Evaluation of the nondiabaticity of quantum molecular dynamics with the dephasing representation of quantum fidelity

TL;DR

This paper introduces a computationally efficient method based on the dephasing representation to evaluate the significance of non-Born-Oppenheimer effects in quantum molecular dynamics, applicable to various potential energy surfaces.

Contribution

It generalizes the dephasing representation of quantum fidelity to multiple diabatic surfaces, enabling easy integration into molecular dynamics simulations with on-the-fly electronic structure data.

Findings

Accurately describes fidelity decay near the diabatic limit.

Captures subtle quantum effects beyond population transfer.

Applicable to complex molecular systems to assess nonadiabatic effects.

Abstract

We propose an approximate method for evaluating the importance of non-Born-Oppenheimer effects on the quantum dynamics of nuclei. The method uses a generalization of the dephasing representation (DR) of quantum fidelity to several diabatic potential energy surfaces and its computational cost is the cost of dynamics of a classical phase space distribution. It can be implemented easily into any molecular dynamics program and also can utilize on-the-fly ab initio electronic structure information. We test the methodology on three model problems introduced by Tully and on the photodissociation of NaI. The results show that for dynamics close to the diabatic limit the decay of fidelity due to nondiabatic effects is described accurately by the DR. In this regime, unlike the mixed quantum-classical methods such as surface hopping or Ehrenfest dynamics, the DR can capture more subtle quantum effects than the population transfer between potential energy surfaces. Hence we propose using the DR to estimate the dynamical importance of diabatic, spin-orbit, or other couplings between potential energy surfaces. The acquired information can help reduce the complexity of a studied system without affecting the accuracy of the quantum simulation.