A phase-space view of vibrational energies without the Born-Oppenheimer framework

TL;DR

This paper proposes a phase-space approach to vibrational energies in quantum chemistry, replacing the Born-Oppenheimer approximation with a Hamiltonian that includes nuclear momenta, leading to more accurate vibrational energy calculations.

Contribution

It introduces a non-perturbative phase-space electronic Hamiltonian that incorporates nuclear momenta, improving vibrational energy predictions over traditional Born-Oppenheimer methods.

Findings

Phase-space Hamiltonian yields meaningful electronic momenta.

Results show improved vibrational energies for a three-particle system.

Method has similar computational cost to standard Born-Oppenheimer calculations.

Abstract

We show that following the standard mantra of quantum chemistry and diagonalizing the Born-Oppenheimer (BO) Hamiltonian $\hat H_{\rm BO}(\bm R)$ is not the optimal means to construct potential energy surfaces. A better approach is to diagonalize a phase-space electronic Hamiltonian, $\hat H_{\rm PS}(\bm R,\bm P)$, which is parameterized by both nuclear position $\bm R$ and nuclear momentum $\bm P$. The foundation of such a non-perturbative phase-space electronic Hamiltonian can be made rigorous using a partial Wigner transform and the method has exactly the same cost as BO for a semiclassical calculation (and only a slight increase in cost for a quantum nuclear calculation). For a three-particle system, with two heavy particles and one light particle, numerical results show that a phase space electronic Hamiltonian produces not only meaningful electronic momenta (which are completely ignored by BO theory) but also far better vibrational energies. As such, for high level results and/or systems with degeneracies and spin degrees of freedom, we anticipate that future electronic structure and quantum chemistry packages will need to take as input not just the positions of the nuclei but also their momenta.