The Modulation Effect of MoS2 Monolayers on the Nucleation and Growth of Pd Clusters: First-Principles Study

The geometries, electronic structures, adsorption, diffusion, and nucleation behaviors of Pdn (n = 1–5) clusters on MoS2 monolayers (MLs) were investigated using first principles calculations to elucidate the initial growth of metal on MoS2. The results demonstrate that Pd clusters can chemically adsorb on MoS2 MLs forming strong Pd–S covalent bonds with significant ionic character. We investigated the initial growth mode of Pd clusters on MoS2 monolayers and found that Pdn clusters tend to adopt pyramid-like structures for n = 4–5 and planar structures lying on MoS2 substrates for n = 1–3. It can be explained by the competition between adsorbate–substrate and the intra-clusters’ interactions with the increasing coverage. Compared with pristine MoS2 MLs, the work function was reduced from 5.01 eV upon adsorption of Pd monomer to 4.38 eV for the case of the Pd5 clusters due to the charge transfer from Pd clusters to MoS2 MLs. In addition, our calculations of the nucleation and diffusion behaviors of Pd clusters on MoS2 MLs predicted that Pd is likely to agglomerate to metal nanotemplates on MoS2 MLs during the epitaxial stacking process. These findings may provide useful guidance to extend the potential technological applications of MoS2, including catalysts and production of metal thin films, and the fabrication of nanoelectronic devices.


Introduction
In recent years, two-dimensional (2D) layered transition metal dichalcogenides (TMDs), particularly MoS 2 , exhibiting excellent electronic and optical properties, have drawn great attention due to their potential applications in flexible nanoelectronics, photonic devices, memory devices, etc. [1][2][3][4]. A series of experimental and theoretical studies have confirmed that MoS 2 monolayers (MLs) decorated with metal nanoparticles (NPs) could potentially extend its functionalities as novel catalysts, spintronic devices, and thermoelectric and photoelectric materials, which is owing to the unique size-dependent properties of metal nanoparticles [5][6][7][8]. For instance, Chen et al. [5] reported the metal clusters (Pd, Pt, and Ag) supported on MoS 2 MLs tend to display excellent electrocatalytic activity compared to those on graphene. Fu et al. [6] found that Au nanoparticles on two-dimensional MoS 2 nanosheets can be used to fabricate an attractive alternative photoanode for efficient photoelectron chemical miRNA detection. Recently, Burman and co-workers [7] successfully fabricated Pt decorated MoS 2 nanoflakes, and further confirmed its potential application as the sensing layer of an ultrasensitive resistive humidity sensor. Besides, Li et al. [9] reported that Au NPs imposed remarkable p-doping A plane wave basis set with the projector-augmented plane wave (PAW) was performed to describe the ion-electron interaction [22]. The plane-wave cutoff corresponding to a kinetic energy of 450 eV was adopted. The k-point meshes were generated according to the Monkhorst-Pack scheme [23] and 9× 9 × 1 mesh was used to sample the supercell which consisted of 4 × 4 MoS 2 units in the calculations. In order to prevent the interactions between neighboring slabs, a thick vacuum layer of more than 15Å was adopted in a direction perpendicular to the surface. During structural relaxation, all the atomic coordinates (including Mo, S, and Pd) were fully relaxed until the Hellmann-Feynman forces were smaller than 0.01 eV/Å.
To describe quantitatively the energetic trends of adsorbed Pd clusters on the MoS 2 ML and to further explore the modulation of MoS 2 substrate on the growth mechanism of Pd clusters, we introduce adsorption energy E A , binding energy E B , and intra-cluster binding energy E IB , which are defined as the following: (1) The adsorption energies E A , where E Pd n /MoS 2 tot and E MoS 2 are the total energies of the MoS 2 monolayer with and without Pd n clusters, E Pd n is that of the floating Pd n clusters consisting of n Palladium atoms. E A can be used to describe quantitatively the strength of the adsorbate-substrate interaction.
(2) The binding energy E B , where E Pd is the total energy of an isolated Palladium atom in a cubic supercell of 20 Å × 20Å × 20Å. The binding energy E B reflects the relative stability of the Pd n clusters supported by the MoS 2 ML. (3) The intra-cluster binding energy E IB , which could qualitatively reflect the strength of the Pd-Pd interactions. In order to compare directly, all considered energy terms were normalized with respect to the number of Pd atoms, given per adatom.
To get insight to the nucleation mechanism and growth mode of Pd clusters, we also calculated the diffusion properties of Pd n (n = 1-5) clusters supported by the MoS 2 ML. The diffusion barrier and transition states were determined from the minimum energy pathway by employing the climbing-image nudged elastic band (NEB) method [24,25]. All geometries were optimized until the maximum force in every degree of freedom was less than 0.005 eV Å.

