  Hydrogen is a key player in global strategies to reduce greenhouse gas
emissions. In order to make hydrogen a widely-used fuel, we require more
efficient methods of storing it than the current standard of pressurized
cylinders. An alternative method is to adsorb H$_2$ in a material and avoid the
use of high pressures. Among many potential materials, layered materials such
as graphene present a practical advantage as they are lightweight. However,
graphene and other 2D materials typically bind H$_2$ too weakly to store it at
the typical operating conditions of a hydrogen fuel cell. Modifying the
material, for example by decorating graphene with adatoms, can strengthen the
adsorption energy of H$_2$ molecules, but the underlying mechanisms are still
not well understood. In this work, we systematically screen alkali and alkaline
earth metal decorated graphene sheets for the adsorption of hydrogen gas from
first principles, and focus on the mechanisms of binding. We show that there
are three mechanisms of adsorption on metal decorated graphene and each leads
to distinctly different hydrogen adsorption structures. The three mechanisms
can be described as weak van der Waals physisorption, metal adatom facilitated
polarization, and Kubas adsorption. Among these mechanisms, we find that Kubas
adsorption is easily perturbed by an external electric field, providing a way
to tune H$_2$ adsorption.
