Quasi-classical description of molecular dynamics based on Egorov's theorem

TL;DR

This paper explores the connection between Egorov's theorem and quasi-classical methods in molecular dynamics, providing error estimates and numerical validation for different models.

Contribution

It establishes a theoretical link between Egorov's theorem and quasi-classical molecular dynamics methods, with error analysis and numerical experiments.

Findings

Different accuracies are achievable for expectation values and densities.

Numerical experiments validate theoretical error estimates.

Methods are tested on Morse and Henon-Heiles models.

Abstract

Egorov's theorem on the classical propagation of quantum observables is related to prominent quasi-classical descriptions of quantum molecuar dynamics as the linearized semiclassical initial value representation (LSC-IVR), the Wigner phase space method or the statistical quasiclassical method. The error estimates show that different accuracies are achievable for the computation of expectation values and position densities. Numerical experiments for a Morse model of diatomic iodine and confined Henon-Heiles systems in various dimensions illustrate the theoretical results.