Quantum Cluster Equilibrium Theory Applied in Hydrogen Bond Number Studies of Water. 1. Assessment of the Quantum Cluster Equilibrium Model for Liquid Water

Different cluster sets containing only 2-fold coordinated water, 2- and 3-fold coordinated water, and 2-fold, 3-fold, and tetrahedrally coordinated water molecules were investigated by applying second-order Moller-Plesset perturbation theory and density functional theory based on generalized gradient approximation functionals in the framework of the quantum cluster equilibrium theory. We found an improvement of the calculated isobars at low temperatures if tetrahedrally coordinated water molecules were included in the set of 2-fold hydrogen-bonded clusters. This was also reflected in a reduced parameter for the intercluster interaction. If all parameters were kept constant and only the electronic structure methods were varied, large basis set dependencies in the liquid state for the density functional theory results were found. The behavior of the intercluster parameter was also examined for the case that cooperative effects were neglected. The values were 3 times as large as in the calculations including the total electronic structure. Furthermore, these effects are more severe in the tetrahedrally coordinated clusters. Different populations were considered, one weighted by the total number of clusters and one depending on the monomers.