  Molybdenum disulfide (MoS$_2$) attracts attention as a high efficient and low
cost photocatalyst for hydrogen production, but suffers from low conductance
and high recombination rate of photo-generated charge carriers. In this work,
we investigate the MoS$_2$ heterostructures with graphene variants (GVs),
including graphene, graphene oxide, and their boron- and nitrogen-doped
variants, by using first-principles calculations. Systematic comparison between
graphene and graphene oxide composites is performed, and contrary effect of B
and N doping on interface function and hydrogen evolution is clarified. We find
that upon the formation of the interfaces some amount of electronic charge
transfers from the GV side to the MoS$_2$ layer, inducing the creation of
interface dipole and the reduction of work function, which is more pronounced
in the graphene oxide composites. Moreover, our results reveal that N doping
enhances the interface functions by forming donor-type interface states,
whereas B doping reduces those functions by forming acceptor-type interface
states. However, the B-doped systems exhibit lower Gibbs free energy difference
for hydrogen adsorption on GV side than the N-doped systems, which deserves
much consideration in the design of new functional photocatalysts.
