We study the low temperature properties of a single layer of parahydrogen adsorbed on graphene, by means of Quantum Monte Carlo simulations. The computed phase diagram is very similar to that of helium on the same substrate, featuring commensurate solid phases with fillings 1/3 and 7/16, as well as domain wall phases at intermediate coverages. At higher coverage the system transitions to an incommensurate, compressible phase. Evidence of promotion of molecules to the second layer is observed at a coverage close 0.112 inverse square Angstroms, significantly above existing theoretical estimates.

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