Geometries and Stabilities for Pd n (n = 1-5) Adsorbed at MoS 2 ML
In order to understand the adsorption properties of Pd n (n =1-5) clusters and explore the nucleation mechanism and initial growth of Pd nanoparticles on MoS 2 MLs, it is essential to identify the structural and electronic properties of pure MoS 2 ML for comparison. Figure 1a shows the top and side view of a 4 × 4 supercell of the MoS 2 ML; the calculated results show that the thickness of the MoS 2 ML was 3.14 Å and the bond length of the S-Mo was 2.84 Å, which is consistent with previous studies [26,27]. Besides, we calculated the band structures of the MoS 2 ML as shown in Figure 1b. The calculated results indicate that the MoS 2 ML presented semiconducting character with a direct gap of 1.75 eV at the K point, which is in good agreement with the previous theoretical results of 1.70 eV [28] and experimental results of 1.80 eV [29]. We first investigated the geometries and adsorption properties of a single Pd adatom on the MoS 2 ML. For the case of Pd monomer, we considered the binding of Pd on four high-symmetry sites: the hollow (H) site at the center of a hexagon, the top site directly above Mo (t-Mo) and S (t-S), and the bridge (B S-S ) site at midpoint of the S-S bond, as shown in Figure 1a. It is known that the larger the adsorption energy E A , the stronger the interaction between the adsorbate and substrate. Table 1 lists the structural parameters and adsorption energies for all considered adsorption configurations of Pd monomer adsorbed at the MoS 2 ML. The calculated results show that the t-Mo site with the adsorption energy of 2.16 eV was the most energetically favorable location, which is consistent with previous studies [26,30]. The Pd monomer adsorbed at the t-S and H sites were 0.57 and 0.37 eV, respectively, less stable than that of the t-Mo adsorption configuration. Our calculated results show that Pd monomer located at the B S-S site finally relaxed to the t-Mo configuration, which indicates that Pd monomer adsorbed at the B S-S site was unstable. As summarized in Table 1 [26,30]. The Pd monomer adsorbed at the t-S and H sites were 0.57 and 0.37 eV, respectively, less stable than that of the t-Mo adsorption configuration. Our calculated results show that Pd monomer located at the BS-S site finally relaxed to the t-Mo configuration, which indicates that Pd monomer adsorbed at the BS-S site was unstable. As summarized in Table 1   We have chosen several initial configurations to search the most stable configurations of Pdn (n = 2-5) clusters adsorbed at the MoS2 ML, which is shown in Figure 2. The calculated structural parameters and adsorption, binding, and intra-cluster binding energies for the lowest energy configurations of Pdn (n = 1-5) adsorbed on the MoS2 ML are summarized in Table 2. The most preferential configuration of Pd dimer adsorbed at the MoS2 ML was that two Pd atoms both adsorbed at the top of Mo, and they were separated by 3.05 Å, which was smaller than the calculated lattice constant of MoS2 ML, as shown in Figure 3a. For the cases of Pd3 cluster adsorbed at MoS2 ML, the calculated results show that the t-(Mo)3-S configuration with the largest adsorption energy of 1.44  We have chosen several initial configurations to search the most stable configurations of Pd n (n = 2-5) clusters adsorbed at the MoS 2 ML, which is shown in Figure 2. The calculated structural parameters and adsorption, binding, and intra-cluster binding energies for the lowest energy configurations of Pd n (n = 1-5) adsorbed on the MoS 2 ML are summarized in Table 2. The most preferential configuration of Pd dimer adsorbed at the MoS 2 ML was that two Pd atoms both adsorbed at the top of Mo, and they were separated by 3.05 Å, which was smaller than the calculated lattice constant of MoS 2 ML, as shown in Figure 3a. For the cases of Pd 3 cluster adsorbed at MoS 2 ML, the calculated results show that the t-(Mo) 3 -S configuration with the largest adsorption energy of 1.44 eV presents higher stability than the t-(Mo) 3 -h configuration due to the extra binding of S1 atom, in which Pd trimer stands in a plane parallel to the MoS 2 surface. Besides, it is not surprising that the considered t-(Mo) 3 -L with three Pd atoms in a line adsorbed at the top of Mo is higher in energy than the triangular islands because of the decrease in the number of intra Pd-Pd bonds. The average bond length of Pd-Pd and the height of Pd 3 cluster above the MoS 2 surface are 2.94 and 1.49 Å, respectively. The ∆-(Mo) 3 structure where two Pd atoms were located at the t-Mo sites and the third one was located at the bridge site of the two Pd atoms was also considered for the case of the Pd 3 cluster. However, different from the case of Pt 3 on MoS 2 ML, such vertical configuration is unstable as it is about 0.65 eV less stable than the t-(Mo) 3 -S configuration. For the case of Pd tetramers adsorbed at MoS 2 surface, we considered three possible configurations, including aplanar-(Mo) 4 (four Pd atoms located at the t-Mo site, not shown here), pyramid-like t-(Mo) 4 -h, and t-(Mo) 4 -S configurations. The computed results show that the most favorable structure is t-(Mo) 4 -h (shown in Figure 2c) for Pd tetramer adsorbed at the MoS 2 ML, implying the growth mechanism transitions from a two-dimensional (2D) to a three-dimensional (3D) mode from the formation of Pd 4 cluster. Based on the most stable configuration of Pd 4 tetramers supported by the MoS 2 ML, we considered three initial geometries for Pd pentamer. After full structural optimization, the most stable structure was asquare pyramid t-(Mo) 5 , shown in Figure 2d, which could be obtained by adding one additional Pd atom adsorbed at a neighboring t-Mo site with respect to the t-Pd 4 -h configuration. Table 2. Calculated distance between Pd clusters and MoS 2 surface (d Pd-substrate ), bond length of Pd-S (d Pd-S ), Pd-Pd distance (d Pd-Pd ), adsorption energy E A , binding energy E B , and intra-cluster binding energy E IB for the lowest energy Pd n (n =1-5) configurations on the MoS 2 ML. The units of structural parameters and energies are Å and eV, respectively.

