C-C bond. When the hydrogens are bent inward, they approach the nodes and their coefficients decrease. This means that CH bonding character is diminished. The opposite is true when the hydrogens are bent back. Not only additional CH but also enhanced CC bonding develops. The energy of the azu orbital is lower when the HCC angles are enlarged. This orbital is comprised largely of s components and has CC antibonding character. The latter is reduced on bending.
When the carbon p-orbitals are aligned perpendicular to the C-C bond, degenerate MO's of pseudo-n: (e,) and pseudo-n* (e,) symmetry result. The energies of both sets of these orbitals increase at larger CCH angles since the CH bonding character is diminished. Of course, ethane distortion from the equilibrium geometry raises the overall energy, but the effects are distributed differently. A large CCH angle favors CC bonding, whereas this is decreased when this angle becomes smaller. The effects of these distortions on the CH bond energies are opposite.
Distortion also alters the hybridization. With an ethane HCC angle of go", the bonds to the hydrogens are nearly sp2 hybridized, whereas very little s-character is present in the C-C bond. Conversely, a widened HCC angle increases the s-character along the C-C bond. This rehybridization effect, long familiar in cyclopropane, is more dramatic in tetrahedrane, as the external bonds have roughly sp ~haracter."~] Hence, the central C(sp)-C(sp) bond in 7 can be compared with thecentral bond in 1,3-butadiyne (Table 1). Not just the hybridization in the latter, but also the conjugation and the lower coordination reduce the bond length to 1.38 A (Table 1). Hence, the value calculated for 7 is somewhat larger.
As has been pointed out by Ermer, Szeimies, et al. it might be possible to prepare the hexa-tert-butyl derivative of 7.[4b1 They suggested that the X-ray central bond length of 1.440(2) A in a bi-[l-tricyclo[3.1 .0.02~6]hexyl] derivative might be taken as the upper limit for the C1-C1' value in 7. Our 6-31G* calculations agree. We predict the central bond in 7 to be 1.438 -t 0.01 A in length. The 3-21G rotational barrier is 2.3 kcal mot -considerably smaller than the ca. 10 kcal mol barriers for typical tert-butyl group rotations. "']