Donors, Acceptors, and a Bit of Aromatics: Electronic Interactions of Molecular Adsorbates on hBN and MoS$_2$ Monolayers

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.


Introduction
Hybrid materials formed by carbon-conjugated molecules adsorbed on low-dimensional semiconductors and insulators have been attracting attention due to the their structural versatility and electronic tunability. [1][2][3][4][5][6][7][8][9] Depending on their density on the substrate and on their physico-chemical characteristics, physisorbed moieties can introduce localized electronic states, 10-12 dispersive bands, 7 or a combination thereof. [13][14][15] The electronic structure of the interface results from the level alignment between the organic and inorganic components [16][17][18][19][20] and the hybridization between their electronic wave-functions. 15,[21][22][23][24] As both these effects depend on the intrinsic nature of the building blocks, the need for systematic analyses on the electronic structure of hybrid systems are in high demand.
Electronic structure calculations based on density-functional theory (DFT) are particularly suited for this purpose 25,26 and for exploring various material combinations without requiring empirical parameters. With the electron density being its central quantity, DFT grants immediate access to the charge redistribution induced by adsorption. 13,14,21,27 This way, it is possible to assess the type of ground-state doping and to gain insight into the spatial extension of the electron cloud at the interface. Furthermore, DFT calculations are able to deliver work functions, level alignments, band structures, and (projected) density of states, among other important properties. 2,[13][14][15]27 While state-of-the-art first-principles methods to obtain the electronic structure of solid-state materials are currently based on many-body perturbation theory, 18,28 the choice of range-separated hybrid functionals to approximate the exchange-correlation potential in DFT offers the optimal trade-off between accuracy and computational costs. 15,27 Proper inclusion of van der Waals interactions improves the prediction of structural arrangements and hence the description of electronic properties. 29 The level of accuracy currently achieved by such ab initio calculations ensures reliable results complementary to experiments. 2,27,30 In this work, we present a DFT study on the structural, energetic, and electronic properties of five representative organic molecules, including donor and acceptor compounds as well as a purely aromatic moiety, adsorbed on freestanding hexagonal boron nitride (hBN) and molybdenum disulfide (MoS 2 ) monolayers. The former is a known insulator, widely used as a substrate and/or as an encapsulating material in low-dimensional heterostructures, 17 which has been receiving increasing attention in surface and interface science, [31][32][33][34][35][36][37] for instance to sustain the growth of well-defined organic thin films. 9,38,39 MoS 2 belongs to the family of transition-metal dichalcogenides, the most promising emerging class of lowdimensional semiconductors. By performing geometry optimizations using the generalizedgradient approximation (GGA) and refining the analysis of the electronic structure using a range-separated hybrid functional, we rationalize how the nature of the constituents of the hybrid interface determines the level alignment and the projected density of states. Our findings offer useful indications to interpret and predict the electronic properties of similar low-dimensional hybrid interfaces from the character of substrates and adsorbates.

Computational details
All results presented in this work are obtained from DFT 40 electronic structure calculations through the solution of the Kohn-Sham equations. 41 The structures are optimized at the GGA level of theory, using the Perdew-Burke-Ernzerhof (PBE) functional. 42 To compute electronic properties on each optimized structure, including densities of states, energy levels alignment and molecular orbitals, the Heyd-Scuseria-Ernzerhof (HSE06) 43 range-separated hybrid functional is adopted.
For all complexes with hBN as a substrate, we employ the Gaussian and plane-wave formalism, as implemented in the CP2K package. 44 We choose the short-range-double-ζ MOLOPT basis sets 45 for the expansion of the valence electron density, while the interaction with the atomic cores is represented by Godecker-Teter-Hutter (GTH) pseudopotentials. [46][47][48] The expansion of the density in an auxiliary plane waves basis is truncated at the kinetic-energy cutoff of 600 Ry. The van der Waals (vdW) contributions are included either according to the Grimme-D3 scheme 49 or by augmenting the exchange-correlation functional with the self-consistent rVV10 functional, 50 which in combination with PBE is known to provide reliable structural properties for similar hybrid interfaces. 51 We apply the quasi-Newtonian Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to find the minimum on the potential energy surface, with a convergence criterion of 5×10 −4 Ha/bohr in the energy gradients. The Brillouin zone is sampled at the Γ-point only.

