Magic Clusters of MoS2 by Edge S2 Inter-Dimer Spacing Modulation

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials 2

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Magic Clusters of MoS by Edge S Inter-Dimer Spacing Modulation Junga Ryou, and Yong-Sung Kim J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00689 • Publication Date (Web): 05 May 2018 Downloaded from http://pubs.acs.org on May 6, 2018

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The Journal of Physical Chemistry Letters

Magic Clusters of MoS2 by Edge S2 Inter-Dimer Spacing Modulation Junga Ryou† and Yong-Sung Kim∗,†,‡ †Korea Research Institute of Standards and Science, Daejeon 34113, Korea ‡Department of Nano Science, University of Science and Technology, Daejeon 34113, Korea E-mail: [email protected]

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Abstract Edge atomic and electronic structures of S-saturated Mo-edge triangular MoS2 nanoclusters are investigated using density-functional theory calculations. The edge electrons described by the S2 -px px π ∗ (S2 -Πx ) and Mo-dxy orbitals are found to interplay to pin the S2 -Πx Fermi wavenumber at kF =2/5 as the nanocluster size increases, and correspondingly the ×5 Peierls edge S2 inter-dimer spacing modulation is induced. For the particular sizes of N =5n-2 and 5n, where N is the number of Mo atoms at one edge representing the nanocluster size and n is a positive integer, the effective ×5 inter-dimer spacing modulation stabilizes the nanoclusters, which are identified here to be the magic S-saturated Mo-edge triangular MoS2 nanoclusters. With the S2 -Πx Peierls gap, the MoS2 nanoclusters become far-edge S2 -Πx semiconducting and sub-edge Mo-dxy metallic as N →∞.

Graphical TOC Entry Magic Clusters of MoS2

N=3

N=5

N=15

N=8

N=13

N=10

2


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Molybdenite (MoS2 ) has been widely used as a hydro-desulfurization reaction catalysis 1 and recently attracted great attention for application to hydrogen evolution reaction catalysis. 2–6 The edges of MoS2 have been known to play the central role in the catalytic activity 2–6 and their detailed atomic and electronic structures have been intensively studied. 7–21 The edges are manifested in nanoclusters. Chemical exfoliation of a bulk sample, 4 direct growth of a sub-monolayer, 2,3,5–9 growth of a sub-monolayer on a patterned substrate, 22,23 and direct lithography of a monolayer 24 have been used to fabricate the nanoclusters, where the shapes are less or more controllable. The direct chemical vapor deposition growth of MoS2 in typical S-rich condition yields as precursors S-saturated Mo-edge MoS2 triangular nanoclusters. 7–9 The MoS2 nanoclusters have also been used in field-effect transistors, and the edge electronic states have been found to contribute significantly. 25 Among the various possible edges of MoS2 , such as the {10¯10} Mo-terminated (Moedge) [Fig. 1(a)] and {¯1010} S-terminated (S-edge) [Fig. 1(b)] zigzag edges, the Mo-edge with S2 -addimers (S2 -Mo-edge) [Fig. 1(c) and (e)] is the particularly important, since it is the predominant 7 and most stable 8,10,13,14 in S-rich conditions, and with 8–14 or without 17 edge S-vacancies where the catalytic reactions take place. The atomic structure of the S2 Mo-edge MoS2 triangular nanocluster is shown in Fig. 1(c) and (e), for the size of N =5, representatively, where the size N is defined as the number of Mo atoms at each edge, as indicated in Fig. 1(c). With the two S adatoms per Mo at one edge [Fig. 1(d)], all the edge Mo atoms are fully saturated by S, forming the six-fold coordination as in bulk MoS2 , and the two S adatoms are dimerized along the vertical (z) direction, as seen in Fig. 1(e). 7–21 An interesting feature is that the edge S2 dimers are not equally spaced laterally along the edge (x) directions. In scanning tunneling microscopy (STM) 7 and density-functional theory (DFT) 13–15 studies, the ×2 pairing has been suggested. For nanoribbons, on the other hand, the ×1 equally spaced S2 dimers have been supposed in most DFT studies. 10–12,16–21 The S2 -Mo-edge has been known to be metallic 16–21 and suggested to be catalytically active by itself without S-vacancies, 17 based on the studies on MoS2 nanoribbons. The S2 -

