High-order geometric integrators for representation-free Ehrenfest dynamics

TL;DR

This paper introduces high-order geometric integrators for representation-free Ehrenfest dynamics, enabling efficient, accurate, and structure-preserving simulations of quantum-classical molecular systems without relying on electronic state representations.

Contribution

The authors develop and demonstrate efficient, high-order, geometric integrators for Ehrenfest dynamics that preserve key physical properties regardless of the time step size.

Findings

Integrators are norm-conserving, symplectic, and time-reversible.

They outperform non-geometric integrators in accuracy and efficiency for nonadiabatic simulations.

Applicable to complex molecular systems near conical intersections.

Abstract

Ehrenfest dynamics is a useful approximation for ab initio mixed quantum-classical molecular dynamics that can treat electronically nonadiabatic effects. Although a severe approximation to the exact solution of the molecular time-dependent Schr\"odinger equation, Ehrenfest dynamics is symplectic, time-reversible, and conserves exactly the total molecular energy as well as the norm of the electronic wavefunction. Here, we surpass apparent complications due to the coupling of classical nuclear and quantum electronic motions and present efficient geometric integrators for "representation-free" Ehrenfest dynamics, which do not rely on a diabatic or adiabatic representation of electronic states and are of arbitrary even orders of accuracy in the time step. These numerical integrators, obtained by symmetrically composing the second-order splitting method and exactly solving the kinetic and potential propagation steps, are norm-conserving, symplectic, and time-reversible regardless of the time step used. Using a nonadiabatic simulation in the region of a conical intersection as an example, we demonstrate that these integrators preserve the geometric properties exactly and, if highly accurate solutions are desired, can be even more efficient than the most popular non-geometric integrators.