Cluster expansions for hydrogen-bonded fluids. III. Water

The cluster theory of hydrogen-bonded fluids, described previously H. C. Andersen, J. Chem. Phys. 59, 4714 (1973); 61, 4985 (1974), is extended to describe fluid water. For classical nonvibrating models of the water molecule, we show that the intermolecular potential can be separated into a reference potential and a hydrogen-bonding potential and that the hydrogen-bonding potential can be separated into parts corresponding to the four hydrogen-bonding functional groups on a molecule. These separations of the potential are accomplished by defining a set of characteristic functions, one for each of the eight types of hydrogen bonds that can form between a pair of molecules. The characteristic functions also allow us to define precisely the average number of hydrogen bonds that are made by each functional group in fluid water in terms of the pair correlation function. The cluster expansion method for classical fluids is used to develop approximation methods for calculating this average number of hydrogen bonds as a function of temperature and density. These approximations will be used in the following paper to calculate the thermodynamic properties of a simple model for water.