Hypemetted chain approximation

From the various possible closures, the mean spherical approximation (MSA) [189] has found particularly wide attention in phase equilibrium calculations of ionic fluids. The Percus-Yevick (PY) closure is unsatisfactory for long-range potentials [173, 187, 190]. The hypemetted chain approximation (HNC), widely used in electrolyte thermodynamics [168, 173], leads to an increasing instability of the numerical algorithm as the phase boundary is approached [191]. There seems to be no decisive relation between the location of this numerical instability and phase transition lines [192-194]. Attempts were made to extrapolate phase transition lines from results far away, where the HNC is soluble [81, 194]. 

The Linearized tind Quadratic Hypemetted-Chain Approximations.238... 

In Enderby et (12) was simply assumed on the basis of an observation made by Johnson et that it is satisfied in the Bom-Green, Percus-Yevick, and hypemetted-chain approximations. [The results of our appendix are formally rather than rigorously exact, because we do not fully investigate the convergence properties of the series expansions we use, and we assume certain plausible smoothness properties of h(l 2). Thus we have given a demonstration, in the sense of Kac, rather than a proof of our equations—see footnote 2 of Mermin for a characterization of the distinction.]... 

A fundamental approach to liquids is provided by the integral equation methods (sometimes called distribution function methods), initiated by Kirkwood and Yvon in the 1930s. As we shall show below, one starts by writing down an exact equation for the molecular distribution function of interest, usually the pair function, and then introduces one or more approximations to solve the problem. These approximations are often motivated by considerations of mathematical simplicity, so that their validity depends on a posteriori agreement with computer simulation or experiment. The theories in question, called YBG (Yvon-Bom-Green), PY (Percus-Yevick), and the HNC (hypemetted chain) approximation, provide the distribution functions directly, and are thus applicable to a wide variety of properties. 

Two of the classic integral equation approximations for atomic liquids are the PY (Percus-Yevick) and the HNC (hypemetted chain) approximations that use the following closures... 

Fries, P. H. and G. N. Patey. 1985. The solution of the hypemetted-chain approximation for fluids of nonspherical particles—A general-method with application to dipolar hard-spheres. Journal of Chemical Physics. 82, 429. 

HNCB hypemetted chain approximation plus bridge HS hard-sphere... 

Kusalik PG, Patey GN The solution of the reference hypemetted-chain approximation for water-hke models. Mol Phys 65(5) 1105—1119, 1988. 

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