Study of the electronic structure of molecules. XIII. Bond energy analysis for the ethane molecule

Abstract

The total energy of the C2H6 molecule has been decomposed into one-, two-, three-, and four-center energy contributions, according to a scheme previously proposed ("bond energy analysis"). This was done for the eclipsed, for the staggered configurations, and for rotational angles of 10°, 30°, and 50°. It has been found that the 4 two-center energies of the carbon atom with its four nearest neighbors are nearly equal (the C-H being 94% of C-C), that the hydrogen-hydrogen repulsion within a given methyl group is about one-tenth of the two-center C-C attraction, and that the repulsion of a carbon on one methyl group with the hydrogens on the other methyl group is about 1.5 tenths of the C-C interaction. The repulsion of one hydrogen on one methyl group with a hydrogen on the other methyl group is small and varies around 0.2 tenths of the C-C interaction. During rotation, the field within each methyl group (taken as a unit) varies in such a way as to bring about an energy variation which opposes the barrier. On the other hand, the methyl-methyl interaction more than compensates this effect, yielding a barrier of about 3.1 kcal. In greater detail we conclude that whereas the carbon-carbon interaction favors the barrier, the rearrangement within the carbon opposes the barrier but not as much as to compensate the C-C interaction, that the rearrangement of the Hs group is more important than the interaction between the two HS groups, and that the carbon on a methyl group interacting with the Hs of the second methyl group has an interaction of such a sign as to favor the barrier, whereas the opposite is true for the interaction of a carbon atom and H3 on the same methyl group. The bond energy analysis seems to propose a model of "checks and balances" involving local energy variations much larger than the small rotational barrier (computed within good agreement of the experimental barrier) ; thus, the barrier is a result of heavy cancellation of large energies with opposite sign. A word of caution concerning some of the arbitrariness of the "bond energy analysis" formalism has been inserted frequently in this paper. However, the bond energy analysis on the C2He molecule seems to be a too! of value for explaining not only the balance of forces but also to give a detailed model of the barrier to internal rotation.