Dielectrically Nontrivial Closures for the RISM Integral Equation

We report three new closures to the reference interaction site method (RISM) integral equation. The formulation of the closures is motivated by an analogy with an alternative form of the Ornstein−Zernike hypernetted-chain closure for a simple ionic mixture. Unlike other RISM integral equation closures proposed to date, the closures reported here predict nontrivial results for the dielectric constant ε 0 of model polar fluids. Interestingly, we find that, for models of polar fluids comprising molecules with only two nonequivalent interaction sites (such as dipolar dumbbells or the popular three-site representations of water), all of the new closures give simple analytical formulas for ε 0 . These simple analytical results indicate that only one of the closures is based on a relation that can account for the dependence of ε 0 upon the thermodynamic state parameters of the liquid and the features of the molecular model (size and shape) separately, rather than in the ubiquitous dipolar strength parameter combination 4πρμ 2 /3 k B T . For this promising closure we solve numerically the RISM integral equation and calculate the site−site correlation functions g jl ( r ) and the dielectric properties for dipolar dumbbell liquids, for the SPC/E model of water, and for a four-site interaction site model of dimethyl sulfoxide.