Abstract
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.
Highlights
The study of liquids is important since it involves systems with several applications in biological sciences, condensed matter systems and industry, for example
The integral equation theory (IET) has the advantage of being less time consuming
The accuracy of this approach will depend on some approximations such as the model potential of interaction in the system and the relation between correlation functions, which will be discussed
Summary
The study of liquids is important since it involves systems with several applications in biological sciences, condensed matter systems and industry, for example. Predicting thermodynamic properties of these systems will demand some theoretical approach, such as molecular dynamics, Monte Carlo (MC) or the integral equation theory (IET). The accuracy of this approach will depend on some approximations such as the model potential of interaction in the system and the relation between correlation functions, which will be discussed. One well known IET to obtain distribution functions, which can be used to calculate thermodynamic quantities, was proposed by Ornstein and Zernike.[1] this approach needs an additional equation to be solved, called closure relation. Several approximations for the closure relation have been published, such as Percus-Yevick (PY),[2] Hypernetted-Chain (HNC)[3,4] Verlet,[5] Tsednee and Luchko[6] and Carvalho and Braga.[7]
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