We investigate the rotational properties of molecular hydrogen and its
isotopes physisorbed on the surfaces of graphene and hexagonal boron nitride
(h-BN), grown on Ni(111), Ru(0001), and Rh(111), using rotational excitation
spectroscopy (RES) with the scanning tunneling microscope. The rotational
thresholds are in good agreement with ΔJ=2 transitions of freely
spinning para-H2 and ortho-D2 molecules. The line shape variations in RES
for H2 among the different surfaces can be traced back and naturally
explained by a resonance mediated tunneling mechanism. RES data for
H2/h-BN/Rh(111) suggests a local intrinsic gating on this surface due to
lateral variations in the surface potential. An RES inspection of H2, HD,
and D2 mixtures finally points to a multi molecule excitation, since either
of the three J=0→2 rotational transitions are simultaneously
present, irrespective of where the spectra were recorded in the mixed
monolayer