Structure of molecular liquids: cavity and bridge functions of the hard spheroid fluid

TL;DR

This paper develops methods to compute correlation and bridge functions for molecular liquids using Monte Carlo simulations, comparing results with integral equation theory for hard spheroid fluids, and explores the accuracy of different theoretical closures.

Contribution

It introduces a novel approach to calculate cavity and bridge functions from simulations and integrates these into existing integral equation closures for molecular liquids.

Findings

Good agreement at low densities between theory and simulation.

HNC results improve with approximate bridge functions at higher densities.

Significant discrepancies remain at high densities despite improvements.

Abstract

We present methodologies for calculating the direct correlation function, c(1,2), the cavity function, y(1,2), and the bridge function, b(1,2), for molecular liquids, from Monte Carlo simulations. As an example we present results for the isotropic hard spheroid fluid with elongation e=3. The simulation data are compared with the results from integral equation theory. In particular, we solve the Percus-Yevick and Hypernetted Chain equations. In addition, we calculate the first two terms in the virial expansion of the bridge function and incorporate this into the closure. At low densities, the bridge functions calculated by theory and from simulation are in good agreement, lending support to the correctness of our numerical procedures. At higher densities, the hypernetted chain results are brought into closer agreement with simulation by incorporating the approximate bridge function, but significant discrepancies remain.