Chemical Control of Mechanical Anisotropy and Band Alignment in Perylene-based Two-dimensional MoS$_2$-Organic Hybrids

TL;DR

This paper investigates how chemical modifications of organic molecules can control the mechanical anisotropy and electronic band alignment in MoS₂-organic hybrid materials, revealing tunable properties for potential applications.

Contribution

It demonstrates the ability to tailor mechanical and electronic properties of MoS₂ hybrids through chemical modifications of attached organic molecules using density functional theory.

Findings

Distinct differences in properties due to chemical composition and geometry.

PO exhibits the greatest mechanical anisotropy.

Organic molecules alter band alignment and work function.

Abstract

This study presents a comprehensive investigation of hybrid interfaces formed by monolayer MoS$_2$ coupled with the organic molecules perylene (P), perylene diimide (PDI), and perylene orange (PO). Using density functional theory, we demonstrate the extent to which the mechanical and electronic properties of a hybrid system can be altered by the chemical modification of a given chromophore. The three systems exhibit distinct differences due to their chemical composition and van der Waals contact enabled by their geometry. All systems are structurally stable. The binding energies follow the order PD$>$P$>$PO due to the large $\pi$-system (PD) and strong structural distortion (PO). Young's modulus and Poisson's ratio exhibit pronounced anisotropy in all cases. PO exhibits the greatest anisotropy due to steric effects and a permanent dipole, which introduce directionality to the molecule-surface interaction. Physisorption is accompanied by net charge transfer in the same order as the binding energies. The associated interfacial polarization results in a change in the work function compared to pristine MoS$_2$ in the order P$>$PO$>$PD. Finally, the presence of organic molecules introduces states into the MoS$_2$ energy gap, with the band alignment being either type II (P, PO) or type I (PD).

Tables

Table 1. Table 1: Elastic constants (C 11 , and C 12 ), Young modulus ( Y Y ), shear modulus ( G G ), Poisson’s ratio ( ν \nu ), and bulk modulus ( K K ) of MoS 2 , MoS 2 /P, MoS 2 /PD, and MoS 2 /PO.

System	$C_{11}$ (N/m)	$C_{12}$ (N/m)	$Y$ (N/m)	$G$ (N/m)	$\nu$	$K$ (N/m)
MoS2	138.5	31.37	131.4	53.6	0.23	85.2
MoS2/P	130.2	31.34	122.6	49.4	0.24	80.8
MoS2/PD	129.7	31.6	122.0	49.1	0.24	80.6
MoS2/PO	140.9	18.2	138.6	61.4	0.13	79.5

Table 2. Table 2: Energy levels for MoS 2 /organic molecule hybrid and separate systems with respect to vacuum level. Here X@MoS 2 refers to the isolated molecule having the geometry it will adopt at the surface.

System	VBM (eV)	CBM (eV)	HOMO (eV)	LUMO (eV)
MoS2	–5.90	–4.25
P			–4.70	–2.78
PD			-5.80	-4.25
PO			–5.69	–4.17
P@MoS2			–4.70	–2.78
PD@MoS2			–5.80	–4.29
PO@MoS2			–5.48	–4.05
MoS2/P	–5.89	–4.24	–4.20	–2.40
MoS2/PD	–5.90	–4.25	–5.83	–4.37
MoS2/PO	–5.96	–4.31	–5.57	–3.97

Table 3. Table 3: Calculated overall band gap E g E_{\rm g} , MoS 2 band gap E g1 E_{\rm g1} , organic molecule band gap E g2 E_{\rm g2} , and band alignment type for MoS 2 /organic molecule hybrid systems.

System	$E_g$ (eV)	$E_{\mathrm{g1}}$ (eV)	$E_{\mathrm{g2}}$ (eV)	Band Alignment
MoS2/P	0.81 (HOMO-CBM)	1.65	1.80	Type II
MoS2/PD	1.46 (HOMO–LUMO)	1.65	1.46	Type I
MoS2/PO	1.26 (HOMO–CBM)	1.65	1.60	Type II