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(a)

^ͳͲͳത Ͳ`

(d)

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(c)

Mo S (bulk) S (edge)

N

x

(e) z x

(f)

¯ and (b) S-edge {¯1010} Figure 1: As-cleavage atomic structures of the (a) Mo-edge {1010} triangular nanoclusters. (c) Top and [(d),(e)] side views of the N =5 S2 -Mo-edge MoS2 triangular nanocluster (d) before and (e) after edge S2 dimerization. (f) The measured size distribution of MoS2 triangular nanoclusters in STM (gray), 7 and DFT edge energies (red).

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Mo-edge triangular nanoclusters are expected to have different electronic structures, due to the edge S2 inter-dimer spacing modulations as well as the finite sizes N , 13–15 and the different stoichiometry. Meanwhile, the measured size distribution of the nanoclusters 7 has shown that there are the particularly abundant sizes [Fig. 1(f)], of which the causes remain still puzzling. In this Letters, we show that the edge S2 dimers in the S2 -Mo-edge MoS2 triangular nanoclusters prefer ×5 lateral spacing modulation. It is a consequence of the Peierls instability of the edge S2 -px px π ∗ (S2 -Πx ) electrons interacting with the Mo-dxy sub-edge electrons. The preference of the ×5 modulation affects the edge energies of the finite-size nanoclusters, and the especially stable sizes are found to be N =5n-2 and 5n, where n is a positive integer. The S2 -Mo-edge becomes S2 -Πx semiconducting and sub-edge Mo-dxy metallic as N →∞. The obtained stable sizes and the edge modulation structures of the nanoclusters are found to be in good agreement with the experiments. The edge energies (Λ) of the S2 -Mo-edge MoS2 triangular nanoclusters are calculated for √ N =3-15 in DFT, 26–28 and plotted as a function of the nanocluster area, A= 3{(N +2)a}2 /4 (see the Supporting Information for the area calculations), as shown in Fig. 1(f), where a is the lattice constant of monolayer MoS2 . We fully relax the atomic structures, including the edge S2 inter-dimer spacings. We find that the N =3, 5, 8, 10, 13, and 15 sizes are particularly small in edge energy, and they seem to have ×5 periodicity, that is, the stable sizes are N =5n-2 and 5n, where n is a positive integer. The stable sizes are found to agree with the peaks in the measured size distribution of MoS2 triangular nanoclusters, 7 as shown in Fig. 1(f). Let us first suppose the ionic limit. In bulk MoS2 , each Mo atom donates four electrons resulting in the Mo4+ ionic state and each S atom accepts two electrons with fully ionized into S2− . In this case, the valence states are composed of one Mo-dz2 orbital state and six S-p orbital states per formula unit and the conduction states are composed of four Mo-d orbital states per a Mo atom. In the S2 -Mo-edge MoS2 triangular nanocluster of size N , the number

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of Mo atoms is N (N +1)/2 and the number of S atoms is N (N +1)+4N . Then, the number of excess S atoms is 4N . In this case, the 4N S-p empty orbital states are distributed over the 6N edge S atoms. Through the vertical dimerization of the edge S atoms, the 3N pz pz σ ∗ orbital states become obviously empty with the high energy levels, and then the remaining N S-p empty orbital states belong to the next highest 3N px px π ∗ orbital states. The Fermi level may cross the px px π ∗ orbital states, and hereafter, we denote them by Πx . In average, (4/3)−

each edge S2 dimer is ionized into S2

rather than S2− 2 with the 2/3 Πx holes.

