We use dispersion-corrected density-functional theory to determine the relative energies of competing polytypes of bulk layered hexagonal post-transition-metal chalcogenides, to search for the most stable structures of these potentially technologically important semiconductors. We show that there is some degree of consensus among dispersion-corrected exchange-correlation functionals regarding the energetic orderings of polytypes, but we find that for each material there are multiple stacking orders with relative energies of less than 1 meV per monolayer unit cell, implying that stacking faults are expected to be abundant in all post-transition-metal chalcogenides. By fitting a simple model to all our energy data, we predict that the most stable hexagonal structure has P$6_3$/mmc space group in each case, but that the stacking order differs between GaS, GaSe, GaTe, and InS on the one hand and InSe and InTe on the other. At zero pressure, the relative energies obtained with different functionals disagree by around 1-5 meV per monolayer unit cell, which is not sufficient to identify the most stable structure unambiguously; however, multi-GPa pressures reduce the number of competing phases significantly. At higher pressures, an AB$$-stacked structure of the most stable monolayer polytype is found to be the most stable bulk structure; this structure has not been reported in experiments thus far.
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