Embedded-fragment methods have extended the reach of ab initio molecular orbital (MO) theories from small molecular clusters to molecular crystals and liquids. By dividing a system into overlapping fragments embedded in the local electrostatic environment, electron-correlated MO theories can be applied to the subsystems in a parallel, asymptotically linear scaling procedure. Full-system energetic and response properties are then accurately constructed from the corresponding fragment quantities.

We applied this technique with second-order Møller-Plesset perturbation (MP2) theory to several phases of solid and liquid water. Our studies of proton-disordered ice Ih reproduce three thermodynamic anomalies: negative thermal expansivity below 70 K, an isotope effect rendering the volume of D2O larger than that of H2O, and a pressure-induced transition to high-density amorphous ice. We show how these phenomena are manifestations of vibrational anharmonicity in ice. On-the-fly MP2 forces were also used for ab initio molecular dynamics simulation of liquid water. At the experimental density and 250 K, the predicted radial distribution function and vibrational spectra are in good agreement with the observed at ambient conditions.