The S2 -Πx orbitals are directional along the edges and arranged in one dimension at each edge, by which strong lateral hybridization is expected (see the Supporting Information for the S2 -Πx orbital structures). We consider a zigzag MoS2 nanoribbon model, in which the S2 dimers at the S2 -Mo-edge are equally spaced and 4/3 electrons per unit length are doped to match the stoichiometry to the nanoclusters (see the Supporting Information for the nanoribbon model details). The Πx (k) band calculated in DFT is shown in Fig. 2(c), where k is the wavenumber along the edges in unit of π/a. Since the S2 -Πx orbitals are antisymmetric, the Πx (0) is the higher energy anti-bonding and the Πx (1) is the lower energy bonding state. The band width is about 3.3 eV. In the ionic limit, the Πx (k) is 2/3 partially filled as aforementioned, and then the Fermi level crosses the Πx (k) at k=1/3 [the red dashed lines in Fig. 2(c)]. We denote this Fermi level by EFI , and the S2 -Πx Fermi wavenumber, at which the EFI crosses the Πx (k) band, by kFI . The densities of S2 -Πx states (projected to the edge S2 dimers) for the N =3-15 nanoclusters and the nanoribbon model with the equally spaced edge S2 dimers are shown in Fig. 2(a). With increasing N , the highest and lowest S2 -Πx levels of the nanoclusters approach the Πx (0) and Πx (1) levels, respectively. By the C3 symmetry of the triangular nanoclusters, the three edge states split into a1 singlet and e doublet states. The energy splitting is about 0.2 eV in DFT for N =3 and decreases with increasing the size N . For each N , there are found to be N a1 -e triplets, and thus the S2 -Πx states of the nanoclusters can be considered as the selected k states from the Πx (k) band of the nanoribbon model, for the finite size.

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Figure 2: Electronic densities of [(a),(e)] S2 -Πx and [(b),(f)] Mo-dxy states of the N =3-15 S2 -Mo-edge MoS2 nanoclusters and the nanoribbon model with [(a),(b)] equally spaced edge S2 dimers and [(e),(f)] edge S2 inter-dimer spacing modulation. The (c) Πx (k) (red) and (d) dxy (k) (green) band structures of the nanoribbon model. The EFI and kFI are indicated by the red dashed lines, and the EF and kF are by the green dashed lines. The gray shaded regions are monolayer MoS2 bands. In (a), the filled square symbols indicate the e state (the tall peaks), the circle symbols the a1 states (the small peaks). 7



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Table 1: Sizes (N ), amounts (2t) of the Πx -dxy electron transfer, effective Fermi wavenumbers (kF∗ ) from the finite-size nanoclusters, HOMO and LUMO orbital characters, and HOMO-LUMO gaps (Eg ) of the S2 -Mo-edge MoS2 triangular nanoclusters. N N /3N 3 3/9 4 4/12 5 5/15 6 6/18 7 7/21 8 8/24 9 9/27 10 10/30 11 11/33 12 12/36 13 13/39 14 14/42 15 15/45

t (N +t)/3N 0 3/9 2 6/12 1 6/15 0 6/18 2 9/21 1 9/24 0 9/27 2 12/30 1 12/33 3 15/36 2 15/39 1 15/42 3 18/45

kF∗ (π/a) HOMO/LUMO 1/3 Πx /dxy 1/2 dxy /Πx 2/5 dxy 1/3 Πx /dxy 3/7 dxy /Πx 3/8 dxy 1/3 Πx /dxy 2/5 dxy /dxy 4/11 dxy 5/12 dxy 5/13 dxy /dxy 5/14 dxy 2/5 dxy

Eg (eV) 0.887 0.142 0 0.142 0.182 0 0.059 0.160 0 0 0.114 0 0

So far, we suppose the Mo4+ ionized state, in which only the Mo-dz2 orbital state is fully occupied among the five Mo-d orbital states, as in bulk MoS2 . However, at the S2 Mo-edge, there is found to be Mo-dxy orbital state contribution. The calculated densities of Mo-dxy states (projected to the edge Mo atoms) for the N =3-15 triangular nanoclusters and the nanoribbon model are shown in Fig. 2(b). The Mo-dxy band of the nanoribbon model is shown in Fig. 2(d). In addition to the Mo-dz2 , the Mo-dxy states are found to be occupied partially by the electrons from the higher energy S2 -Πx states, and then the actual Fermi level (EF ) becomes lower than the EFI , as indicated by the green and red dashed lines, respectively, in Fig. 2. We call this process Πx -dxy electron transfer, representing the electron back-donation from the anion far-edge to the cation sub-edge. The sub-edge Mo atoms are then less ionized than 4+; the ionization states are {4-2t/3(N -1)}+ for sub-edge Mo and (4/3-2t/3N )- for edge S2 in average, where 2t is the amount of the Πx -dxy electron transfer per nanocluster. In Table 1, for N =3-15, the numbers of empty (N ) and total (3N ) Πx orbital states in the format of N /3N are listed without the Πx -dxy electron transfer. Unless N is a multiple of 8