Results and Discussion
Structural Properties All molecules adsorb approximately flat on top of hBN, thus maximising dispersion interactions. The distance of the molecular species from the substrate plane ranges from 3.3 to 3.4Å. Upon adsorption, the molecular structures do not change appreciably compared to the gas-phase configurations. Exceptions concern a concave bending of TTF of about 11 • towards the substrate (see Fig. 1b), in contrast with previous results on metallic surfaces, 58,59 where the molecule bends in a convex fashion due to the strong interactions with the metal electronic charge density. Furthermore, the 2T undergoes a backbone "twist" with a dihedral angle of 7 • (Fig. 1c). Finally, hBN is subject to a slight rippling as a result of the attractive π-π interactions with the physisorbed molecules. Corresponding values of 0.21Å, 0.23Å, 0.27Å, and 0.29Å are found in the heterostructures with TTF and 2T, with TCNQ, with  In the hybrid heterostructure including the MoS 2 substrate (Fig. 2a), the donor molecules TTF and 2T exhibit the same concave bending and backbone twisting as in the hBN-based ones discused above (see Fig. 2b,c). As a result, in these molecules, the hydrogen atoms are closer to the substrate than the carbon atoms, at a distance of 3.39Å. The acceptors TCNQ and F 4 −TCNQ are slightly bent, too, when physisorbed on MoS 2 , with the nitrogen atoms pointing towards the substrate and being displaced 0.2Å downwards with respect to the backbone plane lying at 3.39Å above the monolayer (see Fig. 2e,f). This behavior is analogous to the one exhibited by these molecules on ZnO, 60 on graphene, 61 and on the hydrogenated Si(111) surface. 62,63 Finally, pyrene, which is planar in the gas phase, 57 remains such also upon adsorption, and lays at a distance of 3.32Å from MoS 2 . Table 1: Adsorption energy (E ads ) calculated for the hBN-based heterostructure at the PBE-vdW level, using both the D3 and rVV10 scheme for the vdW contributions; interaction energy (E int ) and dispersion energy (E disp ) computed at the PBE-rVV10 level of theory. All values are in eV. In order to quantify the energetic stability of the considered hybrid heterostructures, we introduce the adsorption energy defined as:

Energetics
where the superscript "opt" refers to the optimized geometries and the subscripts "mol" and "surf" stand for the molecular and surface total energies, respectively. In the hBN-based interfaces, the adsorption strength increases from donor-like systems to the acceptors (see Ta-ble 1) with F 4 −TCNQ, the most electron-withdrawing molecule among the considering ones, leading to the most stable heterostructure precisely on account of this characteristic. 37,64 To better characterize the nature of the molecule-substrate interactions in the considred hybrid interfaces, it is convenient to single out the dispersion contribution from the interaction strength, by introducing the interaction energy where E surf and E mol are the single-point energies computed for the individual subsystems taken with the same coordinates as in the optimized complex. The dispersion contribution to each term is defined as the energy difference at fixed coordinates between a calculation with the vdW correction and one without it. The final contribution to the adsorption is given by the dispersion energy, defined as: As expected, in the case of the hBN-based heterostructures, the dispersion contribution turns out to be predominant (see Table 1), confirming that no chemical bond is formed between the molecules and the monolayer. The small, yet noticeable, differences between adsorption and interaction energies (20-40 meV) indicate that the charge distribution and also the original geometries of both molecules and substrate are slightly perturbed upon physisorption. When comparing the interaction energy with the dispersion contribution, one observes that the latter is slightly more negative. This result points to a minor destabilization effect due to distortions upon molecular adsorption. Indeed, the interaction term must include some repulsive (Pauli) contributions owing to the overlap of the electronic distributions of molecule and substrate, whereas the dispersion part is purely attractive.
Depending on the choice of vdW functional, the relative magnitude of dispersion vs.
interaction may somewhat vary, but our comparison between two approaches demonstrates the same qualitative picture (see Table 1). In both cases, all adsorption energies lie between -0.9 and -1.4 eV and the relative trends in stability are the same. The following electronicstructure calculations involving the hBN substrate are then restricted to the rVV10 approach only, which proved to yield reliable adsorption and structural properties. 51 The adsorption of TCNQ and TTF on hBN was investigated in a previous work by Tang and coworkers 65 who applied DFT with the PBE functional and no additional vdW correction. The resulting adsorption energies are -0.112 eV and -0.041 eV, respectively, i.e., significantly weaker due to the missing dispersion contribution. Moving now to the MoS 2 -based interfaces, we find a qualitatively similar trend in the adsorption energies as the one discussed above for the heterostructures with hBN (see Table 2). Among the considered systems, the least stable one is 2T@MoS 2 , due to the twisted backbone of the molecule that reduces the attractive π-π interactions with the substrate.
Unsurprisingly, the most negative value of E ads is found for pyrene, which adsorbs flat on  Table 1). A reason for these contrasting behaviors can be ascribed to the chemical nature of the two substrates: While hBN is characterized by a N-rich surface, MoS 2 has instead a S-rich one. Such bare distinction in the composition of the two inorganic materials affects the affinity of the adsorbates towards them. Indeed, N-containing molecules such as TCNQ and its fluorinated sibling adsorb more favorably on hBN than TTF and 2T which are S-rich, likely as a consequence of orbital overlap between atoms of same kind. Table 2 also exhibit a qualitative difference with respect to their counterparts in Table 1, namely, the dispersion contribution for pyrene on MoS 2 is larger than the one for F 4 −TCNQ. This behavior which can be explained again based on the chemical affinity argument presented above. In the last part of our analysis, we inspect the electronic properties of the considered hybrid interfaces analyzing in particular the energy level alignment and the projected density of states. Again, we start from the hybrid systems including hBN. Like its bulk counterpart 66-69 monolayer hBN is an insulator 70 with a computed value of the quasi-particle band-gap above 7 eV. 71,72 Our result obtained from DFT with the HSE06 hybrid functional (6.08 eV, see Fig. 3) underestimates that value but it significantly improves it with respect to the one obtained from local DFT. 72 The agreement with experimental references is also very good. 37,66,73 The large electronic gap of hBN and the absolute energies of its band edges determine the alignment with respect to the molecular frontier levels (Fig. 3). Both frontier states of TTF, 2T, and pyrene fall within the energy gap of hBN, leading to a type-I lineup.

