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C: Physical Processes in Nanomaterials and Nanostructures

Ab Initio Investigation of Atomistic Insights into the Nanoflakes Formation of Transition-Metal Dichalcogenides: The Examples of MoS, MoSe, and MoTe 2

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Naidel A. M. S. Caturello, Rafael Besse, Augusto C.H Da Silva, Diego Guedes-Sobrinho, Matheus P. Lima, and Juarez L. F. Da Silva J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b07127 • Publication Date (Web): 02 Nov 2018 Downloaded from http://pubs.acs.org on November 3, 2018

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The Journal of Physical Chemistry

Ab initio Investigation of Atomistic Insights into the Nanoflakes Formation of Transition-Metal Dichalcogenides: The Examples of MoS2, MoSe2, and MoTe2 Naidel A. M. S. Caturello,† Rafael Besse,‡ Augusto C. H. Da Silva,† Diego Guedes-Sobrinho,¶,† Matheus P. Lima,§ and Juarez L. F. Da Silva∗,† †São Carlos Institute of Chemistry, University of São Paulo, PO Box 780, 13560-970, São Carlos, São Paulo, Brazil ‡São Carlos Institute of Physics, University of São Paulo, PO Box 369, 13560-970, São Carlos, São Paulo, Brazil ¶Department of Physics, Technological Institute of Aeronautics, 12228-900, São José dos Campos, São Paulo, Brazil §Department of Physics, Federal University of São Carlos, 13565-905, São Carlos, São Paulo, Brazil E-mail: [email protected]

Abstract

atoms, which is followed by 2D nanoflakes with tetrahedral, square pyramidal, and distorted octahedral coordination environments of Mo atoms. Both structure types maintain the same Q-terminated edge configuration, a crucial factor for the increased stability of those nanoflakes in relation to stoichiometric 2H monolayer cuts. The structural properties of the lowest energy configurations evolve smoothly as a function of the nanoflake sizes. We found that more intense effects of charge transfer in the edges is an important factor for the stabilization of the 2D nanoflakes. The smaller charge transfer for larger Q radius leads to the increase of n, which stabilizes the 2D nanoflakes, namely, n = 6, 8, and 9 for MoS2 , MoSe2 , and MoTe2 , respectively.

An atom-level understanding of the evolution of the physical and chemical properties of transition-metal dichalcogenides (TMDs) nanoflakes is a key step to improve our knowledge of two-dimensional (2D) TMDs materials, which can help in the designing of new 2D materials. Here, we report a density functional theory (DFT) study of the evolution of the structural, energetic, and electronic properties of (MoQ2 )n nanoflakes, where Q = S, Se, Te, and n = 1 − 16. All optimized DFT configurations for each system (10n) were generated by an in-house implementation of the tree-growth scheme combined with the modified Eucliden similarity distance algorithm, which reduces a large set configurations (10n million) to 10n trial structures. We found that the energetic favored configurations change between two sorts of clusters: frameworks elongated in one-dimension with tetrahedral and square pyramidal coordination of Mo

1

Introduction

Two-dimensional (2D) transition-metal dichalcogenides (TMDs) have attracted great deal of attention in recent literature due to

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their properties, 1,2 which differ from their bulk material counterparts. 2D TMDs have found potential applications in biomedicine, 3,4 optoelectronics, 5–7 catalysis, 8,9 and energy storage. 10,11 The great interest in this class of materials is in part due to the chemical formula MQ2 , where M is a transition-metal (TM) and Q = S, Se, Te, allowing a large variety of atomic combinations resulting in broad range of possibilities for their properties. 1,12 Furthermore, the edges of 2D TMDs can exhibit unique properties, such as topological states 13,14 and the coexistence of metallic and semiconducting states. 15 Besides edge effects, 16–18 other factors have been investigated to change the properties of 2D TMDs such as the variation of the number of layers 19,20 and the spacial group symmetry. 21 The structures of 2D TMDs are composed of layers made of metal planes sandwiched by chalcogen planes, and van der Waals (vdW) interactions bind the layers. The geometries around the metal atoms vary from trigonal prismatic (2H) to octahedral (1T) and distorted octahedral (1T0 ). 21 The relative stability between each of those polytypes in periodic monolayers is determined by the dmetal electron count and the 2H phase is the most stable for group-VI 2D TMDs. 1,21 The methods for obtaining 2D TMDs have evolved from former top-down methods, such as mechanical 22 and electrochemical exfoliation, 23 to bottom-up approaches, such as the chemical vapor deposition (CVD), 24 the most widely used technique for direct growth of 2D TMDs nowadays. 25 Certain aspects about the growth of 2D TMDs nanoflakes have been a matter of discussion in recent literature, such as the factors which influence the growth modes, the nanoflake geometries, and the formation mechanism under the CVD regime. Factors such as screw dislocations 26,27 and relative proportions of precursor/promoter gases have been proved to be fundamental for the formation of nanofaflates along the CVD process. 25 The generally accepted mechanism of formation of TMDs nanoflakes was proposed by Cain et al., 25,28,29 which is processed through

