Cyclooctane Conformational Analysis Via Mechanical and Computational Models Jeffrey P. Fitzgerald United States Naval Academy, Annapolis, MD 21402 Anumber of oaners have ameared recentlvin this Journal describing ih; use of both'gandheld mecLanical models and com~utationalmodels i n teachine conformational analysis to students of organic chemistG(l,2). The handheld models help students visualize the three-dimensional arrangements of atoms in each conformation of a molecule and how these arrangements cause differing amounts and types of strain-bond, angle, torsional, or van der Waals. Through manipulations of the mechanical model, students realize that conformational changes that relieve a particul a r strain in one part of the molecule often induce new strains elsewhere in the molecule. Computational models (i.e., molecular mechanics calculations) complement the students' understanding of conformational analysis by quantifying the strain energy for any conformation of a molecule. However, the output of most molecular mechanics programs--and the emphasis of most authors in this area-is the total strain energy for the optimized geometry of each wnfiguration: the sum of the bond, angle, torsional, and van der Waals energies. Useful information and a valuable learning experience can be had by comparing the various components of the strain energy among different conformational isomers.' Typically, students lack a "gut level" feeling for the relative importance of each type of strain. They tend to overemphasize contributions to the total energy due to angle strain and van der Waals repulsions and deemphasize or fail to recognize contributions due to torsional strain caused by eclipsing or partially eclipsing carbon-carbon bonds. In f a d , torsional strain is oRen the greatest contributor to the energy difference between the ground state and higher energy conformations. For example, over 60% of the 5.5 kcal separating chair and twist h a t cyclohexane is due to increased torsional strain i n t h e twist boat form, whereas increased van der Waals repulsions (the "flagpole" interaction) accounts for only about 20% of the energy gap.2 We describe here a n exercise in which students use both mechanical and computational models to identify and quantify the various types of strain in different conformations of a molecule. This exercise helps students develop a more quantitative appreciation for the relative importance of each type of strain while it reinforces the idea that the strains a& interdependent. 'Caution should be exercised when comparing the various components of strain enemv between conformations.Aforce field miaht correctlv Dredict the rekive total eneroies of two wnformers buifor the " wrong reason An exaggerate0 component of the stran energy s compensated for by one or more Jnoereatmateo components rlow ever, sLcn a colnc dence becomes ncreas ng.y ess I ke y the more times a forcefield correctly predicts the relative energies of two conformations. Comparisons of the wmponent energies in the present study are justified given the close agreement between the different forcefields used (ALCHEMY,MM2, SYBYL),the wide acceptance of the forcefields used, and the factthat the structures being compared are .related. .... 'Base0 on the averaged o~fputfrom ALCHEMY I and MM2 forcefleo ca c~iatlonsSee a so Cox. P J J Chern Educ 1982, 59,275277
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Journal of Chemical Education
TBC
Cyclooctane conformattons compl ea from tne I tera1Jre (S7) Alternate vjews of some wnformationsare given.
The Conformations of Cyclooctane, the Model System After considering several possibilities, cyclooctane was chosen as the system to be modelled. I t meets all the criteria of Biali (2) for a good model system: I t is a well-studied compound of low molecular weight with several possible conformations and a global minimum t h a t is not obvious. Additionally, due to its cyclic structure, cyclooctane cannot adopt a conformation i n which all types of strain are simultaneously a t their minimum values. Possible unique conformations of cyclooctane reported in the liwrature (3-7)and shown in the figure include low-energy forms (boaffchair, twist chairlchair, twist boaffchair, and twist boat) structures of mterm~dmtrmrrg) ,crown, cham char, w d hoaubmt) high-energy forms (boat, chair, and twist chair)
Not all of these conformations wrrespond to energy minima. The hatlchair form is thought to be the global mini-
mum, followed by the twist chairlchair form a t a n energy that is no more than 2 kcavmol higher.
Strain Energies of Cyclooctane Conformations from Alchemy I1
Experimental The Assignment The following exercise has been conducted during the first semester of the organic chemistry sequence. Classes had between fifteen and twenty-five students, primarily sophomore chemistry majors. I n a "dry" lab, students were given line structures for four of the above cyclooctane conformations, typically, the crown, b o a t h a t , chair, and boat. They were asked to build and compare handheld models of each. For each model theywere also required to estimate the relative angle and the torsional and van der Waals strains a s small, average, or large. Students were to indicate strain on each line structure using a heavy c i d e over carbon atoms suffering from angle strain a heavy line over carbon-carbon bonds experiencing a large torsional strain an arrow betwem hydrogen atoms suffering from van der Wads repulsions The Need for a Computational Model
A request to rank the four given conformers in order of increasine e n e m generated much discussion but no consensus. ~Yhestuze& recognized that there were tradeoffs in the various types of strain between each conformation; without quantitative measures of the strains, ranking the conformations would be subjective. This led nicely into a discussion of force-field calculations and iterative energy minimization. t o ~ i c that s have been reviewed in this Jour-
ALCHEMY 11 Molecular mechanics calculations were run using the program ALCHEMY I1 (Tripos AssociatesY on an 80386DX personal computer with EGA graphics. This program offers many advantages over the multiprogram exercises presented to date. There is no need to defme atomic coordinates(eitherinternal or Cartesian)to use as input for the minimization program. The molecule is constructed on the screen usinc- a menndriven subroutine. The molecule is displayed during the minimization routine, allowing the students to follow changes in structure as strain is relieved. The energy output from ALCHEI&' is broken down into bond, angle, torsional, van der Waals, and out-of-planewmponents. Students find this interactive, user-friendly,and very visual program a lot of fun and easy to use. Students were typically working independently after a 10-min tutorial.
