How accurate is molecular dynamics?

TL;DR

This paper demonstrates that Born-Oppenheimer dynamics accurately approximates time-independent Schrödinger observables for molecular systems with an electron spectral gap, especially in the large mass ratio limit, offering new insights into molecular simulation accuracy.

Contribution

It provides a novel derivation of the Born-Oppenheimer approximation using Hamiltonian systems, including caustic states, without assuming nuclei localization, and offers a new perspective on molecular dynamics modeling.

Findings

Born-Oppenheimer dynamics accurately approximates Schrödinger observables

The derivation does not require nuclei localization assumptions

Includes analysis of caustic states and Hamilton-Jacobi stability

Abstract

Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schr\"odinger observables for a molecular system with an electron spectral gap, in the limit of large ratio of nuclei and electron masses, without assuming that the nuclei are localized to vanishing domains. The derivation, based on a Hamiltonian system interpretation of the Schr\"odinger equation and stability of the corresponding Hamilton-Jacobi equation, bypasses the usual separation of nuclei and electron wave functions, includes caustic states and gives a different perspective on the Born-Oppenheimer approximation, Schr\"odinger Hamiltonian systems and numerical simulation in molecular dynamics modeling at constant energy microcanonical ensembles.