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the condensation of MoO3 – x Q y nanoparticles acting as the nucleation seeds for the growth of the TMD monolayer and are then wrapped into their respective MoQ2 fullerene-like shells. Although the mechanistic formation of 2D TMDs have been suggested, it is still necessary to improve the understanding of how atomic interactions and size confinement effects drive the TMDs systems into (1) their 2D dimensionality and (2) signatures of the symmetry of a particular monolayer polytype. Therefore questions underlying how the physical chemical (structural, energetic, and electronic) properties of those clusters evolve with size still lack answers. Hashemi et al. 30 in recent work have applied the method of Oganov et al. 31,32 for generating stoichiometric structures of (MoS2 )n and (MoSe2 )n , for n from 1 to 10, contributing to the understanding of stability and abundance of small Mo-based TMD nanoflakes. However, details of how edge configurations drive the formation of 2D MoQ2 nanoflakes and how the properties of a large set of cluster with competing energy evolve are still missing. Additionally, no evaluation of how the S, Se, and Te atomic radii affect the physical chemical properties of the systems is hitherto reported in literature. These open questions demand an efficient method for the generation of a set of structures to perform a comprehensive search of the potential energy surface (PES), combined with an algorithm for comparison of the obtained structures. In order to shed light in the initial stages of the formation of 2D TMDs nanoflakes, we performed a spin-polarized density functional theory (DFT) investigation of (MoQ2 )n nanoflakes, with Q = S, Se, Te, and n = 1 to 16, with structures generated through the combination of the tree-growth scheme and the modified Euclidean similarity distance algorithm. We found that the lowest energy configurations present Q-terminated edges, and this geometry is the principal stabilizing factor for those structures. Furthermore, the energetically favorable geometries for small clusters are one-dimensional (1D), with the Mo atoms in an equilateral truss structure. On


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the other hand, the largest clusters have twodimensional (2D) lowest energy configurations, with the core in the 1T0 symmetry. The critical cluster size (n) associated with change to the energetic preference for the 2D configuration depends on the atomic radius of the chalcogen, being 6, 8, and 9 for Q = S, Se, and Te, respectively.

2 2.1

equilibrium geometries were found once all the atomic forces on every atom were smaller than −1 0.025 eV Å . For the calculations of periodic systems of 1T, 1T0 , and 2H MoQ2 monolayers, we have used the same parameters, exchange correlation functional, and basis set for the nanoflakes. A vacuum thickness of 15 Å was set between periodic images of the monolayers, and a 18×18×1 k-points mesh was used. To ensure that all lowest energy structures are true local minimum configurations, we performed the vibrational analysis, where we identified that all the eigenvalues (frequencies) are positive.

Theoretical Approach and Computational Details Total Energy Calculations

2.2

Our spin-polarized DFT calculations for the dichalcogenides systems were performed within the Perdew–Burke–Ernzerhof (PBE) 33 formulation for the exchange-correlation functional, which yields energetic properties for TMDs nanoclusters comparable to the ones obtained with hybrid functionals with less computational effort. 30 The Kohn– Sham molecular orbitals were expanded in numerical atom-centered orbitals (NAOs), as implemented in the all-electron full-potential Fritz–Haber institute ab initio molecular simulations (FHI-aims) package. 34 We employed the second improvement in the NAOs compared with the minimal basis set, namely, the light-tier 2 (FHI-aims terminology), 34 which provides efficient description of the nanoflakes, with convergence comparable to basis sets with further improvements, light-tier 3 and light-tier 4, Figure S1. The electrons were described by the zeroth-order relativistic approximation (atomic ZORA). 35 The total energy convergence criterion was set to 1 × 10−5 eV using a Gaussian broadening parameter of 1 meV for all calculations, which plays a crucial role for finite size systems, i.e., it helps to eliminate possible fractional occupation of the electronic states near to the highest occupied molecular orbitals (HOMO). The geometric optimizations were carried using the modified Broyden–Fletcher– Goldfarb–Shanno (BFGS) algorithm, 36 which takes into account the trust radius method as implemented in the FHI-aims package. 34 The