Equations

$$E_{\mathrm{b}}=E_{{\mathrm{MoS}}_2/\mathrm{organic}}-E_{{\mathrm{MoS}}_2}-E_{\mathrm{organic}}.$$

$$\epsilon =\frac{100\%\times (a-a_0)}{a_0},$$

$$C_{11}$$

$$C_{12}$$

$$Y=\frac{C_{11}^2-C_{12}^2}{C_{11}},G=\frac{C_{11}-C_{12}}{2},\nu =\frac{C_{12}}{C_{11}},K=\frac{C_{11}+C_{12}}{2}.$$

$$Y(\theta )=\frac{C_{11}^2-C_{12}^2}{C_{11}+C_{12}+(C_{11}-C_{12})\cdot \cos (2\theta )},$$

$$\nu (\theta )=\frac{C_{12}+(C_{11}-C_{12})\cdot \cos (2\theta )}{C_{11}+C_{12}+(C_{11}-C_{12})\cdot \cos (2\theta )}.$$

$$E_{\mathrm{S}}=\frac{1}{n}\left(U_{\mathrm{strained}}-U_{\mathrm{unstrained}}\right),$$

$$\Delta \rho (\mathbf{r})={\rho }_{{\mathrm{MoS}}_2/\mathrm{Organic}}(\mathbf{r})-{\rho }_{{\mathrm{MoS}}_2}(\mathbf{r})-{\rho }_{\mathrm{Organic}}(\mathbf{r}),$$

$$\Delta \rho (z)=\frac{1}{A_0}\int \int \Delta \rho (x,y,z)dxdy.$$

$$\Phi =E_{\mathrm{v}}-E_{\mathrm{F}},$$

Full text

1 Introduction

Transition metal dichalcogenides (TMDs) have emerged as key materials in research due to their tunable layered structures and exceptional electronic properties. With the general formula MX2 (where M is a transition metal and X is a chalcogen atom), TMDs exhibit a wide range of electronic behaviors, from insulating to metallic states. Their ”sandwich-like” structure, a result of strong in-plane covalent bonding and weaker van der Waals (vdW) forces between layers, combined with the ability to modify layer thickness easily, makes TMDs promising candidates for innovations in optoelectronics, photovoltaics, and even space technology [1, 2, 3, 4, 5].

Among the TMD family, semiconducting variants such as MoX2 and WX2 (where X = S, Se, Te) stand out due to their tunable band gaps, which distinguish them from other 2D materials like graphene. This tunability makes TMDs highly adaptable for nanoelectronics applications [6, 7]. However, a key challenge for integrating TMDs into optoelectronic devices is the dependence of their electronic properties on layer thickness [8, 9, 10, 11, 12, 13].

Molybdenum disulfide (MoS2), a prototypical semiconducting TMD, is particularly notable due to its scalable production and remarkable optoelectronic properties [14, 15, 16, 17, 18]. Its band structure gives rise to distinct exciton species, including A and B excitons resulting from spin-orbit splitting of the valence band, and a non-emissive C exciton. These excitons, which have large binding energies and exhibit significant delocalization, show observable shifts in their photoluminescence (PL) spectra as the number of layers varies [19]. Properties like quantum confinement, valley polarization, tunable ferroelectricity, and robust light-matter interactions further enhance MoS2’s appeal for optoelectronic applications [20, 21, 22, 23].

Parallel to the development of TMDs, the field of organic semiconductors has advanced rapidly. Organic materials are renowned for their strong light absorption, cost-effectiveness, and compatibility with flexible substrates [24, 25, 26, 27]. A particularly promising area is the integration of TMDs with organic semiconductors, leading to organic/inorganic hybrid systems with potentially improved optoelectronic properties [28]. Hybrid systems combining MoS2 with organic molecules, such as 9-(2-naphthyl)-10-[4-(1-naphthyl)phenyl]anthracene (ANNP) [29], vanadyl phthalocyanine (VOPc) [30], and tin (IV) phthalocyanine dichloride (SnCl2Pc) [30] exhibit improved interfacial charge transfer (CT) and PL performance. For instance, the MoS2/VOPc heterostructure shows significant quenching of MoS2 PL due to efficient CT from VOPc to MoS2, generating interlayer excitons via mid-gap states.

In organic electronics and high-performance pigment technology, the perylene family plays a pivotal role due to its exceptional optical and electronic properties [31, 32, 33, 34, 35]. Perylene derivatives can be customized with various substituents to fine-tune their characteristics. Prominent examples are perylene diimide and perylene orange as shown in Fig. 1. Known for their vivid colors, high photostability, and excellent electronic performance, perylene derivatives are widely used in organic solar cells, organic light-emitting diodes, bioimaging, and sensing applications [36, 37, 38, 39, 40, 41, 42].

