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Integral equations for interaction site fluids --- The influence of connectivity constraints and auxiliary sites

Lue, L. and Blankschtein, D. (1995) Integral equations for interaction site fluids --- The influence of connectivity constraints and auxiliary sites. Journal of Chemical Physics, 102 (13). pp. 5460-5470. ISSN 0021-9606

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Abstract

We examine two central features of two well-known integral equations for interaction site fluids: ~i! the Chandler?Silbey?Ladanyi equations, and ~ii! the site?site Ornstein?Zernike equation. The first feature involves the influence of connectivity constraints. Specifically, we identify the restrictions imposed on the site?site correlation functions arising from the constraints of connectivity between sites within a molecule. We find that when the Chandler?Silbey?Ladanyi ~CSL! equations, a set of diagrammatically proper integral equations, are combined with a general approximate closure, they do not necessarily satisfy these connectivity constraints. On the other hand, the site?site Ornstein? Zernike ~SSOZ! equation, combined with a simple fluid closure, does satisfy these constraints. These findings profoundly affect the long-range behavior of the correlation functions and the dielectric constant of the bulk fluid. These findings are also important for the development of computational methods to obtain accurate numerical solutions of the CSL and SSOZ equations. When theories do not satisfy the above-mentioned connectivity constraints, we find that the resulting correlation functions do not satisfy the local neutrality constraints, which is a necessary requirement for any theory to properly predict the fluid dielectric constant. Instead, the correlation functions satisfy the constraints applicable to ionic fluids, that is, the Stillinger?Lovett moment conditions. This leads to the prediction of an infinite fluid dielectric constant. The second feature which we examine involves the influence of auxiliary sites on the prediction of the site?site total correlation functions.We prove that the addition of certain types of auxiliary sites does not affect the correlations between real sites when the Chandler?Silbey?Ladanyi equations are combined with a general approximate closure. The predictions of the SSOZ equation, combined with a general approximate closure, have been shown to depend on the presence of auxiliary sites. However, in the case of the Percus?Yevick closure for systems characterized by hard-sphere interaction sites, we are able to prove that the SSOZ equation does not exhibit this dependence for certain types of auxiliary sites.