Energy Corrections to the Born–Oppenheimer Approximation. The Best Adiabatic Approximation

Abstract

Procedures are presented for solving the previously derived exact coupled Schrödinger equations for the internal motion of a diatomic system, using both nonadiabatic variation methods and adiabatic perturbation methods. A “best adiabatic” (BA) approximation is variationally derived to give the energetically best possible adiabatic vibration–rotation energies and potential‐energy curves. The BA electronic wavefunctions are shown to satisfy a set of coupled equations, involving the complete internal Hamiltonian of the system, which leads immediately to a generalization of the noncrossing rule for potential‐energy curves. Methods for solving these coupled electronic equations to obtain corrections to the Born–Oppenheimer approximation, valid in the presence of rotational degeneracies, are presented. And finally, some upper‐and lower‐bound properties of various adiabatic approximations are investigated.