The interaction between MoS2 and perylene-based organic semiconductors results in particularly rich optoelectronic behaviors. For instance, the MoS2/PTCDA heterostructure demonstrates a substantial increase in PL intensity, driven by strong interfacial interactions and crystalline ordering of the PTCDA layer. This behavior leads to a significant PL peak shift, reflecting robust coupling at the interface that can be exploited to tune optoelectronic properties [30, 43, 44]. In a recent study, the PL of MoS2/perylene orange interface was investigated [45]. It was found that molecular PL is quenched by efficient interfacial charge separation. This was in accord with band structure calculations, pointing to a type II band alignment [46]. In Ref. [46] it was further shown that the type of alignment depends on the applied strain, i.e. upon compression of the MoS2/perylene orange interface a transition to type I alignment was proposed. Controlled application of strain thus may provide a means for tuning interfacial properties of hybrid systems.

Considering organic/inorganic interfaces it is frequently highlighted that chemical design of the organic part provides a high degree of flexibility for tuning mechanical and optoelectronic properties. Here we explore, using Density Functional Theory (DFT), to what extent key interfacial properties can be tuned for a given class of chromophores. As a specific example we will use perylene (P) and its derivatives perylene diimid (PD) and perylene orange (PO). Specifically, we focus on mechanical and electronic properties of the hybrid interface. By examining band alignment, work function variation, and charge density distribution, we specifically aim to elucidate the molecular-level interactions that govern the optoelectronic behavior of these hybrid systems.

2 Computational Details

First-principles calculations were performed using DFT with the projector augmented-wave (PAW) method and the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) functional, as implemented in the Vienna ab initio Simulation Package (VASP) [47, 48, 49, 50]. To prevent interlayer interactions, a vacuum layer of 20 Å was added along the $z$-axis, with dipole corrections applied to mitigate spurious interactions between periodic images. A $9\times 9\times 1$ supercell of MoS2 was employed to model interactions between the MoS2 monolayer and the organic molecules. Note that we consider the limit of low coverage, i.e. only a single organic molecule per supercell is taken into account. We performed geometry optimization starting from parallel and perpendicular orientations with the molecules being initially in gas phase geometry. Energy and force convergence thresholds were set to $10^{-6}$ eV and 0.01 eV/Å, respectively. Computational parameters, including plane-wave cutoff energy (450 eV), smearing width (0.05 eV), and $k$-point density ($1\times 1\times 1$), were optimized to achieve a balance between precision and computational efficiency.

DFT exchange-correlation functionals, such as those based on the Local Density Approximation (LDA) [16] and the GGA [31], are generally effective in describing covalent and ionic bonding. However, these functionals are not appropriate for systems involving weak vdW interactions, as they do not explicitly account for such forces. For example, GGA functionals like PW91 and PBE [31] fail to accurately describe interactions between layered materials, such as h-BN or graphene, or between these layers and transition-metal (111) surfaces [36, 49]. In systems involving MoS2 and organic molecules, the relevance of vdW interactions is not immediately clear. To account for these interactions, the empirical PBE+D3 method was employed, as opposed to the computationally more demanding vdW-DFT approach [37, 38].

To determine the binding energies ($E_{\rm b}$) of MoS2/organic hybrid interfaces, the following equation was used

[TABLE]

Here, $E_{\rm{MoS}_{2}/\rm{organic}}$ is the total energy of the MoS2-organic composite system, $E_{\rm{MoS}_{2}}$ represents the energy of the isolated MoS2 monolayer, and $E_{\rm{organic}}$ refers to the energy of the isolated organic molecule. The geometries of all subsystems are geometry-optimized.

Additional electronic structure calculations for isolated molecules were performed at the DFT/PBE level with a 6-311G(d,p) basis set using the Q-Chem 5.3 package [51].

To systematically investigate mechanical property modulations in a monolayer of MoS2 and its composite interfaces with perylene-based molecules, in-plane uniaxial strains were applied. The strain magnitude ($\varepsilon$) was characterized by the alteration in the lattice parameter, defined as

[TABLE]

where $a_{0}$ and $a$ represent the lattice constants of the unstrained and strained systems, respectively. The focus centered on the analysis of planar elastic stiffness coefficients, specifically $C_{11}$, $C_{12}$, and $C_{22}$. These coefficients were extracted by fitting the supercell’s energy, $U$, for certain values ($\epsilon_{11}$, $\epsilon_{22}$).