Configurations
Pd Pd 2 Pd 3 Pd 4 Pd 5 From the above calculations, it is clear that the palladium clusters are energetically preferred to lying planar to the surface for the initial growth of Pd n clusters on MoS 2 ML at very low coverage (from Pd 1 to Pd 3 ). With increasing the coverage, the Pd n clusters immediately form islands clusters, such that the morphology of t-(Mo) 4 -h and t-(Mo) 5 -h are the most stable configurations for Pd tetramer and pentamer, respectively. Therefore, under situations dominated by the thermodynamic effects, the clusters with planar structures may be expected to only appear in the very early growth stage and the size of these clusters are very small (e.g., Pd 2 and Pd 3 ), which is immediately followed by the Vomler-Weber growth mechanism. Nanomaterials 2018, 8, x FOR PEER REVIEW 6 of 15 Figure 2. (a-d) Top and side views for most stable configurations of palladium dimer, trimer, tetramer, and pentamer adsorbed at the MoS2 monolayer, respectively. The yellow, lavender, and orange balls represent S, Mo, and Pd atoms, respectively.

t-Mo t-(Mo) 2 t-(Mo) 3 -S t-(Mo) 4 -S t-(Mo) 5 -h d
In our previous study on the initial growth of Pdn/NiAl(110) [32], we reported that small-size Pdn (n=1-5) clusters favor the planar structures on the NiAl(110) surface, which was explained by the stronger interaction between Pdn clusters and NiAl substrate than the interaction among Pd adatoms in clusters. In order to explore the modulation of MoS2 substrate on the growth mechanism of Pdn clusters, it is crucial to understand the evolutions of the metal-metal and metal-slab interactions with the increase of cluster size. We summarize the adsorption, binding, and intra-cluster binding energies as well as structural parameters for the most stable structures of Pdn (n = 1-5) adsorbed on the MoS2 ML in Table 2. It was found that the adsorption energies, EA, decreased from 2.16 to 0.86 eV when the Pd coverage increased from Pd1 to Pd5 clusters, which indicates the strength of the interactions In our previous study on the initial growth of Pd n /NiAl(110) [32], we reported that small-size Pd n (n = 1-5) clusters favor the planar structures on the NiAl(110) surface, which was explained by the stronger interaction between Pd n clusters and NiAl substrate than the interaction among Pd adatoms in clusters. In order to explore the modulation of MoS 2 substrate on the growth mechanism of Pd n clusters, it is crucial to understand the evolutions of the metal-metal and metal-slab interactions with the increase of cluster size. We summarize the adsorption, binding, and intra-cluster binding energies as well as structural parameters for the most stable structures of Pd n (n = 1-5) adsorbed on the MoS 2 ML in Table 2. It was found that the adsorption energies, E A , decreased from 2.16 to 0.86 eV when the Pd coverage increased from Pd 1 to Pd 5 clusters, which indicates the strength of the interactions between the Pd n (n = 1-5) clusters and MoS 2 gradually weakened. The results are reasonable since the height of Pd clusters above MoS 2 increases from Pd monomer to Pd 3 cluster with planar structures. For the case of pyramid-like structures, Pd 5 waslocated at 0.03 Å higher than that of Pd 4 above the MoS 2 ML as listed in Table 2; however, the additional Pd-Pd bonds weakened the Pd-S bonds resulting in less stability of Pd 5 cluster. The binding energy, E B , that reflects the relative stability of the Pd n (n = 1-5)/MoS 2 system, gradually increased from 2.21 eV for Pd 2 to 2.38 eV for Pd 5 , which indicates the relative stability of larger Pd clusters adsorbed at the MoS 2 ML was higher than that of smaller ones. With the increase of Pd coverage (from Pd 2 to Pd 5 ), the intra-cluster binding energy E IB rapidly increased from 0.37 to 1.52 eV, which suggests that the interaction among the Pd adatoms in the Pd 5 cluster was stronger than those of smaller ones. Besides, it was noticeable that the E IB was larger than E A for Pd 4 and Pd 5 , which indicated that intermetallic Pd-Pd bonds in clusters were stronger than the bonds between Pd and surrounding S or Mo. This can be used to explain the fact that the most stable structures for Pd 4 and Pd 5 started to appear around the three-dimensional structures with smaller Pd-Pd bond lengths (about 2.63 Å). Compared with a previous study on Pd n cluster/graphene [33], in which size-selected monodisperse nanoclusters were identified by scanning tunneling microscopy, Pd n clusters supported by MoS 2 are more stable due to larger binding energies and shorter distance between Pd n and MoS 2 substrate, which indicated that the MoS 2 ML was inert and an ideal template for deposition of the metal NPs to some extent.

