First-order corrections to semiclassical Gaussian partition functions for clusters of atoms

TL;DR

This paper introduces a first-order correction to Gaussian approximations of the Boltzmann operator, improving accuracy at low temperatures for atomic clusters, exemplified by the argon trimer.

Contribution

It presents a novel first-order correction method for Gaussian propagators, enabling assessment of approximation quality and optimal parameter selection.

Findings

Correction term indicates the Gaussian approximation's validity range.

Identifies the temperature at which the Gaussian method becomes unreliable.

Provides insights into the thermodynamic transition of the argon trimer.

Abstract

Gaussian approximations to the Boltzmann operator have proven themselves in recent years as useful tools for the study of the thermodynamic properties of rare gas clusters. They are, however, not necessarily correct at very low temperatures. In this article we introduce a first-order correction term to the frozen Gaussian imaginary time propagator and apply it to the argon trimer. Our findings show that the correction term provides objective access to the quality of the propagator's results and clearly defines the "best" Gaussian width parameter. The strength of the correction monitored as a function of the temperature indicates that the results of the Gaussian propagator become questionable below a certain temperature. The interesting thermodynamic transition from a bounded trimer to three body dissociation lies in the temperature range for which the Gaussian approximation is predicted to be accurate.