Revisiting an approximation in the Wilson G-matrix formalism and its impact on molecular quantum dynamics

TL;DR

This paper examines the impact of assuming a constant Jacobian determinant in the Wilson G-matrix formalism for quantum molecular dynamics, demonstrating potential errors and proposing a strategy to mitigate them.

Contribution

It revisits a key approximation in the Wilson G-matrix formalism, quantifies its error, and offers a method to improve the accuracy of quantum dynamics simulations.

Findings

The constant Jacobian determinant approximation can introduce significant errors.

The error is demonstrated using a harmonic oscillator model.

A new strategy is proposed to prevent this approximation error.

Abstract

Quantum dynamics simulations of reactive molecular processes are commonly performed in a low-dimensional space spanned by highly optimized reactive coordinates. Usually, these sets of reactive coordinates consist of non-linear coordinates. The Wilson G-matrix formalism allows to formulate the Hamiltonian in arbitrary coordinates. In our present work, we revisit an approximation in this formalism, namely the assumption that the Jacobian determinant is constant. We show that the approximation can introduce an error and illustrate it for a harmonic oscillator. Finally, we present a strategy to prevent this error.