(476d) Computational Cluster-Integral Methods for Solutions

Cluster-integral ideas underlie many theoretical methods in statistical mechanics. The most widely recognized and widely used approach is in the form of the virial equation of state. This framework identifies coefficients of a density expansion of the pressure (and other properties) in terms of integrals of multimolecular interactions in a vacuum. The pairwise-additive intermolecular potential forms frequently encountered in molecular simulations are often used in this context. A corresponding framework is available for properties of solutions. Here the expansion is (typically) for the osmotic pressure, as a series in solute concentration. The coefficients again can be given as cluster integrals, but now the interactions are among solutes as mediated by their interactions with the solvent. Typically a pairwise-additive approximation for solute-solute interactions is not as effective in such applications. Numerical evaluation of the indicated cluster integrals is not as easily accomplished, and require methods different from those that have been developed for gas-phase virial coefficients. In this paper we present and examine novel and very effective methods, and demonstrate them for several model systems. We consider in particular the performance of the methods, the nature of the effective multibody interactions, and the effectiveness of the overall framework for describing solution properties.