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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 114, 2016 - Issue 16-17: Special Issue in Memory of Yiping Tang
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Articles

Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function

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Pages 2446-2450 | Received 28 Jan 2016, Accepted 03 Mar 2016, Published online: 28 Mar 2016
 

ABSTRACT

Explicit analytical expressions are presented for the density derivative, ∂gHS(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/V3 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 gHS(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.

Supplemental data for this article can be accessed at http://dx.doi.org/10.1080/00268976.2016.1164908.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

B. D. Kelly and W. R. Smith are grateful for the financial support of the Natural Sciences and Engineering Research Council of Canada [Discovery Grant Number OGP1041].

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