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3, the numbers of empty (N ) and filled (2N ) states are not multiples of 3. The calculated t’s for N =3-15 are listed in Table 1 (see the Supporting Information for the t calculations), and with the Πx -dxy electron transfer, the numbers of empty (N +t) and filled (2N -t) Πx orbital states are found to be all multiples of 3 [see the (N +t)/(3N ) column in Table 1], which implies that there is strong tendency to preserve the triangular symmetry. We would like to find the effective Fermi wavenumbers kF∗ for the N =3-15 nanoclusters, which correspond to the Fermi wavenumber kF in the nanoribbon model, taking the Πx -dxy electron transfer into account. From the finite-size nanoclusters, the kF∗ can be obtained as the ratio of the number (N +t) of empty Πx orbital states to the total number (3N ) of Πx orbital states, as listed in the (N +t)/3N column in Table 1 (see the Supporting Information for the kF∗ calculations). The kF∗ ’s in the reduced fractional form are listed in the kF∗ column in Table 1, and interestingly the kF∗ converges to 2/5 with increasing the size N (see the Supporting Information for the plot of kF∗ with respect to N ).

(a)

(b)

E-EF (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(c)

Πx gap

EF

(d) ´1 (E = 0.00 eV/a)

3.18 3.18 3.18 3.18 3.18 3.18

(e) ´5 (E = -0.02 eV/a)

G

kF=2/5

X

G

X1/5

G

X1/5

3.57 2.89 3.28 3.28 2.89 3.57

Figure 3: Calculated Πx (k) (red) and dxy (k) (green) band structures for the MoS2 nanoribbon model in the (a) ×1, (b) ×5 unrelaxed (band folding), and (c) ×5 relaxed supercell. The grey shaded regions are monolayer MoS2 bands. The Fermi level (EF ) and Πx Fermi wavenumber (kF =2/5) are indicated by the green dashed lines. The energy difference and inter-dimer distances (in ˚ A) are shown in the (d) ×1 and (e) relaxed ×5 edge atomic structures.

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For the MoS2 nanoribbon model, the calculated S2 -Πx and Mo-dxy band structures are shown together in Fig. 3(a)-(b). With keeping the equal spacing between the edge S2 dimers, the calculated ×1 band structure [Fig. 3(a)] shows that the S2 -Πx Fermi wavenumber considering the Πx -dxy electron transfer is located at kF =2/5. The ×5 folded band structure is shown in Fig. 3(b). With allowing relaxation of the edge S2 inter-dimer spacing, in the ×5 periodic supercell, the band structure is shown in Fig. 3(c), and the apparent Πx bandgap (0.64 eV) emerges. The obtained inter-dimer spacings are 3.57, 2.89, 3.28, 3.28, and 2.89 ˚ A, as shown in Fig. 3(e), while the equal spacing in ×1 is 3.18 ˚ A [Fig. 3(d)]. The total energy of the ×5 reconstructed edge is 0.02 eV/a smaller than that of the ×1 edge. The magic sizes of S2 -Mo-edge MoS2 triangular nanoclusters (N =5n-2 and 5n) shown in Fig. 1(f) can be explained by the ×5 S2 inter-dimer spacing modulation. The effective Fermi wavenumber, kF∗ , prefers to locate at 2/5 with considering the Πx -dxy electron transfer. By the ×5 Peierls instability, the inter-dimer spacing modulation gains energy with generating a finite Πx gap, which is critical when kF∗ is n/5. The sizes of N =5n are the exactly the cases as shown in Table 1, and the N =5n-2 have the kF∗ very close to 2/5, making the N =5n-2 the secondary stable sizes. The deviation of kF∗ from 2/5 is found to correlate with the edge energy Λ (see the Supporting Information for details). The denominator of the reduced fractional form of kF∗ becomes the minimum periodicity of the S2 inter-dimer spacing modulation. For N (kF∗ ) = 6 (1/3), 7 (3/7), and 8 (3/8), the periodicities are 3, 7, and 8, respectively, as shown in Fig. 4(a) (see the Supporting Information for details). We would like to describe the edge lateral S2 inter-dimer spacing modulation structures in the triangular nanoclusters. The atomic structures and the Πx charge densities of the edge S2 dimers for the N =6, 7 and 8, representatively, are shown in Fig. 4(a). The lateral modulation structure is not found to be as simple as the ×2 pairing, contrary to the previously known. 7,13–15 In order to understand the lateral modulation structure, we adopt the bond order (ρi ) concept in the molecular orbital theory. In Fig. 4(a), we plot the calculated Πx orbitals schematically, and for each adjacent S2 dimer pair (i) and for each Πx orbital state

