Free-Electron Treatment of the Barrier to Internal Rotation in Ethane

Abstract

The cylindrical-model approach to the barrier to internal rotation in ethane first proposed by Karplus and Parr is extended using a free-electron charge distribution. A double-perturbation treatment including both a nuclear geometry and an electronic-repulsion perturbation permits us to distinguish a nuclear repulsion, a polarization, and a polarization-electronic-repulsion contribution to the barrier. The threefold part of the nuclear perturbation is solely responsible both for the nuclear-repulsion contribution (+4.7 kcal/mole) and for the polarization contribution (−3.2 kcal/mole). This last term arises from the differential polarization of the initially cylindrical electron cloud, which is accompanied by a relative increase in electronic density near the center of the eclipsed system. A result of this differential density change is a slight increase in the eclipsed electronic repulsion energy, yielding a third energy contribution (polarization-electronic-repulsion) of +1.5 kcal/mole. A discussion compares the present work to other recent treatments of the internal rotation barrier in ethane.