Quantum cluster equilibrium theory of liquids: Illustrative application to water

The Quantum Cluster Equilibrium (QCE) theory, developed in a previous paper, is illustrated with a simple 7-cluster RHF/3-21G model for liquid water. We first describe a simplified QCE(0) model that corresponds to an ideal gas cluster mixture (neglect of all cluster–cluster interactions), but is nevertheless able to exhibit many characteristic features of a true gas/liquid phase transition (macro-clustering, volume collapse, specific heat increase, Clausius–Clapeyron pressure dependence). We employ the QCE(0) model to illuminate the interplay between macroscopic and microscopic properties (dependence on particular cluster species, cooperative binding energetics, vibrational entropy factors, etc.) in a purely ab initio framework. We then introduce two simple corrections for the neglected cluster–cluster interactions: (i) a mean-field correction for residual inter-cluster attractions and (ii) a van der Waals-like correction for excluded volume effects. The numerical accuracy of the resulting QCE model is de...

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