  The design of low-dimensional organic-inorganic interfaces for the next
generation of opto-electronic applications requires an in-depth understanding
of the microscopic mechanisms ruling electronic interactions in these systems.
In this work, we present a first-principles study based on density-functional
theory inspecting the structural, energetic, and electronic properties of five
molecular donors and acceptors adsorbed on freestanding hexagonal boron nitride
(hBN) and molybdenum disulfide (MoS$_2$) monolayers. All considered
heterostructures are stable, due to the crucial contribution of dispersion
interactions, which are maximized by the overall flat arrangement of the
physisorbed molecules on both substrates. The level alignment of the hybrid
systems depends on the characteristics of the constituents. On hBN, both type-I
and type-II heterostructures may form, depending on the relative energies of
the frontier orbitals with respect to the vacuum level. On the other hand, all
MoS$_2$-based hybrid systems exhibit a type-II level alignment, with the
molecular frontier orbitals positioned across the energy gap of the
semiconductor. The electronic structure of the hybrid materials is further
determined by the formation of interfacial dipole moments and by the
wave-function hybridization between the organic and inorganic constituents.
These results provide important indications for the design of novel
low-dimensional hybrid materials with suitable characteristics for
opto-electronics.
