Electronic Properties of Triangle Molybdenum Disulfide (MoS2) Clusters with Different Sizes and Edges

The electronic structures and transition properties of three types of triangle MoS2 clusters, A (Mo edge passivated with two S atoms), B (Mo edge passivated with one S atom), and C (S edge) have been explored using quantum chemistry methods. The highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap of B and C is larger than that of A, due to the absence of the dangling of edge S atoms. The frontier orbitals (FMOs) of A can be divided into two categories, edge states from S3p at the edge and hybrid states of Mo4d and S3p covering the whole cluster. Due to edge/corner states appearing in the FMOs of triangle MoS2 clusters, their absorption spectra show unique characteristics along with the edge structure and size.


Introduction
Since the successful isolation of graphene [1,2], atomic layer-thick two-dimensional (2D) nanomaterials have attracted a great deal of attention due to their excellent mechanical flexibility and optical transparency, as well as their ultrahigh specific surface, which are related to their strong in-plane covalent bond and atomic thickness [3][4][5][6][7]. Beyond graphene, single-layer transition-metal dichalcogenides (TMDs) have been receiving increasing interest. For example, the structural and physical properties of the MoS 2 monolayer and bulk have been extensively studied both theoretically and experimentally. The monolayer of MoS 2 consists of a layer of Mo atoms sandwiched between two layers of S atoms, forming a trilayer. The absence of inversion symmetry and dominant d-electron interactions of the heavy transition metal atom Mo, endow the monolayer (MoS 2 ) with intriguing physical properties that are not found in sp-bonded nanomaterials [8][9][10][11].
In recent years, an increasing amount of effort has been devoted to 2D materials with ultrasmall sizes, due to increasing demand for miniaturizing photonic and optoelectronic devices. For MoS 2 , from the three-dimensional (3D) bulk structure to the 2D monolayer, the band gap transforms from an indirect band gap (∼1.2 eV) to a direct band gap (∼1.8 eV, in the visible frequency range) [12,13]. Compared with their 2D and one dimensional (1D) counterparts, zero dimensional (0D) MoS 2 clusters possess tunable energy levels, more active edges, and larger surface-area-to-volume ratios, which give them fascinating properties. This makes them promising candidates for application in fields such as optoelectronics [14,15], electrochemical technology [16,17], biology [18], catalysis [19] and so forth [20][21][22]. Jaramillo et al. [23] pointed out that 2D TMDs are hydrogen evolution reaction (HER) active because of their highly active edges, which makes them potential candidates for electrocatalytic hydrogen evolution. Yin et al. [24] pointed out that a strong second-harmonic generation (SHG) can be observed at the edges and corners of MoS 2 clusters, implying the important role that edges and corner states play in determining the properties of the 0D structures. However, the detailed transition natures are ambiguous. In order to shed light on the essence of the various applications and obtain full use of the MoS 2 clusters, it is crucial to gain a comprehensive understanding of the electronic structures and their transition properties.
It is well known that when the physical size of the material is comparable to or smaller than the Bohr radius, the excitons are confined in all three dimensions, so there exists a 3D quantum confinement effect. Superimposed on the intrinsic size-dependent electronic structure, one thus has the effect of edges, corners, atomic vacancies and so forth, all these are likely to induce additional local effects. As a result, the electronic properties become increasingly sensitive not only to sizes, but to the shapes, edge atomic structures, and compositions [25][26][27]. Despite the breakthroughs in preparation of MoS 2 clusters over the years, mainly including top-down [28][29][30][31][32][33] and bottom-up methods [34][35][36], a cost-effective yet efficient technique for the high yield production of MoS 2 clusters with desirable sizes remains a challenge. Consequently, it is still difficult to provide a specific illustration about the properties of MoS 2 clusters experimentally. Aiming to obtain the whole picture in relation to MoS 2 clusters and to clarify the relationships between structures and properties, the density-of-states (DOS), frontier molecular orbitals (FMOs), electronic absorption spectra, and electron-hole characteristics of a series of triangular MoS 2 clusters with different sizes and edges will be explored using quantum chemistry methods in the present paper. This will be of great significance not only in fundamental physics exploration but also in device applications.

