Which masses are vibrating or rotating in a molecule?

Abstract

The traditional formulation of a molecular wave function describing the motion of the electrons and the nuclei in terms of the Born hierarchy does not allow us to account for the participation of the electrons in vibrational or rotational motion, except by resorting to a fully non-adiabatic treatment, abandoning completely the concept of a single potential energy surface for one electronic state of the molecule. An alternative approach is presented that is based on an exact separation in all possible dissociation limits. One obtains a wave function of a generalized valence bond form in terms of neutral fragments with the adiabatic ansatz in the limit of infinite nuclear masses. An energy expression is obtained correct to O(M −2), where M is a representative nuclear mass in units of the electron mass. This expression involves a single potential energy surface, but a geometry-dependent reduced mass for vibration and rotation, in which the participation of the electrons is taken care of. The vibrational mass differs from the rotational mass. For and H2, approximations to these effective masses are obtained for the first time in a simple way in terms of a LCAO or a Heitler–London formalism, respectively. In the electron participates to roughly 60% in vibration, but only about 30% in rotation. Similar values are found for H2. Such a fractional participation appears typical for valence electrons, whereas inner-shell electrons are likely to participate fully both in vibration and rotation.