Weeks-Chandler-Andersen theory

As we have already pointed out, the theoretical basis of free energy calculations were laid a long time ago [1,4,5], but, quite understandably, had to wait for sufficient computational capabilities to be applied to molecular systems of interest to the chemist, the physicist, and the biologist. In the meantime, these calculations were the domain of analytical theories. The most useful in practice were perturbation theories of dense liquids. In the Barker-Henderson theory [13], the reference state was chosen to be a hard-sphere fluid. The subsequent Weeks-Chandler-Andersen theory [14] differed from the Barker-Henderson approach by dividing the intermolecular potential such that its unperturbed and perturbed parts were associated with repulsive and attractive forces, respectively. This division yields slower variation of the perturbation term with intermolecular separation and, consequently, faster convergence of the perturbation series than the division employed by Barker and Henderson. 

An elegant theory to go beyond the hard-sphere cavity was presented by Pratt and Chandler [17], where the attractive part of the solute-water interaction was treated perturbatively (in the spirit of the Weeks-Chandler-Andersen (WCA) theory [18]). The central quantities in the Pratt-Chandler theory are two radial distribution functions, gAw f) that give, respectively, the... 

The eelebrated Pratt-Chandler (PC) theory is usually the starting point of any diseussion on the hydrophobie effeet. This theory ean be regarded as an application of the Weeks-Chandler-Andersen (WCA) perturbative theory of liquids to the solvation of one and a pair of non-polar solute moleeules. While Stillinger discussed the ehemieal potential involved in ereating a hard-sphere cavity in water using the scaled partiele theory, the Pratt-Chandler theory used an integral equation deserip-tion and showed how to properly discuss the effect within a general statistieal mechanical theory. 

Although a large nrunber of theoretical approaches can be used to describe 2D Letmard-Jones systems, the Reddy-O Shea and the Cuadros-Mulero expressions for the equation of state are the most usefril from a practical point of view. In particular, the Cuadros-Mulero equation is the simplest expression and can be easily applied over a wide range of temperatures and densities. Moreover, it is based on the Weeks-Chandler-Andersen perturbation theory, thus permitting the study of the effects of the intermolecular repulsive and atlractive forces. 

A very successfiil first-order perturbation theory is due to Weeks, Chandler and Andersen pair potential u r) is divided into a reference part u r) and a perturbation w r)... 

Similarly in the perturbation theory of Weeks, Chandler and Andersen [5,28] (WCA) the Lennard-Jones potential is decomposed according to... 

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