The elastic stiffness coefficients were computed as follows

[TABLE]

where $A_{0}$ is the equilibrium (zero-strain) lateral area of the supercell used to model the MoS2/organic interface. For a hexagonal lattice, $C_{11}$ is inherently equal to $C_{22}$. The Young’s modulus ($Y$), shear modulus ($G$), Poisson’s ratio ($\nu$), and bulk modulus ($K$) were calculated using the following relationships

[TABLE]

In addition, the angular-dependent material properties were evaluated using the following equations, valid for a hexagonal lattice, to get Young’s modulus ($Y(\theta)$) and Poisson’s ratio ($\nu(\theta)$)

[TABLE]

[TABLE]

The strain range spans from $-8\%$ to $8\%$, with a step size of 0.02, elucidating detailed changes in the mechanical and structural properties of the MoS2 monolayer and its hybrid configurations under controlled strain conditions. To evaluate whether the strain remains within the elastic limit, the per-atom strain energy ($E_{\rm S}$) was calculated using

[TABLE]

where $n$ is the total number of atoms in the simulation supercell. This normalization allows comparison of strain energy on a per-atom basis, independent of system size.

Obtaining accurate band alignment for organic/inorganic hybrid structures using DFT is, in general, a challenging task. Polarization effects are not well described in Kohn-Sham theory and more accurate fully self-consistent many-body perturbation theory (GW) is computationally not feasible and one has to resort to the G0W0 approximation [52]. System-specific nonempirically tuned range-separated hybrid functionals, that show very good performance for isolated molecules [53], are in general difficult to adjust [54]. Krumland et al. suggested a pragmatic method based on the subsystem idea [55, 54]. Applying this model to phthalocyanine on MoS2 it has been found that a good approximation for the band alignment is obtained from PBE and PBE0 DFT calculations of the isolated subsystems [56]. In case of the MoS2/PO interface in Ref. [46] we have found decent agreement with the PBE result. Hence we will assume that PBE is reliable also for the two other perylenes investigated in the present study.

At the MoS2/organic interface, charge transfer modifies the electrostatic potential profile, leading to shifts in vacuum levels and work functions. This built-in potential drives electron flow until Fermi level alignment is achieved, establishing equilibrium. The resulting interfacial electric field influences carrier dynamics, band bending, and exciton dissociation. To assess CT effects and the resulting electrostatic potential alignment at the MoS2/organic interfaces, we computed the planar-averaged charge density difference for the electronic ground state. These quantities allow visualization and quantification of electronic charge redistribution due to interfacial interactions and their electrostatic consequences.

The three-dimensional charge density difference is defined as

[TABLE]

where $\rho_{\mathrm{MoS}_{2}/\mathrm{Organic}}(\mathbf{r})$ is the total charge density of the hybrid system, and $\rho_{\mathrm{MoS}_{2}}(\mathbf{r})$ and $\rho_{\mathrm{Organic}}(\mathbf{r})$ correspond to the isolated MoS2 monolayer and organic molecule, respectively, computed in the same supercell geometry without electronic interaction.

To analyze the charge redistribution perpendicular to the interface (i.e. in stacking direction), we perform a planar average over the $xy$ plane:

[TABLE]

Finally, we also report on the work function, $\Phi$, of a surface given by

[TABLE]

where $E_{\rm v}$ is the electrostatic potential in the vacuum region (i.e., the vacuum level), and $E_{\rm F}$ is the Fermi energy relative to the internal potential of the material.

3 Results and Discussion

The three considered molecules have different structural and thus electronic characteristics that are pertinent to the interfacial binding. Comparing the planar P and PD we notice not only the heteroatoms in PD, but also its larger $\pi$-electron system providing an increased vdW contact area with the MoS2 surface. PO also consists of seven fused rings, but its bulky side groups make it notably non-planar and provide steric hindrance for the interaction with the surface. In what follows, we will present and discuss results, which highlight how these differences are reflected in structural, mechanical and electronic properties of the hybrid interfaces.

