In this paper we discuss a known variational principle for the Percus–Yevick integral equation and then generalize the procedure to obtain a variational principle for any integral equation associated with the Ornstein–Zernike equation. In particular we rederive a variational principle for the mean spherical model and then derive a variational principle for the hypernetted chain equation and compare these to the exact numerical results of Rasaiah and Friedman and to the Monte Carlo data of Rasaiah, Card, and Valleau for the restricted primitive model of electrolyte solutions.
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Olivares et al. (1976) studied this question.
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