Electronic Properties of Pd n (n=1-5)/MoS 2 Monolayer
In order to better understand and control how the deposition of Pd clusters affect the structure and electronic properties of MoS 2 , we calculated the density of states (DOS) of MoS 2 ML with and without the adsorption of Pd n (n = 1-5) clusters shown in Figure 3. It is clear that the 4d states of isolated Pd atom was very sharp at 0.35eV, while 4d states of Mo hybrids with the 3p states of neighboring S atoms for pure MoS 2 ML. Upon the adsorption of Pd monomer on MoS 2 (Figure 3b), the band gap decreased to about 1.09 eV, which is mainly attributed to the hybridization of the 4d states of Pd atoms with 4d states of underlying Mo and 3p states of the nearest surrounding S at 0.50 eV below Fermi level. For the case of Pd dimmer adsorbed at MoS 2 ML (Figure 3c), a gap state emerged at the 0.80 eV above the Fermi level, which resulted from the hybridizations between Pd atoms and the nearest-neighboring Mo and S atoms. For the case of Pd 3 cluster, the partial density of states (PDOS) of three Pd adtoms were similar due to the identical atomic environments as shown in Figure 3d. We found that Pd adatoms hybridize more strongly with the S atom located at the hollow site of the Pd trimer (labeled by S1 in Figure 2b) than the nearest-surrounding S atoms (labeled by S2 in Figure 2b

Charge Redistribution and Work Functions
In order to analyze the character of bonds between adsorbates and MoS2 substrate as well as the charge redistribution of MoS2 upon the adsorption of Pd clusters, we calculated and analyzed the electron density difference, which is defined as the free-floating Pd clusters in the frozen geometry they adopted on the Pdn/MoS2 system, respectively. Figure 4 shows the corresponding difference in electron densities for all considered optimized stable configurations, yellow and blue region represent charge accumulation and charge loss, respectively. As shown in Figure 4, the charge redistributions upon the deposition of Pdn cluster mainly involved Pd clusters and surrounding S and Mo atoms, which imply strong charge transfers between the Pdn (n=1-5) clusters and MoS2 substrate. It is clear that there was strong electron density accumulation between Pd atoms and nearest-neighboring S atoms, which indicates that the bonds between Pd adatoms and surface S atoms present a covalent bond with partial ionic features. There are depletion regions close to the Pd atoms along the bond directions of Pd-S, which can be explained by the stronger electronegativity of S than Pd. For the cases of Pd2 and Pd3 clusters, the Pd atoms highly hybrid with the center-S (labeled as S1 in Figure 2). It is also observed that the characteristics of Pd-Pd bond remain strong metallic upon Pd clusters supported by MoS2 ML. However, for the cases of the Pd4 and Pd5 clusters (Figure 4d,e), it is surprising that strong electron density accumulation was found for the topmost Pd atoms (such as Pd4-1 and Pd5-1),which indicates that the

Charge Redistribution and Work Functions
In order to analyze the character of bonds between adsorbates and MoS 2 substrate as well as the charge redistribution of MoS 2 upon the adsorption of Pd clusters, we calculated and analyzed the electron density difference, which is defined as ∆ρ = ρ Pd n −MoS 2 − ρ MoS 2 − ρ Pd n , where ρ Pd n −MoS 2 is the charge density of total system, ρ MoS 2 and ρ Pd n are the charge densities of pristine MoS 2 ML and the free-floating Pd clusters in the frozen geometry they adopted on the Pd n /MoS 2 system, respectively. Figure 4 shows the corresponding difference in electron densities for all considered optimized stable configurations, yellow and blue region represent charge accumulation and charge loss, respectively. As shown in Figure 4, the charge redistributions upon the deposition of Pd n cluster mainly involved Pd clusters and surrounding S and Mo atoms, which imply strong charge transfers between the Pd n (n = 1-5) clusters and MoS 2 substrate. It is clear that there was strong electron density accumulation between Pd atoms and nearest-neighboring S atoms, which indicates that the bonds between Pd adatoms and surface S atoms present a covalent bond with partial ionic features. There are depletion regions close to the Pd atoms along the bond directions of Pd-S, which can be explained by the stronger electronegativity of S than Pd. For the cases of Pd 2 and Pd 3 clusters, the Pd atoms highly hybrid with the center-S (labeled as S1 in Figure 2). It is also observed that the characteristics of Pd-Pd bond remain strong metallic upon Pd clusters supported by MoS 2 ML. However, for the cases of the Pd 4 and Pd 5 clusters (Figure 4d,e), it is surprising that strong electron density accumulation was found for the topmost Pd atoms (such as Pd 4 -1 and Pd 5 -1), which indicates that the top Pd atoms directly receive charge from the underling Pd layers rather than losing charge to the MoS 2 substrate.