3.1 Structure and Binding Energy

The structural properties of the MoS2/organic hybrid interfaces were investigated by considering both parallel and perpendicular molecular orientations. Figures 1(a)–(c) show the chemical formulas of the organic molecules P, PD, and PO, while Figs. 1(d)–(f) present the side and top views of the geometry-optimized MoS2/P, MoS2/PD, and MoS2/PO hybrid interfaces. The perpendicular configurations are shown in the Supplemental Material (Suppl. Mat.), Fig. S1. Due to the missing vdW contact between the $\pi$-system and the MoS2 surface, their binding strength is much reduced compared to the parallel cases.

The calculated in-plane lattice constants for pristine MoS2, MoS2/P, MoS2/PD, and MoS2/PO are 3.18, 3.16, 3.16, and 3.17 Å, respectively. This minimal variation suggests that adsorption induces only weak structural perturbation, indicative of physisorption governed by vdW interactions. The absence of a commensurate overlayer further supports the non-epitaxial nature of the interface. The slightly reduced lattice constants in MoS2/P and MoS2/PD may result from enhanced vdW interactions due to the planar geometry of these molecules, enabling closer contact with the MoS2 surface. In contrast, the marginally larger lattice constant in MoS2/PO is likely attributable to steric repulsion arising from the non-planar molecular structure.

Figure 1(g-i) shows the binding energy as a function of interlayer distance (cf. panels (a-c) for the definition of $d_{\rm int}$). The equilibrium interlayer distances for MoS2/P, MoS2/PD, and MoS2/PO are 2.91 Å, 3.27 Å, and 2.37 Å, respectively, as summarized in Table 1. Comparing results obtained with and without the D3 dispersion correction, it is evident that all systems gain significant stabilization from vdW interactions. Regarding the binding strength among the three molecules, the trend follows the available contact area between the $\pi$-system and the MoS2 surface, i.e. MoS2/PD ($-1.83$ eV) $>$ MoS2/P ($-1.32$ eV)$>$ MoS2/PO ($-1.07$ eV). This trend reflects both the planar nature of PD and P molecules, which facilitates stronger vdW interactions, and the more sterically hindered, non-planar geometry of PO, which limits close contact with the substrate. Regarding the lateral potential energy landscape, the physisorptive nature dominated by vdW forces suggests a relatively smooth and shallow corrugation. Consequently, the molecules are expected to experience, compared to the binding energy, low energy barriers for lateral diffusion on the MoS2 surface, enabling mobility at finite temperatures. However, in particular for PO variations in molecular geometry and local adsorption sites may induce modulations of the lateral potential, warranting detailed exploration through explicit calculations of lateral energy barriers to fully characterize potential diffusion pathways (e.g. [57]).

3.2 Mechanical Properties

To assess the mechanical stability of the investigated hybrid systems, elastic constants were computed. The potential energy variation under uniaxial strain for these interfaces according to Eq. 8 is shown in the Suppl. Mat., Fig. S2. In the considered range of applied strain ($\pm 8$%) all systems are in the elastic regime. The results for the mechanical parameters are compiled in Table 1. Note that the results for MoS2 are consistent with values reported previously [58]. All systems satisfy Born’s stability criteria, specifically $C_{11}>0$ and $|C_{11}|>|C_{12}|$, confirming their mechanical stability.

The in-plane stiffness, quantified by the 2D Young’s modulus, shows significant variation across the systems, with MoS2/PO exhibiting the highest value ($Y=138.6\,\rm{N/m}$). MoS2/PO also shows the lowest Poisson’s ratio ($\nu=0.13$), indicating minimal transverse contraction under axial tension. In contrast, MoS2/P and MoS2/PD display slightly higher values, which may be related to differences in molecular geometry and intermolecular interactions rather than lattice compatibility, since no periodic or commensurate overlayer is formed. The bulk moduli of the three hybrid systems are approximately equal and smaller than for pristine MoS2, i.e. physisorption reduces the resistance to isotropic in-plane deformation. The in-plane shear modulus is largest for MoS2/PO.

The different behavior of PO as compared to P and PD is also visible in the in-plane variations of Young’s modulus and Possion’s ratio as seen in Fig. 2(a,b). The anisotropic nature of Young’s modulus (panel (a)) is evident in all cases, with MoS2/PO exhibiting the most pronounced deviations. Concerning Poisson’s ratio MoS2/PO again shows the largest anisotropy, exhibiting the lowest values at 90∘ and 270∘, corresponding to directions roughly perpendicular to the molecular axis.