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(a)

N=6

2

N=7

2

0

2

N=8

2 3

1

2

2

1

3 3

2

1

2

(b) N=6

N=7

N=8

N=12

(c) N=6

N=7

N=8

N=12

1

2

3

Figure 4: (a) Schematically illustrated Πx molecular orbitals of the S2 -Mo-edge MoS2 triangular nanoclusters of N =6, 7, and 8. In each panel, from the bottom to the top, the energy level increases, and the occupied states are in the green dashed line box. The filled and empty circles represent the Πx orbitals with different parities. The gray circles represent nodes of the Πx orbital chains. For all the adjacent S2 dimer pair, the bonding, antibonding, and nonbonding are indicated by the blue solid, red dashed, and gray dashed lines, respectively. The calculated bond orders ρi are shown by the red numbers. At the top in each panel, the DFT charge density of the occupied states is shown for one edge of the nanocluster. The minimum periodicity in the dimer modulation structure is indicated by the rectangles. (b) Calculated and (c) experimental 7 (reprinted by permission from Springer Nature) STM images of the S2 -Mo-edge MoS2 triangular nanoclusters of N =6, 7, 8, and 12 . The white arrows indicate protrusions in the STM images at the edges.

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(j), the bonding, antibonding, and nonbonding are assigned by the bond characters ρij of 1, -1, and 0, respectively, and indicated by the blue solid, red dashed, and gray dashed lines in Fig. 4(a). The sum of the bond characters over the occupied states [the green dashed box in Fig. 4(a)] is the bond order: ρi =Σoccupied ρij and indicated by the red numbers in j Fig. 4(a). The lower bond order, the weaker inter-dimer bonding and the larger inter-dimer spacing. The simulated STM images are shown in Fig. 4(b) for N =6, 7, 8, and 12 with the laterally modulated S2 dimers. 29 The protrusions at the edges [indicated by the arrows in Fig. 4] indicate larger inter-dimer spacings, and agree with the measured 7 experimental STM images [Fig. 4(c)]. The bond orders, inter-dimer spacings and simulated STM images for all the N =3-15 are given in the Supporting Information. We find that the S2 -Mo-edge MoS2 triangular nanoclusters of the sizes N =5, 8, 11, 12, 14, and 15 have metallic property. They are sub-edge Mo-dxy metallic, where the edge S2 has the apparent Πx gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Thus, the main edge electronic transport channel is the Mo-dxy . As N →∞, we expect they tend to be Mo-dxy metallic, according to the band calculations [Fig. 3(c)]. In experimental STM images, the sub-edge area of the triangular nanoclusters is typically brighter than the far-edge area [see Fig. 4(c)]. This seems to be due to the Mo-dxy metallic and S2 -Πx semiconducting characters. Some small S2 -Mo-edge MoS2 nanoclusters (N =3, 4, 6, 7, 9, 10, and 13) are found to have semiconducting properties (see Table 1), and the HOMO and LUMO characters are either the Mo-dxy or S2 -Πx , depending on the sizes. However, the HOMO-LUMO gaps (Eg ) are rather small (∼0.1 eV) in DFT, except only for the smallest size of N =3 (∼0.9 eV). The electronic densities of S2 -Πx and Mo-dxy states for the N =3-15 nanoclusters and the nanoribbon model with including the edge S2 inter-dimer spacing modulation are plotted in Fig. 2(e) and (f), showing the Peierls S2 -Πx gaps and the HOMO and LUMO orbital characters near the EF (the green dashed lines). In conclusion, the edge electronic states of the S2 -Mo-edge MoS2 triangular nanoclusters

