Coupling electrons and vibrations in molecular quantum chemistry

TL;DR

This paper introduces a new electron-vibration Hamiltonian model in quantum chemistry that captures nonadiabatic effects without relying on potential energy surfaces, demonstrated through pyrazine simulations.

Contribution

The authors develop a simple two-body electron-vibration Hamiltonian derived directly from quantum chemical integrals, enabling new approaches to nonadiabatic dynamics modeling.

Findings

Model Hamiltonian captures key nonadiabatic effects in pyrazine

Demonstrates population transfer between excited states

Applicable to standard quantum chemical methods

Abstract

We derive an electron-vibration model Hamiltonian in a quantum chemical framework, and explore the extent to which such a Hamiltonian can capture key effects of nonadiabatic dynamics. The model Hamiltonian is a simple two-body operator, and we make preliminary steps at applying standard quantum chemical methods to evaluating its properties, including mean-field theory, linear response, and a primitive correlated model. The Hamiltonian can be compared to standard vibronic Hamiltonians, but is constructed without reference to potential energy surfaces, through direct differentiation of the one- and two-electron integrals at a single reference geometry. The nature of the model Hamiltonian in the harmonic and linear-coupling regime is investigated for pyrazine, where a simple time-dependent calculation including electron-vibration correlation is demonstrated to exhibit the well-studied population transfer between the S$_2$ and S$_1$ excited states.