Rationalizing the difference between PO and P/PD in the magnitude of anisotropy one has to notice that not only is PO non-planar, but its distorted structure with respect to the gas phase introduces a considerable dipole moment of about 2 Debye (approximately along the long axis). Both give rise to a more pronounced directionality of the interaction with the MoS2 surface, what is reflected in the response to lateral distortions Notice that this is not reflected in the magnitude of the vdW binding energy (as compared to P and PD), which refers to the perpendicular displacement.

3.3 Interfacial Charge Transfer

Charge redistribution at the MoS2/organic interfaces was analyzed via charge density difference calculations, as shown in Fig. 3. At the MoS2/P interface (Fig. 3(a,b)), charge accumulation is predominantly localized on the planar P molecule, indicating its role as an electron acceptor, while hole accumulation occurs on the MoS2 surface, confirming its function as an electron donor. The presence of the heteroatoms (O,N) leads to a charge transfer to the surface in the respective regions, yielding a more structured charge density difference distribution for PD and PO as seen in Fig. 3(c–f). Net charge transfer follow the trend $\mathrm{MoS_{2}/PD}(0.013~e)>\mathrm{MoS_{2}/P}(0.011~e)>\mathrm{MoS_{2}/PO}(0.006~e)$. Notably it reflects the trend in binding energies. The magnitude of charge transfer is very small, thus confirming the physisorption character of the systems. In passing we note that this is in accord with results obtained for pentacene and PTCDA at MoS2 [44].

Charge transfer and interfacial polarization will also affect the work function. In Fig. 4 the electrostatic potential profiles for pristine monolayer MoS2 (Fig. 4(a)) and its interfaces with P (Fig. 4(b)), PD (Fig. 4(c)), and PO (Fig. 4d) are shown. For MoS2, the electrostatic potential curve displays pronounced minima near -20 eV, while the organic molecules exhibit smaller minima, generally around 0 eV to -2.5 eV. Clearly visible is the spread of charge density in case of the structurally distorted PO. Overall, the notably lower electrostatic potential for MoS2 relative to the organic layers, is confirming the observation of Fig. 3 that MoS2 functions as an electron donor.

The pristine MoS2 monolayer has a work function of 5.67 eV, in accord with previous results [44]. The introduction of organic layers induces shifts in the work function to 4.70, 5.54, and 5.19 eV for P, PD, and PO, respectively. That is, the corresponding shifts are in the order P(-0.97 eV) $>$ PO -0.48 eV $>$ PD (-0.13 eV). In general, the observed shifts in work function upon organic layer addition are due to several factors, including interfacial dipole formation, band-bending effects, and substrate relaxation caused by adsorption. As these effects are not additive it is difficult to relate them separately to the work function change. For instance, the root mean squared deviation of the atomic positions with respect to pristine MoS2 follows the order PO (0.28 Å)$>$ P(0.158 Å) $\sim$ PD(0.156 Å). Comparing the present results with those of Ref. [44] we notice that work function changes are sizable and in between those of pentacene (-1.33 eV) and PTCDA (-0.036 eV).

3.4 Band Structure

The band structure and level scheme for the considered systems are shown in Fig. 5. Using the PBE functional, the band gap of pristine MoS2 is found to be 1.65 eV, consistent with previous theoretical results [54]. Introducing the organic molecules modifies the electronic structure, resulting in new states within the MoS2 band gap. This is reflected in the band structures shown in Fig. 5(a), (c), and (e); the respective Kohn-Sham wavefunctions are given in Fig. 6. For the partial density of states (PDOS), see Suppl. Mat., Figs. S3–S5.

To investigate the extent to which chemical modification of the organic part can be used to tune the hybrid interface, first we will focus on level energies with respect to vacuum for the constituents and the hybrid systems, cf. Tab. 2. Here, we notice that the conduction band minimum (CBM) and the valence band maximum (VBM) of MoS2 are only marginally affected by the presence of the organic molecule. For the organic molecules there are two effects, first the electronic interaction and second the changes geometry at the surface. Noticeable changes of the LUMO (lowest unoccupied molecular orbital)/HOMO (highest occupied molecular orbital) energies due to modification of the geometry at the surface are observed for PO only. The additional effect due to the electronic interaction with the surface is largest for P and moderate for PD and PO. Overall with respect to gas phase the HOMO-LUMO gap decreases by about 6% for P and PD and increases by about 5% for PO. In other words these energies are well preserved upon physisorption.

