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First-principles simulations of electronic properties of hybridinorganic/organic interfaces are challenging, as common density-functionaltheory (DFT) approximations target specific material classes like bulksemiconductors or gas-phase molecules. Taking as a prototypical exampleanthracene physisorbed on monolayer MoS$_2$, we assess the ability of different\textit{ab initio} schemes to describe the electronic structure usingsemi-local and hybrid DFT. For the latter, an unconstrained three-parameterrange-separation scheme is employed. Comparisons against many-body perturbationtheory results indicate that DFT is substantially unable to make reliablepredictions about interfacial properties. Hybrid functionals, while improvingthe accuracy of the MoS$_2$ band structure, do not systematically enhance thedescription of hybrid systems with respect to semi-local functionals. Neitherapproach provides a good starting point for $G_0W_0$, which, consequently,cannot provide much information beyond the correct energy level alignment. Weshow that non-empirically parametrized electrostatic screening models canaccomplish the same task at negligible computational costs. Such schemes caninclude substrates of hybrid interfaces in good agreement with experimentaldata. Our results indicate that currently, fully atomistic, many-bodysimulations of weakly interacting hybrid systems are not worth the requiredcomputational resources. In contrast, ab-initio-parametrized effective modelsmimicking the environment offer a scalable alternative without compromisingaccuracy and predictivity.

Electronic structure of low-dimensional inorganic/organic interfaces: Hybrid density functional theory, $G_0W_0$, and electrostatic models