Atomic Configurations

Structure

To obtain a set of reliable putative global minimum configurations (pGMCs) for the selected dichalcogenides, which plays a crucial role to understand the evolution of the physical and chemical properties of nanoflakes as a function of size, we employed the tree-growth (TG) protocol 37 combined with the modified Euclidean similarity distance 38 (ESD) to generate stoichiometric MoQ2 trial configurations. In the TG-ESD algorithm, which is sketched in Figure 1, the trial configurations for a particular nanoflake size, n + 1, are obtained from the pGMC for n by the addition of a MoQ2 fragment at a random position (adsorption site) near to the (MoQ2 )n pGMC nanoflake. The distance between the (MoQ2 )n pGMC nanoflake and the MoQ2 fragment is defined based on the average bond lengths of the MoQ2 particles increased by 25 %. We considered random orientations for the MoQ2 fragment located at random positions, and hence, we can generate from 1 up to 1 billion trial configurations. In this work, we generated 10×n×106 trial configurations for n = 2 – 16, as indicated in Figure 1. As expected, we cannot optimize 10×n×106 trial configurations using DFT-PBE for every nanoflake size, and hence, we reduced the number of configurations using the modified ESD technique, in which two configurations, α and β, are written as vectors using the


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employing the BFGS local optimizer algorithm.

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Following the procedure described above, we obtained about 10×n local minimum structures for each (MoQ2 )n system, with Q = S, Se, Te, and n from 1 to 16. From now on, the lowest energy local minimum configuration is named putative global minimum configuration (pGMC), and all pGMCs are shown in Figure 2, while the atomic coordinates, (x, y, z), are provided in the Supporting Information. Although we show only the pGMCs, we analyzed all the calculated configurations, which will be taken into account in the following discussion of the structural, energetic, and electronic properties.

Figure 1: Sketch of the tree-growth scheme combined with the Euclidean similarity distance. The steps of (i) generating the adsorbed structures; (ii) comparing the structures obtained in (i) through modified Euclidean metrics; and (iii) evaluate the relative energies are shown.

3.1 3.1.1

S(α, β) =

(xi,α − xi,β )2

i=1 N P i=1

, x2i,α

+

Structural Properties Putative global configurations

minimum

From our analyses, the pGMCs nanoflakes exhibited two types of morphologies with respect to size and shape. The first one, especially for smaller n, is composed of pGMC structures in which there is a mixture of tetrahedral and square pyramidal motifs for the Mo atoms coordination, leading to elongated lattices in one dimension (henceforth termed 1D). The second type is for sizes with n ≥ 6, 8, and 9 for Q = S, Se, and Te, respectively, from where the formation of the 2D nanoflakes starts. This type, henceforth named 1T0 , has a mixture of tetrahedral and square pyramidal coordination for the edge Mo atoms, and distorted octahedral for core Mo atoms. Our results for the stability of the 1T0 polytype for n = 15 were also found by Besse et al. 39 in recent paper. All the pGMCs of both 1D and 1T0 morphologies retain the same Q-terminated edge configuration with Q atoms lying out of the plane defined by the Mo lattices. Therefore, the edge configuration of both 1D and 1T0 pGMCs is henceforth termed Q-terminated.

distance of each atom to the geometric center as one component of the vector, xi . Thus, the similarity between the α and β configurations is calculated as follows, N P

Results and Discussion

(1)

x2i,β

where the denominator is added to obtain a S(α, β) index that does not depend on the nanoflake size, and beyond of that, it yields a dimensionless S(α, β) parameter. In this work, we employed cutoff parameters for S(α, β) that yield reductions from 10×n×106 to about 10×n configurations, which can be seen as a representative set of trial configurations. Furthermore, to increase the variety of structures, we enriched the set of structures with fragments obtained directly from cuts in the 1T and 2H monolayers. Thus, finally, the reduced set of trial configurations were optimized by DFT-PBE calculations


