Topological Quantum Molecular Dynamics

TL;DR

This paper introduces a topological quantum molecular dynamics framework that incorporates quantum geometry to accurately simulate reactive quantum dynamics, capturing both adiabatic and non-adiabatic processes.

Contribution

It presents a novel, divergence-free method that encodes electronic quantum geometry via the electronic overlap matrix, advancing the simulation of quantum molecular dynamics.

Findings

Electronic quantum geometry influences atomic motion.

The method is numerically exact and divergence-free.

Electronic states' variation affects dynamics beyond potential energy surfaces.

Abstract

We develop a unified quantum geometric framework to understand reactive quantum dynamics. The critical roles of the quantum geometry of adiabatic electronic states in both adiabatic and non-adiabatic quantum dynamics are unveiled. A numerically exact, divergence-free topological quantum molecular dynamics method is developed through a discrete local trivialization of the projected electronic Hilbert space bundle over the nuclear configuration space. In this approach, the singular electronic quantum geometric tensor-Abelian for adiabatic dynamics and non-Abelian for non-adiabatic dynamics-is fully encoded in the global electronic overlap matrix. With numerical illustrations, it is demonstrated that atomic motion-whether adiabatic or non-adiabatic-is governed not only by the variation in electronic energies with nuclear configurations (potential energy surface) but also by the variation in electronic states (electronic quantum geometry).