To further give a detailed insight into the charge transfer, we also calculated the atomic populations for the most favorable configurations of Pd clusters adsorbed at the MoS 2 ML, as summarized in Table 3. Upon Pd adatoms adsorbed at the t-Mo site, Pd adatoms lost about 0.26e to the MoS 2 ML by Bader analysis, which suggested Pd-S bonds exhibited a relatively significant ionic bonding component, as illustrated by the substantial charge density difference between Pd and neighboring S atoms shown in Figure 3a. Similarly, Pd adatoms in dimer and trimer averagely contributed about 0.20 and 0.18e to the MoS 2 ML, respectively. However, in the cases of Pd 4 and Pd 5 clusters with pyramid-like geometry, Pd atoms in the first layer and second layer of the clusters behave in a different way. The Pd atoms in the second layer of the cluster (Pd 4 -1 and Pd 5 -1) obtained charge, while the Pd atoms of the first layer lost charge. This result is in good agreement with the phenomenon of charge accumulation near the topmost Pd atoms as shown in Figure 4d,e. Therefore, it is not surprising that the MoS 2 slabs obtained less charge from Pd 4 and Pd 5 clusters than that of the Pd 3 cluster. top Pd atoms directly receive charge from the underling Pd layers rather than losing charge to the MoS2 substrate.
To further give a detailed insight into the charge transfer, we also calculated the atomic populations for the most favorable configurations of Pd clusters adsorbed at the MoS2 ML, as summarized in Table 3. Upon Pd adatoms adsorbed at the t-Mo site, Pd adatoms lost about 0.26e to the MoS2 ML by Bader analysis, which suggested Pd-S bonds exhibited a relatively significant ionic bonding component, as illustrated by the substantial charge density difference between Pd and neighboring S atoms shown in Figure 3a. Similarly, Pd adatoms in dimer and trimer averagely contributed about 0.20 and 0.18e to the MoS2 ML, respectively. However, in the cases of Pd4 and Pd5 clusters with pyramid-like geometry, Pd atoms in the first layer and second layer of the clusters behave in a different way. The Pd atoms in the second layer of the cluster (Pd4-1 and Pd5-1) obtained charge, while the Pd atoms of the first layer lost charge. This result is in good agreement with the phenomenon of charge accumulation near the topmost Pd atoms as shown in Figure 4d,e. Therefore, it is not surprising that the MoS2 slabs obtained less charge from Pd4 and Pd5 clusters than that of the Pd3 cluster.   Figure 5 shows the in-plane averaged electrostatic potential (ESP) for the MoS 2 surface with Pd monomer (solid line) and that of the pristine MoS 2 surface (dotted line), respectively. The same were done for other Pd clusters, which are not shown here. Ionization energy (IE), defined as the energy difference between the vacuum level and valence band maximum (VBM), was determined to be 5.48 eV for the clean MoS 2 ML. Upon the Pd n (n = 1-5) clusters adsorption, the increase of ionization energy (∆I) was observed, which can be quantificationally given by the energy difference between the vacuum levels. In addition, the work function is described as the following equation: W = E vac −E F , where E vac is the electrostatic potential in the vacuum region of the adsorbate side of the MoS 2 surface, while E F refers to Fermi energy. The work function of pristine the MoS 2 ML was estimated to be 5.26 eV, which is slightly higher than the experimental result of 5.03 eV [34].