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Figure 2: Comparison of relative energies between 1D and 1T0 nanoflakes. The relative total energy differences in meV per formula unit between both structures are provided, where the structures assigned with 0.0 meV are the putative global minimum configurations for each n. The pGMCs derived from stoichiometric monolayer cuts are indicated by asterisks over their cluster sizes and species. ACS Paragon Plus Environment

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The Journal of Physical Chemistry Initial structure

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Relaxed structure

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and n = 15, triangular nanoclusters are not the most stable structures for any MoQ. We also observed for the 1D pGMCs of MoS2 a distinctive wave-like pattern for the structures as seen from the top view, Figure S3. This pattern is mitigated as the Q radius increases, being nearly absent for the MoTe2 . More intense distortions are therefore correlated with smaller cluster size of energetic preference transition, thus we can understand that this distortion is associated with the destabilization of the 1D pGMCs.

Figure 3: A (MoSe2 )9 2H monolayer cut before and after relaxation, showing the reconstructions in the edges before geometric optimization. As the Q atoms present electron lone pairs, since they belong to sp2 and sp3 hybridizations, the 2H fragments allow these electron lone pairs from edge Q atoms to interact more intensely than its 1D and 1T0 counterparts. The less intense interactions between edge Q atoms in 1D and 1T0 comes from the mismatch between Q edge atoms in the edges. This feature is opposed to the armchair and zigzag edges 40,41 of the 2H monolayer stoichiometric clusters we used within our analyses, Figure 3. As the Q atoms at the edges interact less intensely in 1D and 1T0 , these atomic configurations are energetically preferred over their 2H counterparts, and this stabilization can be regarded as an edge effect. 42–44 The 1T0 pGMCs for the (MoS2 )n and (MoSe2 )n for n = 8, 9, 12, 14 and 16, and the pGMCs for (MoTe2 )n , n = 9, 10, 11, 13, 14, and 16 are derived from 1T monolayer cuts. The 1T monolayer cuts evolved to distorted 1T0 geometry after optimization, indicating the Peierls 45,46 mechanism as a way of the system to be stabilized. Some of our 2H fragments have undergone significant edge reconstructions, similar to those observed by Cui et al., 2 Figure 3. We also observed the formation of edge Q atoms dimerizations in 2H relaxed structures, Figure 3 and Figure S2. Despite both dimerizations and edge reconstructions, no 2H fragment was found to be more stable than 1D and 1T0 clusters for any cluster size. We observed a triangular pGMC for n = 6 for MoS2 , a morphology which can be experimentally obtained for nanoflakes of comparable sizes, 47,48 depending upon the synthetic conditions. 49 However, for n = 10

3.1.2

Radial distribution functions

In order to quantify the distribution of Mo and Q atoms, we have calculated the radial distribution functions (RDFs) for all our pGMCs, Figure 4. The most symmetric cluster sizes, n = 9, and 12, present smaller numbers of both Mo and S peaks when compared to their neighbor sizes. The RDF plots show a division of the pGMCs in two regions. The first presents a nearly homogeneous distribution between the metal and chalcogen atoms, whereas the second region is defined by distant peaks of chalcogen atoms. The first region for the 1D pGMCs corresponds to the location of three-fold Q atoms, and, on the other hand, the one- and two-fold chalcogen atoms lie within regions that are more distant from the center of the clusters.


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Radial distribution function (Arb. Units)

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


0.4 0.2 0.2 0.2 0.2 0.6 0.4 0.4 0.4 0.4 0.4 0.4 0.4

Mo1S2

0.2

Mo2S4

0.2

Mo3S6

0.2

Mo4S8

0.3

Mo5S10

0.2

Mo6S12

0.2

Mo7S14

0.3

Mo8S16

0.2

Mo9S18

0.5

Mo10S20

0.2

Mo11S22

0.3

Mo12S24

0.4

Mo13S26

0.2

Mo14S28

0.2

Mo15S30

0.3

Mo16S32 2

4

6

8

Mo

Q

0.2

Mo2Se4

0.2

Mo3Se6

0.2

Mo4Se8

0.3

Mo5Se10

0.2

Mo6Se12

0.2

Mo7Se14

0.2

Mo8Se16

0.3

Mo9Se18

0.2

Mo11Se22

0.2

Mo13Se26 Mo14Se28 Mo15Se30 Mo16Se32 2

r (Å)

4

6

8

10

r (Å)

