Conical Intersections and Electronic Momentum As Viewed From Phase Space Electronic Structure Theory

2025/06/13 by Titouan Duston, Duston, Titouan, Nadine C. Bradbury +5 · 3 citations
Chemistry · Materials Science · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Chemical Physics (physics.chem-ph) #Chemical and Physical Properties of Materials #FOS: Physical sciences #Quantum and electron transport phenomena

paper · pdf · doi:10.48550/arxiv.2506.11963

openalex publication_date 2025/06/13 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

We investigate the structure of a prototypical two-state conical intersection (BeH₂) using a phase space electronic Hamiltonian H_PS(\bR,\bP) that goes beyond the Born-Oppenheimer framework. By parameterizing the electronic Schrödinger equation by both nuclear position (\bR) and momentum (\bP), we solve for quantum electronic states in a moving frame that can break time reversal symmetry and, as a result, the branching plane of the conical intersection within a phase space framework now has dimension three (rather than dimension two as found within the standard Born-Oppenheimer framework). Moreover, we note that, if one fixes a geometry in real space that lies in the conical intersection seam and scans over the corresponding momentum space, one finds a double well (with minima at ± \bP_min ≠ 0), indicating that the stationary electronic states of the phase space electronic Hamiltonian carry electronic momentum -- a feature that cannot be captured by a Born-Oppenheimer electronic state. Interestingly, for BeH₂, this electronic momenta (as calculated with full configuration interaction) agrees with what is predicted by approximate complex restricted Hartree-Fock calculations, indicating a physical interpretation of complex instabilities in modern electronic structure calculations. Altogether, this study suggests that we have still have a lot to learn about conical intersections when it comes to electronic momentum, and highlights the urgent need for more experiments to probe what photochemical observables can and/or cannot be captured by standard electronic structure that isolates conical intersections within the Born-Oppenheimer framework.

Cited by

• Phase Space Electronic Structure Theory: From Diatomic Lambda-Doubling to Macroscopic Einstein-de Haas
• Restoring the Conical Intersection Topology using Convex Density Functional Theory
• Convex Hartree-Fock theory: A simple framework for ground state conical intersections

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