Recovering Exact Vibrational Energies Within a Phase Space Electronic Structure Framework

2025/06/09 by Xinchun Wu, Xuezhi Bian, Wu, Xinchun +7 · 3 citations
Physics and Astronomy · #Advanced Chemical Physics Studies #Chemical Physics (physics.chem-ph) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Physics (quant-ph) #Spectroscopy and Quantum Chemical Studies

paper · pdf · doi:10.48550/arxiv.2506.08230

openalex publication_date 2025/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Moving Born-Oppenheimer Approximation
• A phase-space view of vibrational energies without the Born-Oppenheimer framework
• A Basis-Free Phase Space Electronic Hamiltonian That Recovers Beyond Born-Oppenheimer Electronic Momentum and Current Density
• Practical Phase-Space Electronic Hamiltonians for Ab Initio Dynamics
• A Simple One-Electron Expression for Electron Rotational Factors
• Dynamical Theory of Crystal Lattices

Cited by

• Phase Space Electronic Structure Theory: From Diatomic Lambda-Doubling to Macroscopic Einstein-de Haas
• The Phase-Space Way To Electronic Structure Theory and Subsequently Chemical Dynamics
• Conical Intersections and Electronic Momentum As Viewed From Phase Space Electronic Structure Theory

Related

• A phase-space view of vibrational energies without the Born-Oppenheimer framework
• A Basis-Free Phase Space Electronic Hamiltonian That Recovers Beyond Born-Oppenheimer Electronic Momentum and Current Density
• The Phase-Space Way To Electronic Structure Theory and Subsequently Chemical Dynamics
• A Phase Space Approach to Vibrational Circular Dichroism
• Practical Phase-Space Electronic Hamiltonians for Ab Initio Dynamics