In each hybrid system, the interface exhibits, besides the overall band gap $E_{\rm g}$, two distinct band gaps: $E_{\rm g1}$, the difference between the CBM and VBM of MoS2, and $E_{\rm g2}$, the difference between the LUMO and HOMO of the organic molecule. The different band gaps are summarized in Table 3.

In the MoS2/P interface (Figs. 5(a) and 6(a)), the introduction of the P molecule creates localized states within the MoS2 band gap. As shown in the band structure, the HOMO of P lies approximately in the middle of the MoS2 band gap, while the LUMO of P is positioned above the CBM of MoS2. Thus we have a type II (staggered) band alignment.

For the MoS2/PD interface, depicted in Figs. 5(c) and and 6(b), both the HOMO and LUMO levels of PD lie within the band gap of MoS2, with the HOMO positioned close to the VBM and the LUMO near the CBM of MoS2. This energetic configuration corresponds to a type I (straddling) band alignment, where the organic molecule’s frontier orbitals are enclosed within the MoS2 band gap. As a result, the effective band gap of the hybrid system (0.81 eV) is dominated by the HOMO–LUMO gap of PD.

Finally, the MoS2/PO interface, shown in Figs. 5(e) and 6(c), exhibits a type II (staggered) band alignment. Here, the HOMO and HOMO$-1$ levels of PO lie near the VBM of MoS2, while the LUMO of PO is situated slightly above the CBM of MoS2. The overall band gap of the MoS2/PO system is 1.26 eV, defined by the energy difference between the PO HOMO and the MoS2 CBM.

These findings are supported by the PDOS given in the Suppl. Mat., Figs. S3–S5, which also illustrate the contributions of the different molecular orbitals. In the cases of P and PD the relevant HOMO/LUMO levels are of pure C-2p character. For PO the HOMO has additional contributions from O-2P and N-2p atomic orbitals. This distinct composition is reflected in the orbital plots in Fig. 6. A summary of the type of band alignment is provided in Figs. 5(b,d,f).

4 Summary and Conclusions

The objective in choosing perylene and its derivatives was to explore how the interfacial properties of the MoS2/organic hybrid system change with the chemical modification of a given chromophore core. In terms of the optical absorption, PD and PO are similar having the lowest electronic transition around 2.3-2.4 eV. For P this transition is blue-shifted to about 2.8 eV. More relevant for the present discussion is the fact that both P and PD are planar, the latter featuring heteroatoms (O,N) as well as a more extended $\pi$-electron system. Compared to PD, PO has in addition bulky side groups attached to the N-sites along the long axis.

All molecules are bound by vdW interaction to the MoS2 surface. The binding energy of PD is larger than for P due the increased vdW contact with the surface. The bulky side groups of PO diminish the contact of its $\pi$-system with the surface resulting in the lowest binding energy. In addition the structures of PO is substantially distorted upon adsorption.

All systems show a pronounced mechanical anisotropy. However, PO stands out in terms of magnitude. A possible reason could be its distortion PO, leading not only to directionally sensitive steric effect but also causing a permanent dipole directed roughly along the long molecular axis.

Even though there is no appreciable hybridization of electronic orbitals, the interface is polarized, i.e. an interfacial dipole is formed. This comes along with a modification of the work function by up to about -1 eV for P as compared to bare MoS2. The net charge transfer upon binding is on the order of 10*-2* to 10*-3* and reflects the order of binding energies. The pattern of charge density difference is shaped by the presence of the heteroatoms as well as by the structural distortion.

In terms of photophysical behavior band structure and interfacial level alignment is most important. For MoS2 the band gap is almost unaffected by the interaction with the organic molecules. The latter show some shift and also a net change of the HOMO-LUMO gap. For PO the largest change is due to the structural distortion, whereas for P one finds the largest effect of the electronic interaction. The band alignment is found to depend on the actual perylene, i.e. it is of type II for P and PO and of type I for PD. This has consequences for interfacial charge transfer pathways upon photoexcitation (cf. schemes in Fig. 5). Note that in case of PO the predicted band alignment is in accord with experimental PL measurements [45].

In summary, the present findings demonstrate the extent to which the interfacial properties of MoS2/organic systems can be tuned through the chemical modification of a given chromophore. The chemical composition and geometry-enabled van der Waals contact play critical roles in the interfacial polarisation and band alignment of MoS2/organic hybrid systems.

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - SFB 1477 ”Light-Matter Interactions at Interfaces”, project number 441234705”.