Adiabatic coupling between electronic and nuclear motion in molecules

Abstract

The coupling between electronic and nuclear motion in diatomic molecules is investigated, particular attention being devoted to configurations in which the nuclei are separated by large distances. The analysis shows that at these distances nuclear-electronic coupling causes to a first approximation a change in potential energy of the order ( m/M ) times the kinetic energy of the electrons, m being the electronic mass and M the nuclear mass, provided that the molecule separates into atoms in S states . For such cases, nuclear-electronic coupling can in general be ignored, but if at least one of the separated atoms is in a state of non-zero orbital angular momentum, coupling introduces terms which are not negligible compared to the usual van der Waals interaction. Quantitative results over all nuclear separations are given for the 1 sσ g and 2 pσ u states of H + 2 and the 1 Σ g and 3 Σ u states of H 2 , the 1 sσ g state of H + 2 being investigated in detail using both exact and approximate solutions of the static (or fixed nuclei) equation in order to assess the error involved in the use of the latter. Accurate asymptotic expressions valid in the limit of large nuclear separations are obtained for the 1 sσ and 2 pσ states of H + 2 and of HeH 2+ , and a brief discussion is also given of the inert gas molecules.