Thermodynamics and Structural Properties of the High Density Gaussian Core Model

TL;DR

This study investigates the thermodynamic and structural properties of the high-density Gaussian core model, confirming theoretical predictions about phase boundaries and assessing the accuracy of the random phase approximation across different regimes.

Contribution

It provides detailed numerical analysis of the GCM at high densities, validating asymptotic relations for phase boundaries and evaluating RPA's predictive capabilities.

Findings

Phase boundary follows $ ho^{2/3}$ asymptotic relation.

RPA accurately predicts thermodynamics even near phase boundary.

Structural predictions of RPA are limited at interparticle length scales.

Abstract

We numerically study thermodynamic and structural properties of the one-component Gaussian core model (GCM) at very high densities. The solid-fluid phase boundary is carefully determined. We find that the density dependence of both the freezing and melting temperatures obey the asymptotic relation, $\log T_f$, $\log T_m \propto -\rho^{2/3}$, where $\rho$ is the number density, which is consistent with Stillinger's conjecture. Thermodynamic quantities such as the energy and pressure and the structural functions such as the static structure factor are also investigated in the fluid phase for a wide range of temperature above the phase boundary. We compare the numerical results with the prediction of the liquid theory with the random phase approximation (RPA). At high temperatures, the results are in almost perfect agreement with RPA for a wide range of density, as it has been already shown in the previous studies. In the low temperature regime close to the phase boundary line, although RPA fails to describe the structure factors and the radial distribution functions at the length scales of the interparticle distance, it successfully predicts their behaviors at shorter length scales. RPA also predicts thermodynamic quantities such as the energy, pressure, and the temperature at which the thermal expansion coefficient becomes negative, almost perfectly. Striking ability of RPA to predict thermodynamic quantities even at high densities and low temperatures is understood in terms of the decoupling of the length scales which dictate thermodynamic quantities from the interparticle distance which dominates the peak structures of the static structure factor due to the softness of the Gaussian core potential.