As indicated in Figure 5, we also defined the energy difference between Fermi level (E F ) and the CBM of the MoS 2 ML as p-SBH (Φ P ) for convenience, although the well-defined Schottky barrier contact had not formed yet in our considered initial growth stage of Pd clusters. In Table 4 we summarized the calculated work function (W), p-SBH (Φ P ), dipole moments (D i ), and the variation of ionization energy (∆I) for the adsorption of Pd clusters. It became clear that the increasing of Pd coverage leads to decreases in the work function from 5.01 eV of Pd adatom to 4.38 eV of Pd 5 cluster, which may result from the larger amount of CT from Pd n cluster to MoS 2 as listed in Table 3. We think the variations of p-SBH are mainly attributed to the gap states caused by Pd adatoms (as shown in PDOS in Figure 3) and the partial charge transfer from 1stlayers to the second layer Pd atoms. The trend for the variations of ionization energy is obvious: as the cluster size increases (from Pd 1 to Pd 5 ), ∆I reduces rapidly, while ∆I rises in the initial growth stage of Ni clusters supported by MgO (001) [35]. In addition, the dipole moments (D i ) were calculated by the product of transfer charge and the distance of adsorbate-substrate. The calculated dipole moments of Pd n /MoS 2 were not in a monotonic variation, which is different from the monotonic increase of D i with the increase of Ni coverage on MgO (001).We think that the main reason for these distinct phenomena of the two systems is that the Pd n clusters injected electrons into the VBM of the MoS 2 substrate while the Ni n clusters extracted electrons from the MgO (001) surface. Besides, Pd adatom, Pd 2 , and Pd 3 clusters prefer the planar structures as discussed above, and there is only the interface dipole contribution in such systems. For the cases of Pd 4 and Pd 5 clusters with pyramid-like structures, intra-cluster dipoles due to the CT between the topmost layer and the lower part of the cluster also contribute to the dipole moments. Since these two dipoles have opposite directions, the dipole interactions between Pd 4 or Pd 5 clusters and MoS 2 substrate can be cancelled to some extent.
Previous studies have confirmed that the coverage-dependent depolarization effects play a non-negligible role in metal-organic interfaces [36][37][38]. In order to get insight into the coverage-dependent depolarization effects caused by the interaction between the adjacent supercells, we also used a (6 × 6) supercell to study the adsorption of Pd n clusters at the MoS 2 substrate. We found that the CT and work function of Pd n (n = 1-3)/MoS 2 systems have no significant change, while the variation on CT and work function for Pd 4 /MoS 2 and Pd 5 /MoS 2 were less than 0.04 and 0.01 eV, respectively. Therefore, the interactions between Pd n (n = 1-5) clusters within adjacent supercells is ignorable, and thus the coverage-dependent depolarization effects can be ignored in Pd n /MoS 2 considered in this work. The discrepancy between metal-organic interfaces [36][37][38] and Pd n /MoS 2 interface maybe explained by different interactions between adsorbates and substrate and different sizes of adsorbates, such as non-specific bonding between organic molecules and substrates versus the covalent Pd-S chemical bonds in our study, and larger diameters of organic molecules than that of metal clusters. Table 3. Bader charge analysis for the lowest energy configurations of Pd n (n = 1-5) clusters supported by the MoS 2 ML.  Table 4. Calculated work function (W), p-SBH (Φ P ), dipole moment (D i ), and variations of ionization energy (∆I) upon the adsorption of the lowest energy Pd n (n = 1-5) clusters on the MoS 2 ML.

Diffusion of Pd Clusters on an MoS2 Monolayer
In order to investigate the nucleation mechanism and diffusion properties of Pd clusters on the MoS2 ML, we analyzed the diffusion and surface mobility of Pdn (n=1-5) clusters on the MoS2 ML from the most favorable adsorption configurations. We defined the reaction rate k as the following: where = 10 is the rate pre-factor, assumed to be irrelevant to the reaction or the hopping events, and kB and T are the Boltzmann constant and temperature, respectively. The equation indicated that reaction rate k is proportional to temperature T, while k is inversely related to the activation energy barrier ∆ . In here, the activation energy barrier ∆ is computed from the total energy difference between the initial configuration and the saddle points of the minimum energy pathway between two adsorption configurations. The k value is usually used to measure the possibility of nucleation and diffusion by overcoming the energy barrier at the low Pd coverage. The energy diagrams of Pdn (n=1-5) clusters nucleated or diffused on the MoS2 ML are shown in Figure. 