Electronic Properties
In these three interfaces, the band edges lie within the band-gap of hBN, however, they are systematically downshifted by a few hundreds of meV with respect to the frontier states of the molecules. In the interfaces including TCNQ and F 4 −TCNQ, instead, the highestoccupied molecular orbital (HOMO) of the gas-phase molecules lies below the valence-band maximum (VBM) of free-standing hBN, giving rise to a type-II level alignment. In these cases, the highest occupied (lowest-unoccupied) level of the hybrid interface is downshifted to a lesser extent, of pyrene@hBN ( Fig. 4a-c), as well as in the conduction region of the interfaces hosting the molecular acceptors (Fig. 4d-e). With the partial exception of the lowest-unoccupied molecular orbital (LUMO) of TTF and the HOMO of The PDOS calculated for the MoS 2 -based interfaces and reported in Figure 6 illustrate well the distribution of the molecular states of the adsorbates with respect to the electronic bands of the substrate. In the occupied region, hybridization between MoS 2 states and molecular orbitals can be seen especially for the interfaces including the donor molecules and pyrene (Fig. 6a-c). This effect manifests itself as a broadening of the peaks associated with molecular states, which are no longer δ-like maxima as in the isolated counterpart. On the other hand, acceptor molecules do not exhibit any signs of hybridization with the MoS 2 bands, at least in the energy window displayed in Fig. 6d-e.

Summary and Conclusions
In summary, we presented a DFT study of hybrid interfaces formed by hBN and MoS 2 monolyers acting as substrates for five physisorbed molecules: two electron-donor species, TTF and 2T, two acceptors, TCNQ and F 4 −TCNQ, and the aromatic hydrocarbon, pyrene.
All molecules adsorb substantially flat on both substrates, although structural modifica-tions can be seen depending on the chemical nature of adsorbates and substrates: Donor and acceptor compounds undergo minor distortions due to the presence of S and N atoms therein, respectively; hBN ripples slightly when interacting with the physisorbed molecules while, owing to its larger rigidity, the structure of MoS 2 in the hybrid interfaces is unchanged compared to the free-standing configuration. From an energetic point of view, all material combinations form stable heterostructures thanks to the contribution of dispersive interactions, which are quantitatively accounted for in our calculations. As a general trend, pyrene and the acceptors adsorb more favorably on both substrates than the considered donors.
From the analysis of the electronic structure, we noticed weak coupling between molecules and hBN, as expected from the chemically inert and insulating character of this 2D material.
In the considered hBN-based heterostructures, both type-I and type-II level alignments are formed. Straddling lineups appear for the donor molecules, TTF and 2T, and with pyrene;

Data Availability Statement
All data produced in this work are available free of charge at 10.5281/zenodo.6388531.

Conflicts of interest
There are no conflicts to declare.