Recovering Exact Vibrational Energies Within a Phase Space Electronic Structure Framework

TL;DR

This paper develops a rigorous perturbation theory framework to extract exact quantum vibrational energies from a phase space electronic structure approach, addressing theoretical gaps and justifying the method's validity.

Contribution

It provides the first formal method to recover exact vibrational energies within a phase space electronic structure framework using perturbation theory.

Findings

Demonstrates how to extract exact quantum energies from a coupled Hamiltonian

Justifies phase space electronic structure approaches with a rigorous correction method

Addresses theoretical gaps in using phase space eigenvectors for vibrational energies

Abstract

In recent years, there has been a push to go beyond Born-Oppenheimer theory and build electronic states from a phase space perspective, i.e. parameterize electronic states by both nuclear position(R) and nuclear momentum(P). Previous empirical studies have demonstrated that such approaches can yield improved single-surface observables, including vibrational energies, electronic momenta, and vibrational circular dichroism spectra. That being said, unlike the case of BO theory, there is no unique phase space electronic Hamiltonian, nor any theory for using phase space eigenvectors (as opposed to BO eigenvectors) so as to recover exact quantum vibrational eigenvalues. As such, one might consider such phase space approaches ad hoc. To that end, here we show how to formally extract exact quantum energies from a coupled nuclear-electronic Hamiltonian using perturbation theory on top of a phase space electronic framework. Thus, while we cannot isolate an "optimal" phase space electronic Hamiltonian, this work does justify a phase space electronic structure approach by offering a rigorous framework for correcting the zeroth order phase space electronic states.