Cam-pos for many helpful suggestions.

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