Mo1Te2 Mo2Te4 Mo3Te6 Mo4Te8 Mo5Te10 Mo6Te12 Mo7Te14 Mo8Te16

0.5

Mo10Se20 Mo12Se24

0.3

10

Mo1Se2

Mo9Te18 Mo10Te20 Mo11Te22

0.3

Mo12Te24

0.2

Mo13Te26

0.3

Mo14Te28

0.3

Mo15Te30

0.3

Mo16Te32 2

4

6

8

10

12

r (Å)

Figure 4: Radial distribution functions (RDFs) of the (MoQ2 )n (Q = S, Se, Te; n = 1 – 16) pGMCs. r = 0 is the center of gravity of the cluster. For the 1T0 pGMCs, the core region composed of three-fold Q atoms and six-fold Mo atoms have nearly a homogeneous RDF distribution, with one Mo peak at the center of the nanoflake for n = 9, and peaks far from the center of gravity corresponding to edge chalcogen atoms. Although the distinction in the RDFs between two regions are clear for both 1D and 1T0 pGMCs, no feature from the atomic distributions can be used in order to clearly identify differences between the 1D and 1T0 morphologies. To gain deeper knowledge into the evolution of structural properties of the nanoflakes, we calculated the evolution of the chemical order parameter (σ), effective coordination number (ECN), and average weighted bond lengths (dav ), and compared them to the structural properties of periodic 2H, 1T, and 1T0 monolayers, Figure 5. The details of the calculations of these properties are described in the Supporting Information. 3.1.3

size grows, the value of σ among the pGMCs tends to vary from −1 to values close to 0, indicating a trend to the intermediate between species segregation and homogeneous distribution. This result corroborates the observations made for the analyses of the RDFs, and, furthermore, we can observe that the values tend nearer to 0 as the Q radius increases. This result can be understood in terms of effective coordination number. 3.1.4

Average Bond Length

The average weighted bond lengths correlate with ionic radii of S2 – (1.84 Å), Se2 – (1.98 Å), and Te2 – (2.21 Å), 52 explaining the different values of the dav among the compositions. We found an asymptotic increase of dav as the values of n increases. The reason for that is an increasing number of interactions between Mo and Q atoms. The evolution of the dav with cluster size is characterized by a large variation of dav for smaller n, followed by a plateau, because as the cluster size grows, the introduction of a new MQ2 unit does not provide great changes in the overall bonding of the cluster, when compared to smaller sizes.

Chemical Order Parameter

The chemical order parameter, σ, 50,51 has been used to characterize the mixture between atoms composing the clusters. As the cluster


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The Journal of Physical Chemistry 2H

1T’

1T

0.00

σ

-0.30 -0.60

ECN (NNN)

-0.90 8.00 6.00 4.00 2.00 3.00

dav (Å)

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

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2.75

Mo Se Total

Mo S Total

2.50

Mo Te Total

2.25 4 8 12 16 Number of MoS2 units

4 8 12 16 Number of MoSe2 units

4 8 12 16 Number of MoTe2 units

Figure 5: Evolution of σ, ECN, and dav for all the (MoQ2 )n isomers (Q = S, Se, Te; n = 1 – 16) as a function of the nanoflake size. The pGMCs are linked by solid lines, and the open symbols at each cluster size are the higher energy isomers. The dashed, dot-dashed and dot-double dashed lines are the results of the structural properties we calculated for the 1T, 1T0 , and 2H monolayers, respectively. 3.1.5

Effective Coordination Number

can be seen structurally as 2D arrangements of the 1D ground-state nanoflake of the smaller cluster sizes.

The evolution of the effective coordination number 53,54 for the pGMCs and for the other atomic configurations reveals the same behavior of local environment obtained for the dav . This behavior is due to the change in the morphology of the pGMCs, and the increase of ECN as the Q radius grow is due to the fact that greater Q radii allow longer bonds between chalcogen and metal atoms to be considered. There is a mismatch between structural properties values of the clusters and respective periodic 1T0 monolayers. This result is due to the small sizes of the nanoflakes and relevant contribution of edges to the structural properties. In general, no structural property can be used to justify the 1D → 1T0 energetic preference transition due to the smoothness of the curves for the pGMCs. Thus, our results indicate that the 1T0 pGMCs

3.2 3.2.1

Energetic Properties Relative Stability Function

In order to obtain more information about the relative stability of the pGMCs, we have calculated the relative stability function, ∆2 E, defined as 55 ((MoQ2 )n−1 )