Models and Computational Details
Based on different edge structures, there are mainly three types of triangle MoS 2 clusters, as shown in Figure 1. A and B represent the Mo-terminated (commonly referred as Mo-edge) triangle MoS 2 clusters, while C is the S-terminated cluster (commonly referred as S-edge). Considering that a bare Mo-edge is not stable, it is often passivated by one or two S atoms per edge-Mo atom. In A, each edge-Mo atom is passivated with two S atoms forming an S-dimer normal to the basal plane, usually called a Mo edge, with 100% S coverage.
In the case of B, two adjacent edge-Mo atoms share one S atom forming an S-monomer parallel to the basal plane, usually called a Mo edge, with 50% S coverage. Consequently, the S atoms of C dimerize along the direction normal to the basal plane, often called a S edge, with 100% coverage. By changing the number of the edge-Mo atoms n (n = 3, 4, 5, and 6) in A, B, and C, a series of different triangle MoS 2 clusters with different sizes and edges could be gained. In the following discussions, A refers to four triangle MoS 2 clusters with the same edges but different sizes, including 3A, 4A, 5A, and 6A, as B and C.
The density functional theory (DFT) based on Becke's three-parameter hybrid exchange combined with the Lee-Yang-Parr correlation (B3LYP) [37,38] and the LANL2DZ basis set were adopted to optimize the geometries of the triangular MoS 2 clusters. With both the merits of B3LYP and long-range corrected properties, CAM-B3LYP is able to predict molecular charge-transfer spectra properly due to the improved description of the longrange exchange interactions [39][40][41][42]. It is employed to evaluate the electron excitations with the LANL2DZ basis set in the present work.
The DFT calculations were performed using the Gaussian 09 program [43]. The data of DOS, electronic absorption spectra, and electron-hole distributions were obtained with the Multiwfn package [44].

Results and Discussion
In order to indicate the stability of A, B, and C, the formation energy was calculated according to the formula: , and E (S) denote the energy of the cluster having m Mo atoms and n S atoms, the energy of a single Mo atom, and the energy of a single S atom, respectively. The calculated E formation values of A, B, and C are listed in Tables 1-3, respectively. The negative E formation values imply that the clusters are stable. The E formation decrease with increasing the sizes of the cluster, suggesting that the larger the cluster, the more energy is released.
For the three different classes of clusters, their highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies and their energy gaps, as well as the orbital compositions of HOMO and LUMO are listed in Tables 1-3, respectively. The DOS is shown in Figure 2.
For these ultrasmall MoS 2 clusters, the band gap does not decrease monotonically with size as is the case for graphite flakes, which might be attributed the deformation of structures due to large the ratio of number of edge atoms to core atoms in ultrasmall clusters. The energy of HOMO (E H ) in 3A is −5.06 eV, while that of LUMO (E L ) is −6.84 eV, resulting in a 1.78 eV energy gap (E gap ). The E gap value of 4A, 5A, and 6A is 0.70, 0.66, and 0.73 eV, respectively, far smaller than that of 3A. For the Mo-terminated triangle MoS 2 clusters with 100% S coverage, some FMOs contributed from S 3p at the edge exhibit evident edge states, and the other FMOs exhibit hybrid states of Mo 4d and S 3p whose charge distribution covers the whole cluster. By comparing the electronic structures of three classes of clusters, it can be seen that the energy gap of the ultrasmall MoS 2 clusters is dependent on the edge structure, which is similar to graphite flake. For Mo-terminated triangle MoS 2 clusters with 50% S coverage (B) and S-terminated triangle MoS 2 clusters (C), their S atoms at the edge of the cluster are shared by two adjacent Mo atoms. In contrast to the A system, the absence of dangling edge S atoms in the two class clusters increases their HOMO-LUMO gap and evident edge/corner states can be observed in the FMOs