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By Stuart A. Rice

This sequence presents the chemical physics box with a discussion board for severe, authoritative reviews of advances in each zone of the self-discipline.

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Duh and Haymet Division Scheme (DHHDS) To address the problem of uniqueness of the closure, these authors [65] proposed a method for partitioning the potential energy, by defining the perturbation part to be density dependent (see Fig. 4), so that uLR ðrÞ ¼ À4E s6 r  exp À1 s6rà rà r  ð70Þ The physical picture behind this choice is that (1) at high densities, the system is dominated by the repulsive part of the potential, while (2) at low densities, the attractive part begins to play a more important role.

Then (82) can be rewritten as: Z  bmex ¼ r  Z Z 1 1 2 hðrÞcðrÞ qBðr; lÞ h ðrÞ À cðrÞ þ BðrÞ À dl l dr þ r dr hðrÞ 2 2 ql 0 ð88Þ recent advances in the field of integral equation theories 45 The second assumption is the unique functionality [72] of the bridge function, meaning that B ¼ B½gŠ is a simple function of the indirect correlation function, as expressed in the majority of the approximations for the bridge function. Changing the integration variable from l to g, and integrating by parts yields Z r Z1 dr hðrÞ l 0 qBðr; lÞ dl ¼ r ql Z dr½hðrÞBðrÞ À Sðrފ ð89Þ where hðrÞ SðrÞ ¼ gðrÞ gÃZ ðl¼1Þ Bðg0Þdg0 ð90Þ gà ðl¼0Þ Again, a homotopy has to be constructed (the parameter l varies from 0 to 1), so that gà ðr; lÞ ¼ g0 ðrÞ þ lg1 ðrÞ ð91Þ Then, the calculation of the chemical R potential requires the knowledge of the Star function [72] defined by Sà ¼ r drSðrÞ.

After a carefull analysis of diagrams expansion, it has been concluded that it was more efficient to expand Eq. (29) in terms of ½oðrÞ À buLR ðrފ rather than in terms of oðrÞ [24]. Instead of BðrÞ ¼ À1=2o2 ðrÞ, the bridge function is approximated 26 jean-marc bomont by BðrÞ ¼ À1=2½oðrÞ À buLR ðrފ2, providing an extension in terms of gà ðrÞ, so that BðrÞ ¼ ½1 þ 2gà Š1=2 À gà ðrÞ À 1 ð59Þ In this framework, inspired by the BPGG approach, a parameter a, whose role is to fulfil the thermodynamic consistency condition, has been introduced by Charpentier and Jakse [68].

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