∆2 E((MoQ2 )n ) = Etot

((MoQ2 )n+1 )

+ Etot

−

((MoQ ) ) 2Etot 2 n

, (2)

i where, each Etot is the total energy of a given cluster size. This analysis allows the determination of the most stable cluster sizes,


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2

Stability function, ∆ E (eV)

2

leads these structures to be less stable, thus leading the 1D → 1T0 transition of MoTe2 to occur at the greatest cluster size among the three MoQ2 compounds. Therefore, the loss of planarity also explains the topology of the ∆2 E for the MoTe2 and its absence of magic numbers.

MoS MoSe2 MoTe2

1

0

-1

3.2.2 -2

Binding Energies

The binding energies, Eb , have also been calculated in order to gain insights on the stability of the clusters, and are defined as follows, 55

-5.4

Binding energy, Eb (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

MoS2 MoSe2 MoTe2

-8.1

Q i Mo Ebi = Etot /n − Etot − 2Etot

(3)

-10.8

i , of a cluster i where, each total energy, Etot is divided by the number of monomer units, n, and subtracted from the total energies of free atoms of the species which form the cluster, Figure 6. The evolution of the binding energies as the cluster size grows reveals an asymptotic behavior for all species. The most stable clusters belong to MoS2 , and the less stable clusters are the MoTe2 ones, whereas MoSe2 is intermediate. The relative values of Eb can be explained by a simple model of charge attraction. By considering the formal charges of +4 and -2 for the Mo and Q atoms, respectively, 56 the greater charge density of the chalcogen, the more stabilized the clusters. Thus, the effect of composition on the binding energy is dominated by charge effects, rather than orbital electron filling characteristics. With the increase in the cluster sizes, Eb values tend to the cohesive energies of their respective periodic 1T0 monolayers.

-13.5

2

4

6

8

10

12

14

16

Number of MoQ2 units

Figure 6: Stability function and binding energies of MoQ2 , Q = S, Se, Te per unit formula as function of the cluster size. In the lower panel, filled and open symbols indicate pGMCs and higher energy configurations, respectively, and the dashed lines are calculated binding energies per unit formula for the 1T0 monolayers. termed magic number, through peaks in the ∆2 E function, Figure 6. The magic numbers for the MoS2 and MoSe2 are n = 9 and 12. Both of these cluster sizes exhibit four-fold symmetry. We also observe that the peak of the stability function for n = 9 and the partial rise in this function in n = 16 suggest that nanoflakes formed by the junction of triangles for MoS2 and MoSe2 are candidates for the determination of cluster sizes of special stability. However, ∆2 E behaves differently for MoTe2 , not exhibiting peaks. As it has been observed for the wave-like pattern in 1D pGMCs of the MoS2 , 1T0 pGMCs of MoTe2 present distortions of the plane defined by the metallic lattices of the clusters. The loss of planarity observed for the MoTe2 1T0 pGMCs

3.2.3

Boltzmann Statistics

Due to the large quantity of trial configurations, it is relevant to explore in great detail the probability of structures to be obtained at certain temperatures, thus enabling us to trace arguments for temperatures other than 0 K. In order to build these arguments, we have applied the concept of Boltzmann


9


probability, 57,58 written as Ej , p(nj ) = exp − kb T

50 0 -50 35

(4)

where, Ej is the relative energy of the jth cluster, kb and T are the Boltzmann constant and the considered temperature, respectively. Setting the temperature at 298 K and considering the probability of existence of 1 % of the 1D clusters after the 1D → 1T0 energetic preference transition, the maximum relative energy of an isomer per formula unit is around 118 meV. For both MoS2 and MoSe2 , n = 9 and n = 12 – 16, the 1D clusters are beyond the energy cutoff we established. However, for MoTe2 , the only cluster size where the 1D relative energy is beyond our cutoff is 16, Figure 2. The particular stability of the MoS2 and MoSe2 1T0 pGMCs with n = 9 in relation to their 1D counterparts is because this cluster size is a magic number for those systems, but not for MoTe2 . More intense edge effects in smaller Q radii and the loss of planarity of the metallic lattice can be traced as the main factors for the stabilization of the 1T0 in relation to 1D pGMCs. Therefore, effects due to the substitution of chalcogens are responsible for the determination of the probability to obtain 1D clusters at a certain temperature.

