  Ice is one of the most important and interesting molecular crystals
exhibiting a rich and evolving phase diagram. Recent discoveries mean that
there are now twenty distinct polymorphs; a structural diversity that arises
from a delicate interplay of hydrogen bonding and van der Waals dispersion
forces. This wealth of structures provides a stern test of electronic structure
theories, with Density Functional Theory (DFT) often not able to accurately
characterise the relative energies of the various ice polymorphs. Thanks to
recent advances that enable the accurate and efficient treatment of molecular
crystals with Diffusion Monte Carlo (DMC), we present here the DMC-ICE13
dataset; a dataset of lattice energies of 13 ice polymorphs. This dataset
encompasses the full structural complexity found in the ambient and
high-pressure molecular ice polymorphs and when experimental reference energies
are available our DMC results deliver sub-chemical accuracy. Using this dataset
we then perform an extensive benchmark of a broad range of DFT functionals. Of
the functionals considered, we find revPBE-D3 and RSCAN to reproduce reference
absolute lattice energies with the smallest error, whilst optB86b-vdW and
SCAN+rVV10 have the best performance on the relative lattice energies. Our
results suggest that a single functional achieving reliable performance for all
phases is still missing, and that care is needed in the selection of the most
appropriate functional for the desired application. The insights obtained here
may also be relevant to liquid water and other hydrogen bonded and dispersion
bonded molecular crystals.
