Molecular Mechanics in the Undergraduate Curriculum Ronald R. Sauers Rutgers, The State University of New Jersey, New Brunswick, NJ 08903 Instructors routinely introduce strained molecules early in the tv~icalundermaduate wurse in organic chemistnr. At the f&roductnry'ievel ~tudentscan readily appreciate theconcept ofmolecular "stress"associated with fnrmation of small Angs, for example, cyclobutane and cyclopropane. More sophistication is required to understand the factors that influenre molecular strain in the more a~mplexmolecules that are commonly encountered in advanced level c(~urscs. Adctailed understandingofthe structural driving forces of organic chemical proceliies- solvolyses, elimination reactions, oxidations of alcohols, reductions ofketones, enzyme-catalyzed reactions-requires a deeper understanding of the molecular forces that determine geometry and energy. Authors of recent advanced textbooks have recoenized this need and have b e m to incor~oratecommentary and discussion of the useof force field methodolo""w (1) . . as a useful tool for the rapid wm~uter-aidedanalvsis of molecular geometry a n i energy (24). With the advent of several inexpensive graphical input programs and computer terminals, it is feasible to give undergraduates hands-on exposure to molecular mechanics methodology, much ali they arc mtroduced to the use ofspectroscopic instrumentation. We would hke to outline our recent cxpcrience with the introduction of molecular mechanics methodology to a group of 30 juniors, seniors, and first-year graduate students in advanced organic chemistry (5).
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Backaround An excellent recent review of molecular mechanics by Boyd and Lipkowitz appeared in this Journal (4). Briefly, currently in use are designed to the computer calculate the steric energy of input molecules by summation of the individual energies associated with deviations of molecular structure from "ideality". By use of suitable madient search or analvtical methods (2) the proaams - " optimize the geometry and energy of the input structure. Account is taken of several kinds of structural deviations from ideality, including differencesin bond angles, torsion angles, bond lengths, and van der Wads distances (nonbonded interactions). Other features including Coulombic interactions, hydrogen bonding, stretch-bend forces, etc., may also be incorporated depending on the programinuse. Although steric enereies themselves have no direct physical meaning, differences in steric energies are useful in comparisons of experimentally observable physical properties (e.g., conformationalbarriers, heats of formation, bond angles, and other geometric parameters.) In addition, transition structures can also be simulated and used to predict relative reaction rates (6). Procedures Six stations were available a t all times and a graduate teaching assistant was assigned to be available for six hours a week to help out with problems. Each student was given a separate computer account. A few part-time students with industrial positions or home computers were given access to the computer network by modem, and they worked outside the Department. Underlying theory and detailed operating ins&ctions for logging on, drawing structures, carrying out minimizations, etc., were discussed in two 80-minute lectures. Most students spent 3-4 816
Journal of Chemical Education
hours generating structures and fmal data. The input and output files for the minimized structures were sent via internal electronic file transfer to a station operated bv the grader. The graphical output was reconstituted and examined for errors. es~eciallvif the final steric enerw -" looked suspiciouslyhigh.'~hen"problems arose, for example false minima, electronic mail messages were sent back to the student who was given hints about how to rectify the problem. The projects ultimately counted 10%of the final grade in the course and were evaluated on the basis of students' analyses of their results. Discussion The pedagogical value ofthis exercise had many aspects. For example, the students were asked to select their own structures for minimization. To simplify the analyses, they were asked to choose two isomers and to rationalize the difference in the fmal steric energies. This approach encouraged them to ask what kinds of molecules would be strained and whether or not their isomers would have significantly different steric energies. Thus, it would be instructive to compare the steric energies of cis- and trans1,2-dimethylcyclohexanes but not cis-1,3-dimethylcyclohexane with tmns-1,4-dimethylcyclohexane.Many students chose pairs of bicyclic systems, for example bicyclo[2.2.llheptane and bicyclo[4.l.llheptane, or pairs like cis and trans-bicyclo[3.2.01octane.Other examples included o-di-t-butylbenzene and p-di-t-butylbenzene, and one adventurous student constructed a steroid framework. The students were then asked to briefly discuss calculated differences in steric energies for their isomers, that is. identifv the maior source of strain bv examinine the o;tput file for differences in stretching, torsional benlding, and van der Waals enereies. In some cases. a single factor was primarily responsi~lefor the difference in Gteric enerw. for example. angle strain about one or two bonds (see this was not the case, and another ~ g m ~1). l ~ie&ently e obiective of this study was to demonstrate of the ability of m&cules to uccomodate strain by spreading unfavorable interactions among many atoms rExamples 3 and 5). Examples Several examples of student results &e given that illustrate behavior typical of strained molecules. These results can also servcas useful examples in introductory discussions of the methodolorn All calculations were carried out using MODEL Version 2.94 and MM2-1980 parameters. This program uses generalized benzene ring parameters (ring carbon-carbon bond lengths are set equal to 1.40 A). The results are summarized in Table 1. Interpretative Discussion Examples l a and i b In this comparison both isomers display significant steric energy. The major source of steric energy difference is clearly due to angle bending strain associated with the change of a cyclopentane ring in bicyclo[2.2.llheptane to a cyclobutane ring in bicyclo[3.l.l.lheptane.
