The Importance of the Pre-exponential Factor in Semiclassical Molecular Dynamics

TL;DR

This paper investigates the significance of the pre-exponential factor in semiclassical molecular dynamics, proposing new approximation methods and validating their accuracy across complex systems and molecules.

Contribution

It introduces novel analytical and numerical approximations for the pre-exponential factor in semiclassical dynamics, enhancing simulation accuracy for chaotic and complex systems.

Findings

Approximations are accurate for power spectrum calculations.

Methods work well for chaotic model systems.

Validated on molecules with known quantum values.

Abstract

This paper deals with the critical issue of approximating the pre-exponential factor in semiclassical molecular dynamics. The pre-exponential factor is important because it accounts for the quantum contribution to the semiclassical propagator of the classical Feynman path fluctuations. Pre-exponential factor approximations are necessary when chaotic or complex systems are simulated. We introduced pre-exponential factor approximations based either on analytical considerations or numerical regularization. The approximations are tested for power spectrum calculations of more and more chaotic model systems and on several molecules, for which exact quantum mechanical values are available. The results show that the pre-exponential factor approximations introduced are accurate enough to be safely employed for semiclassical simulations of complex systems.