Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function. (1st September 2016)

• Record Type: Journal Article
• Authors: Kelly, Braden D.; Smith, William R.; Henderson, Douglas
• Is Part Of: Molecular physics. Volume 114:Number 16/17(2016)
• Page Start: 2446
• Page End: 2450
• Publication Date: 2016-09-01
• Subjects: Hard-sphere -- Percus-Yevick -- radial distribution function -- integral equation; Molecules -- Periodicals; Chemistry, Physical and theoretical -- Periodicals; Molécules -- Périodiques; Chimie physique et théorique -- Périodiques; 539.6.05
• DOI: 10.1080/00268976.2016.1164908
• Languages: English
• ISSNs: 0026-8976

Abstract

ABSTRACT: Explicit analytical expressions are presented for the density derivative, ∂ g HS ( R ; ρ)/∂ρ, of the Percus–Yevick approximation to the hard-sphere radial distribution function for R ≤ 6σ, where σ is the hard-sphere diameter and ρ = ( N / V )σ 3 is the reduced density, where N is the number of particles and V is the volume. A FORTRAN program is provided for the implementation of these for R ≤ 6σ, which includes code for the calculation of g HS ( R ; ρ) itself over this range. We also present and incorporate within the program code convenient analytical expressions for the numerical extrapolation of both quantities past R = 6σ. Our expressions are numerically tested against exact results. Abstract :