Gaussian Models for the Statistical Thermodynamics of Liquid Water

A gaussian distribution of binding energies, but conditioned to exploit generally available information on packing in liquids, provides a statistical-thermodynamic theory of liquid water that is structurally non-committal, molecularly realistic, and surprisingly accurate. Neglect of fluctuation contributions to this gaussian model yields a mean-field theory that produces useless results. A refinement that accounts for sharper-than-gaussian behavior at high binding energies recognizes contributions from a discrete number of water molecules and permits a natural matching of numerically exact results. These gaussian models, which can be understood as vigorous simplifications of quasi-chemical theories, are applicable to aqueous environments where the utility of structural models based on geometrical considerations of water hydrogen bonding have not been established.