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Ice is one of the most important and interesting molecular crystalsexhibiting a rich and evolving phase diagram. Recent discoveries mean thatthere are now twenty distinct polymorphs; a structural diversity that arisesfrom a delicate interplay of hydrogen bonding and van der Waals dispersionforces. This wealth of structures provides a stern test of electronic structuretheories, with Density Functional Theory (DFT) often not able to accuratelycharacterise the relative energies of the various ice polymorphs. Thanks torecent advances that enable the accurate and efficient treatment of molecularcrystals with Diffusion Monte Carlo (DMC), we present here the DMC-ICE13dataset; a dataset of lattice energies of 13 ice polymorphs. This datasetencompasses the full structural complexity found in the ambient andhigh-pressure molecular ice polymorphs and when experimental reference energiesare available our DMC results deliver sub-chemical accuracy. Using this datasetwe then perform an extensive benchmark of a broad range of DFT functionals. Ofthe functionals considered, we find revPBE-D3 and RSCAN to reproduce referenceabsolute lattice energies with the smallest error, whilst optB86b-vdW andSCAN+rVV10 have the best performance on the relative lattice energies. Ourresults suggest that a single functional achieving reliable performance for allphases is still missing, and that care is needed in the selection of the mostappropriate functional for the desired application. The insights obtained heremay also be relevant to liquid water and other hydrogen bonded and dispersionbonded molecular crystals.

DMC-ICE13: ambient and high pressure polymorphs of ice from Diffusion Monte Carlo and Density Functional Theory