6. As shown in Figure 6a, the calculated activation energies were 0.12 and 0.02 eV for the on-surface diffusion of Pd monomer along the two paths of t-S→t-Mo and H→t-Mo, respectively, which indicates the diffusion of Pd monomer on the MoS2 surface show remarkably anisotropy. The activation energy barrier was much smaller than the value of 0.34eV for Pd monomer diffusion on MgO (100) via single atom hops between oxygen sites [39], implying the Pd adatom on the MoS2 surface was mobile during the in situ growth by deposition. According to Equation (4), the number of hopping events per second between two TMo sites was estimated to be 10 3 s −1 along the Mo-H-Mo path and 10 s −1 along the Mo-S-Mo path at room temperature, respectively. The results indicated that the Pd adatoms are more likely to be mobile for coarsening and growth of large clusters rather than a random dispersion during the deposition. We also found that a newly deposited Pd atom prefers

Diffusion of Pd Clusters on an MoS 2 Monolayer
In order to investigate the nucleation mechanism and diffusion properties of Pd clusters on the MoS 2 ML, we analyzed the diffusion and surface mobility of Pd n (n = 1-5) clusters on the MoS 2 ML from the most favorable adsorption configurations. We defined the reaction rate k as the following: where v 0 = 10 13 s −1 is the rate pre-factor, assumed to be irrelevant to the reaction or the hopping events, and k B and T are the Boltzmann constant and temperature, respectively. The equation indicated that reaction rate k is proportional to temperature T, while k is inversely related to the activation energy barrier ∆E a . In here, the activation energy barrier ∆E a is computed from the total energy difference between the initial configuration and the saddle points of the minimum energy pathway between two adsorption configurations. The k value is usually used to measure the possibility of nucleation and diffusion by overcoming the energy barrier at the low Pd coverage. The energy diagrams of Pd n (n = 1-5) clusters nucleated or diffused on the MoS 2 ML are shown in Figure 6. As shown in Figure 6a, the calculated activation energies were 0.12 and 0.02 eV for the on-surface diffusion of Pd monomer along the two paths of t-S→t-Mo and H→t-Mo, respectively, which indicates the diffusion of Pd monomer on the MoS 2 surface show remarkably anisotropy. The activation energy barrier was much smaller than the value of 0.34eV for Pd monomer diffusion on MgO (100) via single atom hops between oxygen sites [39], implying the Pd adatom on the MoS 2 surface was mobile during the in situ growth by deposition. According to Equation (4), the number of hopping events per second between two T Mo sites was estimated to be 10 3 s −1 along the Mo-H-Mo path and 10 s −1 along the Mo-S-Mo path at room temperature, respectively. The results indicated that the Pd adatoms are more likely to be mobile for coarsening and growth of large clusters rather than a random dispersion during the deposition. We also found that a newly deposited Pd atom prefers to bond to existing Pd adatoms located at t-Mo sites by possible diffusion, which is illustrated in Figure 6b. The energy barrier for the attachment of a Pd adatom to an existing Pd monomer to form Pd dimer is 0.32 eV, and the process is downhill by 0.48 eV. In other words, the deposited Pd adatoms are expected to bond to Pd monomer adsorbed at MoS 2 rather than adsorb at a remote site. According to Equation (4), the higher the reaction temperature is, the easier the reaction occurs. For instance, the reaction rates k for the nucleation of Pd dimer from two Pd adatoms on MoS 2 surface will increase about 140 and 485 times compared to that of room temperature (RT)under T = 500 and 600 K, respectively. The three flat trimers t-(Mo)3-123 • , t-(Mo) 3 -h, and t-(Mo) 3 -S shown in Figure 6b are easily accessible during metal deposition, which can be formed by the low-energy diffusion of Pd monomer on MoS 2 surfaces to reach a Pd dimer. As shown in Figure 6b, although the total energies of the initial states of t-(Mo)3-123 • and t-(Mo) 3 -h configurations were about 0.21 and 0.06 eV higher than that of the most stable configuration of t-(Mo) 3 -S due to the extra binding of the S1 atom, the energy barriers for transforming the flat t-(Mo)3-123 • and t-(Mo) 3 -h configurations to t-(Mo) 3 -S were 1.31 and 0.92 eV, while the reverse processes were examined to surmount the energy barriers of 1.52 and 0.98 eV, respectively. We found that the transition state from t-(Mo) 3 -h to t-(Mo) 3 -S was ∆-(Mo) 3 , which was0.96 and 0.98 eV energetically higher than that of the initial and final states. However, the identical ∆-(Mo) 3 configuration was predicted as the intermediate state with the lowest energy during the transformation between t-(Mo) 3 -h and t-(Mo) 3 -S configurations of Pt 3 clusters on MoS 2 ML as reported in Reference [14]. Such discrepancy may be due to the larger cohesive energy of Pt than that of Pd, which makes it is more likely to form islands for Pt NPs than Pd NPs.