Table 1. Steric Energy (Kcallmol) and Component Energies Compounds Blcyclo[2.2.1]heptane(la) Bicyclo[3.3.1]heptane(I b)
Total Strains 23.09 38.69
Stretch 0.08 1.32
3.52 5.60
Bend 9.05 19.66
Torsion 10.18 13.18
Examples 5a and 56
Examples 2 a and 26 Fusion of the five-and four-membered rings is expected
to be much more d E c u l t with the trans ringjuncture given the small number of atoms in the chains. Surprisingly, this is partially wunterbalanced by a significant decrease in torsional strain caused by ring puckering. Examples 3a and 36 The ex~ectationsare that differences in van der Waals hydroge&hydrogen repulsions will significantly raise the steric enerw -" of o-di-t-butvlbenzenerelative to the paraisomer. Considerable angle strain accompanies these interactions as the molecule alleviates stress by distorting the carbon framework. In p-di-t-butylbenzene, the C=C-C angle between the t-butyl groups expands to 130°, for example, and the aromatic ring itself becomes slightly nonplanar. Examples 4a and 46 This comparison shows students that steric energies can be calculated for unknown or highly unstable molecules that may not be isO1ahle under ordinary conditions. In trans-cyclohexenelarge differences in angle-bending strain are expected due to the considerable distortion of the normallv vlanar arraneement of the atoms associated with the n, system. ~wistin~;fthe n bond causes the large torsional energy difference due to the nonplanar C-C=C-C system (torsion angle = 97.4").
Table 2. Programs for Personal Computers PCMODEL
Van der Waalsa
ChemSD Plus
Versions: MAC-II, IBM PC XTIAT
Version: MAC-II
Silicon Graphics IRIS, Apollo Serena Software Dr. Kevin E. Gilbert P.O. Box 3076 Bloomington, IN 47402 812 333-0823
Dr. Stuart Rubenstein 875 Massachusetts Ave. Suite 41 Cambridge, MA 02139 617 491-6862
This comparison illustrates more subtle changes in carbon frameworks that occur a s molecules adapt to steric strain. One might have expected a large steric energy difference due to adverse van der Waals interactions in cis-dimethylbicy~lot2.2~21octane but not in the trans isomer. In fact. both isomers have almost the same total contribution'from 1,4-van der Waals interactions. The 2 kcaVmol overall steric energy difference is spread among many small wmponents of torsional and bond angle strain.
Conclusions Students gained appreciation for the interplay of molecular forces that governs equilibrium energy and geometry of organic molecules. The project was well-received by most students involved. The general wnsensus was that it was interesting and challenging. It not only gave them an appreciation for wmputer- driven molecular-modeling techniques but also provided a real experience in wmputational chemistry. SoftwareHardware Programs are available for use on IBM PC's (71, Macintosh computers, and larger computers (e.g., VAX 111750).A partial listing of available of these programs is giYen in Tables and 3, Table 3. Other Molecular Mechanics Programs Using Graphical Input MacroModel2.5
QCPE Programs
Model 2.94
Veffiions: VAX, Silicon Graphics IRIS, Convex, Sun, Ardent, IBM, Stellar. Dr. W. Clark Still Department of Chemistry Columbia University New York, NY 10027 212 280-2577
Quantum Chemistry Program Exchange Department of Chemistry Indiana University Bloomington, IN 47045 812 335-4784
Dr. Kosta Steliou Department of Chemistry Montreal, Quebec Canada H3C 3V1
Volume 68 Number 10 October 1991
817
Acknowledgment
Ritchie, C. D. ~ h ~ l olgonie m l chemistry. he f i n d o m n t d concepts. znd d ; Dekker: New York, 1990: p 110. 2. Bnrke", U.;Allnger, N. L. MollculorM~chanics;ACS Monopaph 171; American We are grateful to Attilio DeFaleo for assistance withthe Chemical Society: Washington, DC, 1982. hardware and to for with the 'Oft3. Clark, TAXondbook ofComputotionol Chemistry; W h y , New York, 1985: C h a p t a ware. 2. 4. Boyd, D. B.;Upkawitz, K B. J Cham. E d u e 198B, 59,269-274. 5. For related artidea on introdvetion ofcomputational chemistry into the undergraduLiterature Cited ate~rrkulum,seeLillie,T.S.;Yeager,K. J Cham Educ 1989.66.675-676,and Janet. R. M.; Sin, N. J. Cham. Edvc. 1BW). 67,153-155. 1. (a)Carey.F.A.;Sundberg,R.J.AduodOgonicChami~,PortA,2ndd.;Plenum: . N~~ YO&, 1984: chapter 3. (b) I ~ WT. . H.: fiehardson, K. S. ~ ~ ~ h ~ 6- D~rigo. ~ i A. Es.;Houk ~ K. N. J 0%-Cham. 1 9 M ~1650-1864. T h m v in O~pnleChamistry,3rd ed.; Harper and Row:NewYork, 1987,p 142. (e) 7. (dRager8.D. W . A m r Lab. 1988,2L710), 122131. (b)Welsh, W J. A m r . Lah 1 W , 2K53.128-131. Isaaes, N. S. Physleol Organic ChamlsLry; Wiley: New York, 1987; Chapter 8. (dl
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