Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function |
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Authors: | Braden D Kelly Douglas Henderson |
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Institution: | 1. Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada;2. Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT, USA |
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Abstract: | ABSTRACTExplicit 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/V)σ3 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. |
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Keywords: | Hard-sphere Percus-Yevick radial distribution function integral equation |
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