A resummed thermodynamic perturbation theory for positive and negative hydrogen bond cooperativity in water

In this paper a resummed thermodynamic perturbation theory is developed which accounts for both positive and negative hydrogen bond cooperativity in water. The theory is developed in Wertheim's multi-density statistical mechanics. We demonstrate that the hydrogen bonded structure of water is controlled by positive hydrogen bond cooperativity in homodromic hydrogen bonded clusters. Inclusion of negative anti-cooperativity in antidromic hydrogen bonded structures has little effect on the underlying hydrogen bond structure of liquid water. The resummed perturbation theory is shown to give hydrogen bond statistics consistent with first principles ab initio molecular dynamics simulations. In addition, the theory is shown to be in good agreement with experiment in the prediction of the average number of hydrogen bonds per water molecule in a liquid at ambient conditions. Finally, we develop a full thermodynamic model for water by including contributions to the free energy for isotropic square well attractions. We demonstrate that the model gives good representation of saturated liquid density, hydrogen bonding and vapor pressure. In addition, we show the full model predicts the anomalous minima in isothermal compressibility and isobaric heat capacity.