of these clusters. For B, all the FMOs comes from the hybridization between Mo 4d and S 3p . While the occupied FMOs mainly comes from the S 3p , and the unoccupied FMOs from the hybridization between Mo 4d and S 3p in the case of C. For these ultrasmall MoS2 clusters, the band gap does not decrease monotonically with size as is the case for graphite flakes, which might be attributed the deformation of structures due to large the ratio of number of edge atoms to core atoms in ultrasmall clusters. The energy of HOMO (EH) in 3A is −5.06 eV, while that of LUMO (EL) is −6.84 eV, resulting in a 1.78 eV energy gap (Egap). The Egap value of 4A, 5A, and 6A is 0.70, 0.66, and 0.73 eV, respectively, far smaller than that of 3A. For the Mo-terminated triangle MoS2 clusters with 100% S coverage, some FMOs contributed from S3p at the edge exhibit evident edge states, and the other FMOs exhibit hybrid states of Mo4d and S3p whose charge distribution covers the whole cluster. By comparing the electronic structures of three classes of clusters, it can be seen that the energy gap of the ultrasmall MoS2 clusters is dependent on the edge structure, which is similar to graphite flake. For Mo-terminated triangle MoS2 clusters with 50% S coverage (B) and S-terminated triangle MoS2 clusters (C), their S atoms at the edge of the cluster are shared by two adjacent Mo atoms. In contrast to the A system, the absence of dangling edge S atoms in the two class clusters increases their HOMO-LUMO gap and evident edge/corner states can be observed in the FMOs of these clusters. For B, all the FMOs comes from the hybridization between Mo4d and S3p. While the occupied FMOs mainly comes from the S3p, and the unoccupied FMOs from the hybridization between Mo4d and S3p in the case of C.
The electronic absorption spectra of A, B, and C and their corresponding electronhole distributions where the process of single-electron excitation is described as "an electron goes to the electron from the hole" are given in Figures 3-6, respectively. Moreover, the percentage of Mo4d and S3p in the electron and hole are provided in Tables 4-6, respectively. The maximum absorption shows a red shift along with increasing size of the clusters in the A, B and C systems. For 3A, 4A, 5A, and 6A, the maximum absorption is ~623.61, ~591.50, ~670.54, and 796.87 nm, respectively. From Table 4, the percentage of S3p is larger than that of Mo4d in both the electron and hole in 3A, Mo4d takes the larger proportion in the electron and the hole in 4A and 5A. The S3p and Mo4d make almost the same The electronic absorption spectra of A, B, and C and their corresponding electron-hole distributions where the process of single-electron excitation is described as "an electron goes to the electron from the hole" are given in Figures 3-6, respectively. Moreover, the percentage of Mo 4d and S 3p in the electron and hole are provided in Tables 4-6, respectively. The maximum absorption shows a red shift along with increasing size of the clusters in the A, B and C systems. For 3A, 4A, 5A, and 6A, the maximum absorption is~623.61,~591.50, 670.54, and 796.87 nm, respectively. From Table 4, the percentage of S 3p is larger than that of Mo 4d in both the electron and hole in 3A, Mo 4d takes the larger proportion in the electron and the hole in 4A and 5A. The S 3p and Mo 4d make almost the same contribution to the electron and the hole in 6A. Combined with the data in Figure 4, there are two types of electron transitions: one is a d-d transition of the Mo atoms, and the other occurs at the S atoms along the edges, which is associated with the edge states.     