By Stuart A. Rice
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Additional resources for Advances in Chemical Physics (Volume 139)
Mean-Spherical Approximation This another popular closure  deals with spherical particles fluids that interact through an infinite repulsive potential at short range uðrÞ ¼ þ1 for r
Kiselyov–Martynov Approach On the other hand, there is a possibility to express the excess chemical potential exclusively in terms of the direct correlation function with an exact expression  for bmex equivalent to Eq. (80), namely, Z ð97Þ bmex ¼ Àr cð1Þ ðrÞdr where cð1Þ is the ‘‘one-particle’’ direct correlation function defined as: 1 cð1Þ ðrÞ ¼ hðrÞ À oðrÞ À hðrÞ½oðrÞ þ Bð1Þ ðrÞ 2 ð98Þ Here, Bð1Þ ðrÞ is the ‘‘one particle bridge’’ function  and oðrÞ, the thermal potential that equals the opposite of the excess potential of the mean force [18, 28] given by oðrÞ ¼ hðrÞ À cðrÞ þ BðrÞ ð99Þ Consequently, another formally exact definition for bmex follows from gathering Eqs.
Bomont and Bretonnet: Optimized Division Scheme (ODS). These authors wanted to take advantage of the utility of the test particle insertion usually involved in molecular dynamics, by transfering and adapting this concept to the integral equation method [73, 74]. They showed that it is possible to obtain consistently BðrÞ in good agreement with MC calculations, only if the renormalized gÃ ðrÞ function is conjugated with an optimized separation of the pair potential . To achieve this, a new division scheme has been assumed and developed following the idea emphasized above.