Sept. 5, 1962
METHYL-CYCLOHEXANES AND CYCLOHEPTANES
and then allowed to stand until darkened in a closed flask, which indicates a hydride transfer mechanism for this decomposition. Our studies in this area are continuing with the investigation of solid state spectra, determination
[COSTRIBCTIOS FROM
THE
DEPARTMEST OF CHEMISTRY OF
3355
of association constants and examination of the charge-transfer spectra of substituted tropenium halides. Acknowledgment.-%~e wish to thank Ann B. Harmon for considerable technical assistance.
THE
UNIVERSITY OF CALIFORNIA AT Los ANGELES, CALIF.]
Molecular Geometry. 11. Methyl-cyclohexanes and Cycloheptanesl? BY
JAMES
B.HENDRICKSON3
RECEIVED DECEMBER 23, 1961 Machine computation is applied to the calculation of the energy difference between axial and equatorial methyls on cyclohexane. A value of 1.01 kcal./mole is obtained. Similar calculations for methyl groups on various discrete conformations of the flexible cycloheptane ring are also calculated and the use of these values in delineating the conformational analysis of substituted cycloheptanes is discussed.
The energy difference between axial and equa- part I,* and added to provide the total strain torial substituents on cyclohexane has long been a energy of the molecule. The energy so calculated central feature of conformational analysis. The is more or less meaningless in absolute terms, as it values generally accepted for this difference vary contains no assessment of bond or coulombic enerfrom 1.G-2.0 kcal./mole for axial vs. equatorial gies or of zero-point energies or terms for vibration methyl groups, derived from spectroscopic and and rotation of the various bonds. The exclusion of thermodynamic considerations. The problem of these terms is largely justified on the ground that calculating the energy difference2 between axial they will cancel in any calculation of energy difand equatorial methylcyclohexane seemed to be an ferences between closely related conformers. Neverimportant one for several reasons. Firstly, since theless, such an approximation of second-order conthis energy difference is made up mostly of a large tributions probably puts a serious limitation on the number of fairly minor non-bonded interactions accuracy of the values calculated. I n any event the between the differently placed methyls and the ring, availability of empirical values for some of the enit provides an especially delicate test of the efficacy ergy differences so calculated can serve as a check of a computer approach as well as of the accuracy of on the validity of this approximation, as in the exthe non-bonded interaction functions chosen. amples of part I . 2 Secondly, of course, the computed results inay be ;Is the sum of the three energy terms coiisitlercd coinpared with reliable experimental Tralues, and, here (angle bending, torsional strain and nonfiilally, should the computer technique providc a bonded interactions of hydrogens) was already reasonable approximation to the empirical values available from the previous computations' for tlic it might be used with some confidence to afford as parent ring itself, without added methyl, it was well the corresponding energies of methyls on more deemed simpler to start with this ring value and complex rings. The latter is of particular impor- add to it the changes occasioned by attaching the tance in providing a semi-quantitative basis for con- methyl group. This involves adding the change in formational analysis in the conformationally more angle bending energy5 a t the site of the new methyl, complex cycloheptane system. the torsional strain due to rotation ( w b l ) of thc Dissection of the problem for machine computa- methyl group around its bond to the ring, and tion (see Fig. 1) involves assignment of a specific finally the sum of the new non-bonded H-H interconforniation to the ring and calculation of the actions from the methyl hydrogens t o the ring tvtal energy of the molecule with the methyl group hydrogens and subtraction of those interactioiis attached a t a given carbon, first in one orientation due to that hydrogen replaced by the methyl ((f.axial) and then in the other (cf. equatorial); group on the parent ring. The various H -H dissubtraction then affords the desired energy dif- tances to be calculated from the methyl hydrogens , ference. The choice of functions here follows the il, B and C are functioiis of the bond angles 4 ~ 1 8., discussion in part 1'; energy terms were considered ea, etc., and of the dihedral (torsional) angles, U ~ I to be those arising from bond angle bending. tor- u l r w?, etc.; the latter are given as part of the defisioiial strain arouiid single bonds and non-bonded nition of the parent ring and are modified for interactions between hydrogens; these are sepa- these distance calculations t o substituents (CH:jor rately calculated, using the functions discussed in H) by addition or subtraction of the relevant projection angle, as pbf, in Fig. 2 . (1) This work was supported in p a r t b y a generous g r a n t from t h e I n a general program for the computer, these S a t i o n a l Institutes of Health. ( 2 ) Paper I of t h e series: J. B. Hendrickson, J . A i r z . C h i m . Soc., 83, interactions are all separately computed and added 4337 (1961). for each given parent ring conformation. dlso, in (3) Alfred P Sloan Foundation Fellow. (4) W. G. 1)auben and K . S. Pitzer, Chap. 1 rrf "Steric liflecls in Organic Chemistry," ed. AI. S . Newman, J u h n \4iley and Son., I n c , l e r u York, S . Y . , 1936; C . W.Beckett, I;.S. Pitzer and I