Table 4. Transition between the ground state and the lowest excited state S 0 →S 1 , transition between the ground state and the state with the largest oscillator strength S 0 →S n (normally associate with the intense absorption in the electronic absorption spectrum, n is usually different in different clusters), and the percentage of Mo 4d and S 3p in electron and hole of 3A, 4A, 5A, and 6A. The maximum absorption is~422.32,~609.91,~656.23, and 678.05 nm for 3B, 4B, 5B, and 6B, respectively. The electrons and holes distribute along the edges/corners. The percentage of Mo 4d in the electron is larger than that of S 3p , while the percentage of S 3p in the hole is larger than that of Mo 4d , leaving S atoms with the feature of hole and Mo atoms with the feature of the electron. In other words, the electron prefers to transfer from the S 3p to the connected Mo 4d along the edges/corners of B. The maximum absorption is 502.21,~654.45,~633.81, and 845.93 nm for 3C, 4C, 5C, and 6C, respectively. The electron and hole distribute at the corners with the S atoms at the top vertex acting as hole and the Mo atoms neighboring acting as the electron (see Table 6 and Figure 6). Overall, the S 0 →S n transitions corresponding to the maximum absorption of the Moterminated triangle MoS 2 clusters with 100% S coverage A come from two aspects, the d-d transitions of the Mo atom and transitions of S 3p along the edge. The S 0 →S n transitions of B and C occur at the edges/corners, with an electron transferring from the S atoms to the neighboring Mo atoms. In other words, the S atoms act as the hole and the adjacent Mo atoms act as the electron in the case of the clusters with no dangling of edge S atoms in them. The S 0 →S 1 transition directly leads to the lowest excited state and is always the excited state for luminescence. For the S 0 →S 1 transition of A, the electron and hole mainly distribute throughout the whole triangular clusters; this can be observed faintly at the S atoms along the edges (see Figure 4). Referred to the data in Table 4, the percentage of Mo 4d in electron and hole not only takes a larger proportion but also has nearly the same values, which implies obvious d-d transitions of the Mo atoms. The S 0 →S 1 transitions of B also occur at the edges/corners, as shown in Figure 5. By referring to the data in Table 5, both the Mo and S atoms possess the distribution of electrons and holes, which ascribes the S 0 →S 1 from local transition. For the S 0 →S 1 transitions of C, the percentage of Mo 4d in the electron is larger than that in the hole, while the percentage of S 3p in the hole is larger than that in the electron, implying significant electron transfer from the S atoms to the neighboring Mo atoms along the edges (see Figure 6).

Conclusions
The electronic properties of three types of triangle MoS 2 clusters, A (Mo-edge passivated with two S atoms), B (Mo-edge passivated with one S atom), and C (S-edge) have been explored using quantum chemistry methods in the present paper. The DOS appears to have different features in A, B, and C. For A, the MOs can be divided into two types: the edge state from S 3p along the edges, the hybrid state from Mo 4d and S 3p covering the whole cluster. Evident edge/corner states appear in the FMOs of B and C. The hybridization of Mo 4d and S 3p in B generate the occupied and unoccupied MOs. The occupied MOs mainly come from S 3p , and the unoccupied MOs from the hybridization of Mo 4d and S 3p in C.
For the electron excitation processes of A, B, and C, the absorption peaks show a red shift along with increasing the size of the clusters. Electron-hole analysis indicated that the S 0 →S 1 transitions appear to have different characteristics compared with the S 0 →S n transitions (associated with the intense absorption in the electronic absorption spectrum) in A, B, and C. In A, the S 0 →S 1 transitions mainly stem from the d-d transitions of the Mo atoms, while the S 0 →S n transitions come from the d-d transitions of the Mo atom or transitions of the S 3p along the edges. Both the S 0 →S 1 and S 0 →S n transitions of B occur at the edges/corners, with the local S 0 →S 1 transitions originating from Mo 4d and S 3p , but charge transfer S 0 →S n transitions caused by the electron transferring from S 3p to the connected Mo 4d . In C, the S 0 →S 1 transitions mainly occur along the edge with the S atoms acting as hole and the adjacent Mo atoms as electron, while the S 0 →S n transitions mainly occur at the corners, where the two S atoms at the vertex acts as the hole and the adjacent Mo atoms act as the electron.