Accurate integral equation theory for the central force model of liquid water and ionic solutions

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Abstract
The atom–atom pair correlation functions and thermodynamics of the central force model of water, introduced by Lemberg, Stillinger, and Rahman, have been calculated accurately by an integral equation method which incorporates two new developments. First, a rapid new scheme has been used to solve the Ornstein–Zernike equation. This scheme combines the renormalization methods of Allnatt, and Rossky and Friedman with an extension of the trigonometric basis-set solution of Labik and co-workers. Second, by adding approximate ‘‘bridge’’ functions to the hypernetted-chain (HNC) integral equation, we have obtained predictions for liquid water in which the hydrogen bond length and number are in good agreement with ‘‘exact’’ computer simulations of the same model force laws. In addition, for dilute ionic solutions, the ion–oxygen and ion–hydrogen coordination numbers display both the physically correct stoichiometry and good agreement with earlier simulations. These results represent a measurable improvement over both a previous HNC solution of the central force model and the ex-RISM integral equation solutions for the TIPS and other rigid molecule models of water.