Energies (kcalimol) Conformation
Total
Bond
Angle Torsional van der Waals
boatichair
-9.0
0.1
4.2
twist chairlchair
-8.4
0.1
2.3
twist boaVchair
-7.5
0.1
3.2
twist boat
-6.0
0.1
5.8
twist crown
-1.9
0.1
2.9
twist chair
-1.8
0.1
4.4
boat
0.0
0.2
6.5
boatiboat
0.0
0.1
8.7
A Variety of Minimized Structures Because no restrictions were placed on the input structure, several different minimized structures were obtained by the class because the input structures start a t widely different points on the cyclooctane potential energy surface. This reinforces the concept of local and global minima. Eventually, small groups of students realized that their output was identical, differing only in the perspective view of the o~timizedstructure. The enerw terms for each unique minimized structulp were collected-and d m i h u t e d to the students for comparison with their vredictions based on the mechanical models. I n all. six different creometrv-ovtimized structures were obtained by the studints. ~ 6 e i ;energy parameters are given in the table. Although not found by any student, minimized structures corresponding to the twist chair and the boatmoat conformers are also shown. These high-energy conformers were obtained by manipulating the input structures to be very similar to these conformations. A Possible New Structure
I n their spare time during a "wet" lab (typically distillation), each student was required to build and minimize a cyclooetane molecule using ALCHEMY 11.The various ene r... w terms were recorded and a eood .. three-dimensional view ofthe geometry-optimized structure was printed on a GRAPHTEC MP2300 XY dotter (Western Graohtec)? To build, minimize, and print out a cyclooctane conformation reauired 10-15 min ver student. The students then compared their minimizeb structures and energies.
The four low-energy confoAations of cyclooctane with the proper relative energies were found. Four higher energy structures were also found, including a new structure not described previously in the literature and best described a s a twist crown. This new structure has D2symmetry, which is lower than either the crown or chairlchair forms--conformations reported in the literature but not identified a s e n e r w minima bv ALCHEMY. The twist crown form is c l e z y distinct g o m the twist chairlchair form. which also has D?- svmmetrv. " ".beiue somewhat more circular. This new structure may be an artifact of the ALCHEMY I1 force field because it is not recognized a s an energy minimum by Allinger's MM2 program. It serves a s a useful reminder of one of the limitations of force-field calculations. Other than the differences mentioned above, the output (total and component enegies) from ALCHEMY I1 show the same order, trends, and approximate magnitudes as output from other molecular modelling programs (MM2, SYBYL).
3Tripos Associates, Inc.. 1699 South Hanley Road, Suite 303, St. Louis, MO, 63144. 4WesternGraphtec, 12 Chrysler Street, Irvine, CA, 92718.
From the energy parameters in the table, one sees little variation in the bond strain but wide variations in the
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Volume 70 Number 12 December 1993
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angle and torsional strains and van der Wads repulsions. This reflects the relative "stee~ness"of the ~ o t e n t i a enl ergy well describing bond strain; equilibrium carbon-carbon bond leneths are achieved a t the exDense of inducine other types of strain. The angle, torsional, and van der Waals strains were never simultaneously a t their lowest possible values for any conformation. Angle strain is lowest for the twist chairlchair form. closelv followed bv the twist crown structure. I t is m-ized fd;. the boatmoat form, probably in an attempt to relieve the strong van der Waals repulsions. The range of torsional strains is the largest of any type of strain, reaching a maximum in the boat and twist chair forms and a minimum in the boatiboat conformations. Suprisingly, these are the three highest energy conformations! Finally, the van der Waals repulsions are highest, a s expected, in the boatiboat conformer, followed closely by the twist crown. They are lowest in the boatlchair conformer. Other t h a n t h e two high-energy conformations, all cycloortane conformers ha;; van d&waals terms within 2 krai moi ofearh other. Interestinply, the most stable structure, the boatichair conformati
