  Molecular hydrogen is at the core of hydrogen energy applications and has the
potential to significantly reduce the use of carbon dioxide emitting energy
processes. However, hydrogen gas storage is a major bottleneck for its
large-scale use as current storage methods are energy intensive. Among
different storage methods, physisorbing molecular hydrogen at ambient pressure
and temperatures is a promising alternative - particularly thanks to tuneable
lightweight nanomaterials and high throughput screening methods. Nonetheless,
understanding hydrogen adsorption in well-defined nanomaterials remains
experimentally challenging and reference information is scarce despite the
proliferation of works predicting hydrogen adsorption. In this work, we focus
on Li, Na, Ca, and K, decorated graphene sheets as substrates for hydrogen
adsorption and compute the most accurate adsorption energies available to date
using quantum diffusion Monte Carlo (DMC). Building on our previous insights at
the density functional theory (DFT) level, we find that a weak covalent
chemisorption of molecular hydrogen, known as Kubas binding, is feasible on Ca
decorated graphene according to DMC, in agreement with DFT. This finding is in
contrast to previous DMC predictions of the 4H$_2$/Ca$^+$ gas cluster where
chemisorption is not favoured. However, we find that the adsorption energy of
hydrogen on metal decorated graphene according to a widely-used DFT method is
not fully consistent with DMC and the discrepancies are not systematic. The
reference adsorption energies reported herein can be used to find better
work-horse methods for application in large-scale modelling of hydrogen
adsorption. Furthermore, the implications of this work affect strategies for
finding suitable hydrogen storage materials and high-throughput methods.
