  Standard density functionals without van der Waals interactions yield an
unsatisfactory description of ice phases, specifically, high density phases
occurring under pressure are too unstable compared to the common low density
phase I$_h$ observed at ambient conditions. Although the description is
improved by using functionals that include van der Waals interactions, the
errors in relative volumes remain sizable. Here we assess the random phase
approximation (RPA) for the correlation energy and compare our results to
experimental data as well as diffusion Monte Carlo data for ice. The RPA yields
a very balanced description for all considered phases, approaching the accuracy
of diffusion Monte Carlo in relative energies and volumes. This opens a route
towards a concise description of molecular water phases on surfaces and in
cavities.
