By Stuart A. Rice
This sequence presents the chemical physics box with a discussion board for serious, authoritative reviews of advances in each zone of the self-discipline.
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Moreover, fromwhat we said, it turns out that HNC and PY have somehow complementary behaviors. The former is more accurate for long-range forces, while the latter is better for short-range forces. Another avantageous possibility is to formulate direct approximations for the bridge function based on physical arguments . This part is devoted to the presentation of these improved closures. 1. The HNC–SMSA Approximation The previous basic observations have suggested to adopt a closure that allows us to interpolate continuously between two existing theories.
Bretonnet and Jakse  showed that f ðrÞ could be accurately simplified by setting f ðrÞ ¼ f0 . This last parameter is determined in the same way as f ðrÞ. This is a local consistency criterion that can be adopted with confidence, since f0 turns out to be a slightly 24 jean-marc bomont varying function of the density. The HMSA closure reduces to HNC for f0 ¼ 1 and to SMSA when f0 ! 0. For systems dominated by short-range forces, one has to set uLR ðrÞ ¼ 0, so that uSR ðrÞ ¼ uðrÞ. In this case, gÃ ðrÞ ¼ gðrÞ and HMSA reduces to the famous Rogers and Young (RY)  approximation that reads expff ðrÞgðrÞg À 1 BðrÞ ¼ ÀgðrÞ þ ln 1 þ f ðrÞ ð54Þ It turns out that RY interpolates continuously between HNC (f0 ¼ 1) and PY (f0 !
83]. recent advances in the field of integral equation theories 37 excellent agreement is achieved over all densities. The ZSEP provides very similar results compared to Groot’s construction. As seen, BðrÞ is always negative inside the core, in agreement with most literature closures. In order to obtain such results, the ZSEP necessitates the knowledge of three parameters (per state), determined with the aid of several consistency conditions , whereas the BB requires only the knowledge of a single parameter adjusted in a self-consistent manner so that Eq.
Advances in Chemical Physics (Volume 139) by Stuart A. Rice