Nov. 20, 1961
LfACHIKE
CONPUTATION OF
THE
COMMON KINGS
4537
ORGANIC AND BIOLOGICAL CHEMISTRY [CONTRIBUTION FROM
THE
DEPARTMEXT OF CHEMISTRY OF THE UNIVERSITY OF CALIFORNIA AT Los ANGELES, LOSANGELES 24, CALIF.]
Molecular Geometry. I. Machine Computation of the Common Rings1 BY JAMES B. HENDRICKSON RECEIVED MAY18, 1961 Computation of the energies of hydrocarbon molecule conformations as a function of various geometric parameters is discussed and machine computation advanced as a means of coping with the enormous calculations necessary for their solution. A-ew functions for non-bonded interactions are developed and compared with several previous ones. The cycloalkanes, Cg- 7, are taken as examples, their conformations of minimum energy computed, and these energies compared with experimental values. The conformations and pseudorotations of the flexible forms of these rings are discussed in the light of the calculations, and special attention is paid to a discussion of the more complex conformational analysis of cycloheptanes.
Introduction These simplifications, however, too of ten so drastiThe idea that one might calculate in detail the cally alter the complexion of the problem as to energy of a given molecular conformation has long render the answers either suspect or unreasonable. intrigued chemists, as it offers promise of the predic- The basis of the present work is accordingly an tion of most stable conformations or the intimate effort to break through this barrier of undue simplitransition state geometry and energy in organic fication by employing machine calculation, thus reactions. A number of such calculations has been allowing a far greater magnitude of mathematical made2-* with varying success, and it is well a t the effort in a reasonable time with untiring accuracy, outset of the present work to offer a brief summary and a consequent capability of a more intimate of the problems involved in such ~alculations.~probing into these probIems than is possible with The first and most formidable difficulty is that of hand c a l c ~ l a t i o n . ~The choice of particular funcselecting the particular functions which relate tions relating geometric variables with energies is energy to geometrical parameters of the molecular discussed below. lo conformations being examined; such functions, energy associated 1. Bond Angle Strain.-The discussed in more detail below, are generally derived with bending a single bond angle, 0, from the tetraindirectly from various empirical sources as spectro- hedral angle ( 7 = 109.47’) is derived from spectroscopic or thermodynamic data. Secondly, one scopic evidence and has the form EO = ICe (0 - 7)‘. must choose a particular conformation on which to Values of K O(in kcal./mole/rad.*) are taken from apply these functions. In order to ascertain the Westheimer’s review2: H-C-H, 23.0; H-C-C, most stable conformation of a given molecule, i t is 39.6; C-C-C, 57.5. Since, on change of one angle theoretically necessary to calculate the sum of a t tetrahedral carbon, the others must reasonably energies related t o the various geometrical param- also change to accommodate, the single assumption eters of a given conformation, and to minimize was made that this accommodation would occur this sum with respect to independent variation of such as to minimize the total energy of angle strain each of these parameters (k., by progressive dis- in the six involved angles. Computer programs tortion of the given conformation). This state- were thus set up to locate the configuration of miniment of approach to the problem serves to under- mum strain energy in the total angle set when a score the vast complexity of the calculations in C-C-C angle was given a value other than the any molecule of organic chemical interest, since tetrahedral angle”; the geometry of such a set is the number of independent geometrical variables shown in Fig. 1. I t was generally found that in can be overwhelming while the calculation of the the minimum energy configuration, for changes of total energy of any singbe set of geometric param- less than 10’ from tetrahedral, the angles bore a eters is itself extremely ponderous. In order to substantially linear relation to each other, as indireduce the problem to workable dimensions, it is cated in Fig. 1. Qualitatively, then, a methylene generally necessary to simplify i t by certain assump- angle in a cycloalkane can be changed from the tions of conformation or of parameter constancy, (9) T h e I B l I 709 computer, used in t h e present work, is capable of and frequently by simplifying or simply ignoring certain of the relevant energy functions themselves. 8000 additions or subtractions, 4000 multiplications or divisions or (1) This work was supported in part by a generous grant f r o m the Xational Institutes of Health. (2) An excellent review of t h e problems of calculating conforrnations is given b y F. H. Westheimer, in Chap. 12, “Steric Effects in Organic Chemistry,” ed., M , S . Newman, John Wiley and Sons, Inc., S e w York, N . Y . ,1956. (3) D. H. R . Barton, J. Cheiri . F o r , :340 fIR48j. ( 4 ) K S Pitzer and W-. E U o n a t h , J . A m . C‘heni. .Tor., 81, 8213 f19.59).
( 5 ) (a) E. A . N a s o n and hf. bl. Kreevoy, i b i d , 7 7 , 5808 (1955); (b) M. M. Kreevoy and E. A. Mason, i b i d . , 79, 4851 (19.57). (6) P. Hazebroek and L. J Oosterhoff, Disc. F a v a d u r Soc., 10, 87 (195 1j , ( 7 ) R. Pauncz a n d I ) Ginsburg, l‘clrahedvoiz. 9, 40 (11160). (8) S . Allinger, J . A i n . Chein. Soc , 81, 3717 [lit:
