A random network model calculation of the free energy of liquid water

Abstract

The random network model (RNM) of liquid water previously proposed by the authors is extended by imposition of a self-consistency condition designed to minimize the consequences of approximations used in representing the physical content of the model. The self-consistency condition imposed is the requirement that the computed values of T (∂S/∂T)p and (∂H/∂T)p be identical; this is achieved by modifying the quasiharmonic hindered translational and librational frequencies of the RNM. The temperature dependences of the frequencies so found are in good agreement with experiment. It is shown that the Gibbs free energy of the RNM is a minimum with respect to variation of the width of the hydrogen bond angle distribution when the new frequencies are used. As a test of the adequacy of the self-consistency condition for reduction of the error of prediction of thermodynamic properties, the isotope effect on the vapor pressure of ice I and liquid water is calculated; the RNM predictions are in good agreement with the observed values of ln(pH/pD).