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Density-functional theory (DFT) has been widely used to study water and icefor at least 20 years. However, the reliability of different DFTexchange-correlation (xc) functionals for water remains a matter ofconsiderable debate. This is particularly true in light of the recentdevelopment of DFT based methods that account for van der Waals (vdW)dispersion forces. Here, we report a detailed study with several xc functionals(semi-local, hybrid, and vdW inclusive approaches) on ice Ih and six protonordered phases of ice. Consistent with our previous study [Phys. Rev. Lett.107, 185701 (2011)] which showed that vdW forces become increasingly importantat high pressures, we find here that all vdW inclusive methods consideredimprove the relative energies and transition pressures of the high-pressure icephases compared to those obtained with semi-local or hybrid xc functionals.However, we also find that significant discrepancies between experiment and thevdW inclusive approaches remain in the cohesive properties of the variousphases, causing certain phases to be absent from the phase diagram. Therefore,room for improvement in the description of water at ambient and high pressuresremains and we suggest that because of the stern test the high pressure icephases pose they should be used in future benchmark studies of simulationmethods for water.

On the Accuracy of van der Waals Inclusive Density-Functional Theory Exchange-Correlation Functionals for Ice at Ambient and High Pressures