Is there a general rule for the gauche effect in the conformational isomerism of 1,2-disubstituted ethanes?

The stabilities of the gauche and anti conformations of butane, 1,2-dicyanoethane (DCE), and 1,2-dinitroethane (DNE) have been investigated through theoretical calculations. The gauche effect-the tendency of keeping close vicinal electronegative substituents (thetaX-C-C-X approximately 60 degrees ) in an ethane fragment-is expected to drive the conformational equilibrium of DCE and DNE toward the gauche conformation. It was found that, for butane, where the gauche effect is supposed to be poor/null, the hyperconjugation effect contributes mostly to the anti stabilization in opposition to the traditional sense that the methyl groups repel each other, and this should govern its conformational equilibrium. For DCE the equilibrium was shifted to the anti conformer, essentially due to a gauche repulsion, while for DNE, despite the higher electronic delocalization energies, a predominance of the gauche conformer was obtained, and this was attributed mainly to the attractive dipolar interaction between the two nitro groups. A full orbital energy analysis was performed using the natural bond orbital approach, which showed that bond bending and anti-C-H/C-X* hyperconjugation models, usually applied to explain the origin of the gauche effect in fluorinated derivatives, are not adequate to completely explain the conformational behavior of the titled compounds.