Electric Transition Dipole Moment in pre-Born-Oppenheimer Molecular Structure Theory

TL;DR

This paper develops a full quantum mechanical method to calculate electric transition dipole moments in molecules without using the Born-Oppenheimer approximation, treating electrons and nuclei equally.

Contribution

It introduces a novel pre-Born-Oppenheimer approach for calculating electric transition dipole moments using explicitly correlated Gaussian basis functions.

Findings

First full quantum calculation of electric transition dipole moments without Born-Oppenheimer approximation.

Derived integral expressions in laboratory-fixed Cartesian coordinates.

Applied method to H2 molecule's rovibronic states.

Abstract

This paper presents the calculation of the electric transition dipole moment in a pre-Born-Oppenheimer framework. Electrons and nuclei are treated equally in terms of the parametrization of the non-relativistic total wave function, which is written as a linear combination of basis functions constructed with explicitly correlated Gaussian functions and the global vector representation. The integrals of the electric transition dipole moment are derived corresponding to these basis functions in both the length and the velocity representation. The complete derivation and the calculations are performed in laboratory-fixed Cartesian coordinates without relying on coordinates which separate the center of mass from the translationally invariant degrees of freedom. The effect of the overall motion is eliminated via translationally invariant integral expressions. As a numerical example the electric transition dipole moment is calculated between two rovibronic levels of the H2 molecule assignable to the lowest rovibrational states of the X ^1Sigma^+_g and B ^1Sigma^+_u electronic states in the clamped-nuclei framework. This is the first evaluation of this quantity in a full quantum mechanical treatment without relying on the Born-Oppenheimer approximation.