Orientational correlations and entropy in liquid water

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Abstract
The molecular pair correlation function in water is a function of a distance and five angles. It is here separated into the radial distribution function (RDF), which is only a function of distance, and an orientational distribution function (ODF), which is a function of the five angles for each distance between the molecules. While the RDF can be obtained from computer simulations, this is not practical for the ODF due to its high dimensionality. Two approaches for obtaining an approximation to the ODF are introduced. The first uses a product of one‐ and two‐dimensional marginal distributions from computer simulations. The second uses the gas‐phase low‐density limit as a reference and applies corrections based on (a) the orientationally averaged interactions in the liquid calculated by simulations, and (b) the observed differences in the one‐ and two‐dimensional marginal distributions in the gas and in the liquid. The site superposition approximation was also tested and found to be inadequate for reproducing the orientationally averaged interaction energy and the angular distributions obtained from the simulations. The two approximations to the pair correlation function are employed to estimate the contribution of two‐particle correlations to the excess entropy of TIP4P water. The calculated value is comparable to the excess entropy of TIP4P water estimated by other methods and to the experimental excess entropy of liquid water. More than 90% of the orientational part of the excess entropy is due to correlations between first neighbors. The change in excess entropy with temperature gives a value for the heat capacity that agrees within statistical uncertainty with that obtained from the change in energy with temperature and is reasonably close to the experimental value for water. The effect of pressure on the entropy was examined and it was found that increase in the pressure (density) causes a reduction of orientational correlations, in agreement with the idea of pressure as a ‘‘structure breaker’’ in water. The approach described here provides insight concerning the nature of the contributions to the excess entropy of water and should be applicable to other simple molecular fluids.