Radial Distribution Function for a Hard Sphere Liquid: A Modified Percus-Yevick and Hypernetted-Chain Closure Relations

Establishment of the radial distribution function by solving the Ornstein-Zernike equation is still an important problem, even more than a hundred years after the original paper publication. New strategies and approximations are common in the literature. A crucial step in this process consists in de...

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Published inJournal of the Brazilian Chemical Society Vol. 32; no. 12; pp. 2257 - 2263
Main Authors Carvalho, Felipe, Braga, João Pedro
Format Journal Article
LanguageEnglish
Portuguese
Published Sociedade Brasileira de Química 01.12.2021
Subjects
CHEMISTRY, MULTIDISCIPLINARY
hard sphere system
correlation functions
functional Taylor expansion
Ornstein-Zernike equation
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Summary:Establishment of the radial distribution function by solving the Ornstein-Zernike equation is still an important problem, even more than a hundred years after the original paper publication. New strategies and approximations are common in the literature. A crucial step in this process consists in defining a closure relation which retrieves correlation functions in agreement with experiments or molecular simulations. In this paper, the functional Taylor expansion, as proposed by J. K. Percus, is applied to introduce two new closure relations: one that modifies the Percus‑Yevick closure relation and another one modifying the Hypernetted-Chain approximation. These new approximations will be applied to a hard sphere system. An improvement for the radial distribution function is observed in both cases. For some densities a greater accuracy, by a factor of five times compared to the original approximations, was obtained.
ISSN:0103-5053
1678-4790
DOI:10.21577/0103-5053.20210117