Born-Oppenheimer expansion at constant energy

Abstract

The well-known Born-Oppenheimer procedure considers molecular properties in the limit of large values of the nuclear mass M (in units of electronic mass), with quantum numbers held constant. It is shown that the lowest-order correction to the molecular wave function is proportional to M(-34). Here we consider the same expansion, but with energy held constant instead of quantum numbers. We show that, if the singular coupling term near a conical intersection is removed via a quasidiabatic transformation, the lowest-order remaining correction is proportional to M(-12).