Examination of the Feynman-Hibbs Approach in the Study of Ne$_N$-Coronene Clusters at Low Temperatures

TL;DR

This study evaluates the Feynman-Hibbs effective potential method for modeling Ne$_N$-coronene clusters at low temperatures, highlighting its accuracy above 4 K and limitations below, with a new correction for the FH4 potential.

Contribution

The paper introduces a corrected FH4 effective potential expression and assesses its applicability to Ne$_N$-coronene clusters at low temperatures.

Findings

FH2 and FH4 potentials improve classical results above 4 K

FH approach fails at temperatures below 4 K, especially FH4

Estimated validity range increases with cluster size

Abstract

Feynman-Hibbs (FH) effective potentials constitute an appealing approach for investigations of many-body systems at thermal equilibrium since they allow us to easily include quantum corrections within standard classical simulations. In this work we apply the FH formulation to the study of Ne$_N$-coronene clusters ($N=$ 1-4, 14) in the 2-14 K temperature range. Quadratic (FH2) and quartic (FH4) contributions to the effective potentials are built upon Ne-Ne and Ne-coronene analytical potentials. In particular, a new corrected expression for the FH4 effective potential is reported. FH2 and FH4 cluster energies and structures -obtained from energy optimization through a basin-hoping algorithm as well as classical Monte Carlo simulations- are reported and compared with reference path integral Monte Carlo calculations. For temperatures $T> 4$ K, both FH2 and FH4 potentials are able to correct the purely classical calculations in a consistent way. However, the FH approach fails at lower temperatures, especially the quartic correction. It is thus crucial to assess the range of applicability of this formulation and, in particular, to apply the FH4 potentials with great caution. A simple model of $N$ isotropic harmonic oscillators allows us to propose a means of estimating the cut-off temperature for the validity of the method, which is found to increase with the number of atoms adsorbed on the coronene molecule.