Finite-size integral equations in the theory of liquids and the thermodynamic limit in computer simulations

M Heidari,K Kremer,R Potestio,R Cortes-Huerto

doi:10.1080/00268976.2018.1482429

Abstract

ABSTRACTWe present an efficient method to obtain bulk isothermal compressibilities () and Kirkwood–Buff (KB) integrals of single- and multicomponent liquids using fluctuations of the number of molecules obtained from small-sized molecular dynamics simulations. We write finite-size versions of the Ornstein–Zernike and the KB integral equations and include there finite size effects related to the statistical ensemble and the finite integration volumes required in computer simulations. Consequently, we obtain analytical expressions connecting and the KB integrals in the thermodynamic limit (TL) with density fluctuations in the simulated system. We validate the method by calculating various thermodynamic quantities, including the chemical potentials of SPC/E water as a function of the density, and of aqueous urea solutions as a function of the mole fraction. The reported results are in excellent agreement with calculations obtained by using the best computational methods available, thus validating the method as a tool to compute the chemical potentials of dense molecular liquids and mixtures. Furthermore, the present method identifies conditions in which computer simulations can be effectively considered in the TL.

Highlights

Statistical mechanics establishes the connection between macroscopic thermodynamic quantities and the microscopic interactions and components of a physical system
Integral equations relate the local structure of a fluid with density fluctuations in the grand canonical ensemble that, in the thermodynamic limit (TL), can be identified with equilibrium thermodynamic quantities such as the compressibility and the derivatives of the chemical potential [1,2]
This relation is routinely employed in spite of the fact that the systems under consideration are constrained to the canonical ensemble and usually far away from TL conditions

Summary

Introduction

Statistical mechanics establishes the connection between macroscopic thermodynamic quantities and the microscopic interactions and components of a physical system. Integral equations relate the local structure of a fluid with density fluctuations in the grand canonical ensemble that, in the thermodynamic limit (TL), can be identified with equilibrium thermodynamic quantities such as the compressibility and the derivatives of the chemical potential [1,2]. In computer simulations, this relation is routinely employed in spite of the fact that the systems under consideration are constrained to the canonical ensemble and usually far away from TL conditions.

Simple liquids

Multicomponent systems

V0 δij ρi

Conclusions