Controlling energy conservation in quantum dynamics with independently moving basis functions: Application to Multi-Configuration Ehrenfest

TL;DR

This paper introduces a method to control energy conservation in quantum dynamics simulations using independently moving basis functions, specifically applied to Multi-Configuration Ehrenfest, enabling parallel computation without energy loss.

Contribution

It proposes a Lagrange multiplier approach to enforce energy and norm conservation in independent trajectory methods, improving computational efficiency and accuracy.

Findings

Energy conservation maintained with independent trajectories

Method successfully applied to a vibronic coupling model

Enables parallelization of quantum dynamics simulations

Abstract

Application of the time-dependent variational principle to a linear combination of frozen-width Gaussians describing the nuclear wavefunction provides a formalism where the total energy is conserved. The computational downside of this formalism is that trajectories of individual Gaussians are solutions of a coupled system of differential equations, limiting implementation to serial propagation algorithms. To allow for parallelization and acceleration of the computation, independent trajectories based on simplified equations of motion were suggested. Unfortunately, within practical realizations involving finite Gaussian bases, this simplification leads to breaking the energy conservation. We offer a solution for this problem by using Lagrange multipliers to ensure the energy and norm conservation regardless of basis function trajectories or basis completeness. We illustrate our approach within the Multi-Configuration Ehrenfest method considering a linear vibronic coupling model.