We have considered various possible structures of palladium tetramer , which is formed by the simple extension from t-(Mo) 3 -S and t-(Mo) 3 -h via the attachment of Pd monomer to Pd 3 clusters. The computed results show three-dimensional t-(Mo) 4 -S was favored over t-(Mo) 4 -h only by 0.10 eV in total energy, both of which can be nucleated on the MoS 2 ML. It was clearly observed that transition from t-(Mo) 4 -h to t-(Mo) 4 -S should overcome the energy barrier of 0.83 eV, which is twice that of the transformation barrier of Pt 4 clusters with the identical structures on the MoS 2 ML [14]. It indicated that the diffusion of Pt 4 clusters was likely to be much more accessible compared with Pd 4 clusters on MoS 2 MLs. Similarly, the most preferable configuration can be accessed from configurations t-(Mo 4 )-h and t-(Mo 4 )-S by deposition of new Pd atoms or diffusion of Pd monomers to the nearest-neighboring T Mo site. The two pyramid-like Pd 5 clusters labeled as t-(Mo) 5 -h and t-(Mo) 5 -S are shown in Figure 6e, respectively, which were found to be stable and have a slight energy difference of about 0.03 eV.
The computed results show that the transformation of t-(Mo) 5 -h and t-(Mo) 5 -S was almost barrier less with E a about 0.13 eV.
The diffusion of Pd atoms from the topmost site of a pyramid-like structure to the MoS 2 substrate was a key factor to decide the growth mode of the Pd n cluster on the MoS 2 monolayer. Therefore, we also calculated the diffusion behaviors of Pd atoms from topmost sites of Pd 4 and Pd 5 clusters to the MoS 2 substrate. The calculated results show the topmost Pd atoms moving to the nearest-neighboring t-Mo sites of the MoS 2 substrate needed to overcome the energy barriers of 0.73 and 1.13 eV for Pd 4 /MoS 2 and Pd 5 /MoS 2 systems, respectively. The relative high energy barriers imply that the Pd atoms prefer to form a sheet-supported metal nanotemplate on MoS 2 in the initial growth stage, which is in conformity with the previous experimental study reported by Gong et al. [40] that Pd forms a uniform contact by physical vapor deposited on MoS 2 monolayers.

Conclusions
In summary, we investigated theoretically the stable configurations, electronic structures, and surface mobility of Pdn (n=1-5) clusters on MoS2 monolayers using first principles density functional theory calculations. The results demonstrate that Pd clusters can chemically adsorb on MoS2 MLs and Pd adatoms are strongly bound to the surface S atoms, which exhibit covalent bonds with significant ionic character. The geometries of Pdn cluster varies from a planar structure to a pyramidal morphology when the cluster size increases due to the relative strengths between Pdn-MoS2 and Pd-Pd interactions. Upon the deposition of Pd clusters, the band gaps of MoS2weretunable due to the hybridization between 4d electrons of Pd and 3s electrons of S. The work function was modulated from 5.01 to 4.38 eV with the increase of Pd coverage, which resulted from the charge transfer from Pd clusters to MoS2 ML.
In addition, we investigated the nucleation and diffusion properties of Pdn (n=1-5) clusters on MoS2 ML, e.g., the distant isolated Pd atoms or additional adatoms favor migrating to nearby Pdn clusters, which indicated that Pd is likely to agglomerate to metal nanotemplates on the MoS2 ML during the epitaxial stacking process. These findings may provide useful guidance to extend the potential technological applications of MoS2, including catalysts and production of metal thin films, and the fabrication of nanoelectronic devices.
Author Contributions: P.W. performed the calculation, data analysis, and wrote the manuscript; N.Y. and P.L. discussed the results and analyzed the data; and M.H. conceived the models and revised the manuscript.

Conclusions
In summary, we investigated theoretically the stable configurations, electronic structures, and surface mobility of Pd n (n = 1-5) clusters on MoS 2 monolayers using first principles density functional theory calculations. The results demonstrate that Pd clusters can chemically adsorb on MoS 2 MLs and Pd adatoms are strongly bound to the surface S atoms, which exhibit covalent bonds with significant ionic character. The geometries of Pd n cluster varies from a planar structure to a pyramidal morphology when the cluster size increases due to the relative strengths between Pd n -MoS 2 and Pd-Pd interactions. Upon the deposition of Pd clusters, the band gaps of MoS 2 weretunable due to the hybridization between 4d electrons of Pd and 3s electrons of S. The work function was modulated from 5.01 to 4.38 eV with the increase of Pd coverage, which resulted from the charge transfer from Pd clusters to MoS 2 ML.
In addition, we investigated the nucleation and diffusion properties of Pd n (n = 1-5) clusters on MoS 2 ML, e.g., the distant isolated Pd atoms or additional adatoms favor migrating to nearby Pd n clusters, which indicated that Pd is likely to agglomerate to metal nanotemplates on the MoS 2 ML during the epitaxial stacking process. These findings may provide useful guidance to extend the potential technological applications of MoS 2 , including catalysts and production of metal thin films, and the fabrication of nanoelectronic devices.
Author Contributions: P.W. performed the calculation, data analysis, and wrote the manuscript; N.Y. and P.L. discussed the results and analyzed the data; and M.H. conceived the models and revised the manuscript.