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are described by the S2 -Πx and sub-edge Mo-dxy orbitals. With the Πx -dxy electron transfer, the Πx Fermi wavenumber prefers to pin at kF =2/5, and the ×5 lateral Peierls modulation of the edge S2 dimers is to be induced. The ×5 modulation causes the stability variation in sizes, and the obtained magic sizes of N =5n-2 and 5n with the effective ×5 modulation agree with the measured abundant MoS2 nanoclusters. The details of edge S2 inter-dimer spacing modulation structures are unveiled. Computational Methods. We perform density-functional theory (DFT) calculations, as implemented in the Vienna ab initio simulation package (VASP). 26 The ions are represented by projector-augmented wave (PAW) pseudopotentials 27 and generalized gradient approximation (PBE) 28 is employed to describe the exchange-correlation functional. The plane-wave basis set with the energy cutoff of 350 eV is employed to describe electronic wave functions. The Γ point for the Brillouin-zone integration is used for structural optimizations and total energy calculations. The total energy is converged within 10−5 eV. The calculated hexagonal lattice constant (a) of monolayer MoS2 is 3.18 ˚ A, close to the experimental value of 3.16 ˚ A. The atomic positions of all sizes of the nanoclusters are relaxed within residual forces smaller than 0.02 eV/˚ A. The edge energies (Λ) of the S2 -Mo-edge MoS2 triangular nanoclusters are defined as: Λ = Et − (NMo µMo + NS µS )/3N,

(1)

where Et , NMo , NS , µMo , and µS are the DFT total energy of the nanocluster, the numbers of Mo and S atoms, and the Mo and S chemical potentials, respectively. The total energy of the S orthorhombic crystal per an atom (µS,max ) is chosen for the µS , to represent the S-rich limit condition, and the µMo is obtained from the relation of µMoS2 =µMo +2µS , where µMoS2 is the total energy of the pristine monolayer MoS2 per a formula unit. The calculated edge energies of the armchair and zigzag edges as a function of µS -µS,max are given in the Supporting Information.

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The constant-current STM images are simulated with the Tersoff-Hamann scheme, 29 along with the use of self-consistent Kohn-Sham eigenvalues and wavefunctions. The tunneling current (I) is proportional to the energy-integrated local density of states:

I(r, ±V ) ∝

∑∫ nk

EF ±V

EF

|Ψnk (r)|2 δ(E − Enk )dE,

(2)

where +V and -V represent the sample bias voltages for empty-state and filled-state measurements, respectively.

Acknowledgement This work was supported by the National Research Foundation (NRF) of Korea (Grant No.2017R1A5A1014862, SRC program: vdWMRC center). We acknowledge the use of the computing facilities through the Strategic Supercomputing Support Program from Korea Institute of Science and Technology Information (No. KSC-2016-C2-0061).

Supporting Information Available Edge energies, S2 -Πx orbital structures, nanoribbon model, S2 -Πx Fermi wavenumbers, bond orders, simulated STM images, nanocluster area calculations

References (1) Chianelli, R. R.; Siadati, M. H.; De la Rosa, M. P.; Berhault, G.; Wilcoxon, J. P.; Bearden Jr., R.; Abrams, B. L. Catalytic Properties of Single Layers of Transition Metal Sulfide Catalytic Materials. Catal. Rev. 2006, 48, 1–41. (2) Hinnemann, B.; Moses, P. G.; Bonde, J.; Jørgensen, K. P.; Nielsen, J. H.; Horch, S.;

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Magic Clusters of MoS2 by Edge S2 Inter-Dimer Spacing Modulation

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