3.3 3.3.1

Projected density of states (states/eV)

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Mo s

Mo p

Mo d

Se s

Se p

Mo1Se2 Mo2Se4

20

Mo3Se6

20

Mo4Se8

15

Mo5Se10

15

Mo6Se12

10

Mo7Se14

10

Mo8Se16

6

Mo9Se18

6

Mo10Se20

6

Mo11Se22

6

Mo12Se24

6

Mo13Se26

6

Mo14Se28

6

Mo15Se30

6

Mo16Se32 -4

-2

0

2

Energy (eV) Figure 7: Projected density of states (PDOS) per formula unit for the pGMCs of MoSe2 . The PDOS of the remaining systems can be found in Figure S4, Supporting Information. atoms include more d- than s- and p-orbitals in their highest occupied energy levels, a trend of group-VI TMDs. 59 The decrease of the PDOS near HOMO with increasing number of electrons within the pGMCs indicates that inner electronic levels are being occupied, therefore stabilizing the cluster. The break of degeneracy of Mo d- electronic levels is caused by the Peierls distortion as the pGMCs adopt the 1T0 morphology. Thus, the 1D → 1T0 energetic preference transition is manifested in the electronic levels of the pGMCs as a continuous lowering of the PDOS near HOMO. Although this is a driving force for the process of determination of the pGMC, there are no changes in electronic structure which can be pointed out to define the transition point of morphologies of the pGMCs.

Electronic Properties Projected Density of States

In order to gain more information about the chemical bonds of our pGMCs, we have calculated the projected density of states (PDOS), Figure 7. The near-HOMO states for all cluster sizes are dominated by the Q s- and p-states, and Mo d-states. As the change of morphology among the pGMCs takes place, Mo d-states tend to shift nearer to the HOMO states, and, all along the cluster size evolution, there is the lowering of the PDOS near the HOMO levels. The chalcogen orbitals appearing in the highest occupied states is consistent with the sp2 and sp3 hybridizations of those atoms. On the other hand, the Mo


10

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MoS2 HOMO MoS2 LUMO MoSe2 HOMO MoSe2 LUMO MoTe2 HOMO MoTe2 LUMO

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MoS2

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Hirshfeld charge per atom (e)

-3.2

-4.8

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HOMO-LUMO energy difference (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

The Journal of Physical Chemistry Absolute HOMO/LUMO energy levels (eV)

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1.2 MoS2 MoSe2 MoTe2

Mo 1D Q 1D Mo 2D core Mo 2D edge Q 2D core Q 2D edge

0.00 -0.25 0.40

MoSe2

0.20 0.00 -0.20 0.40

MoTe2

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Number of MoQ2 units 0

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Figure 8: Absolute HOMO and LUMO energy levels and HOMO-LUMO energy differences for the MoQ2 pGMCs as a function of the cluster size. HOMO-LUMO Differences

16

Figure 9: Hirshfeld charges for the pGMCs of MoQ2 (Q = S, Se, Te) separated in core and edge for the 1T0 pGMCs as a function of the cluster size. The dashed lines indicate calculated Hirshfeld charges for the 1T0 periodic monolayers.

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3.3.2

2

have a decreasing trend with cluster size, and as the periodic 1T0 monolayers of MoQ2 have metallic character, 39 it is expected that as the flakes become larger and confinement effects are mitigated, this property is obtained. The sensitivity of the electronic levels of the pGMCs, therefore, relate to the cluster geometry more importantly than to its chemical composition. As it has been observed in Figure 7, the determination of electronic levels depend upon the particularities of the cluster geometries. As a whole, the HOMO-LUMO energy differences and the plot of orbital isosurfaces cannot provide great insight into the factors that drive the MoQ2 pGMCs to have a certain morphology, Figure S5. Thus, effects of electronic structure solely cannot explain the 1D → 1T0 transition of the pGMCs.

Energy

The HOMO levels and the HOMO-LUMO energy differences for all the pGMCs are depicted in Figure 8. As the nanoflake size grows, the HOMO-LUMO energy differences tend to decrease, indicating how the gap opening for smaller cluster sizes are caused by quantum confinement effects. 60,61 The HOMO levels oscillate, and no trend of energetic lowering with size growth is observed. Likewise, the HOMO-LUMO energy differences oscillate with pGMC size. The HOMO levels are as low in energy as the Q size is smaller, due to the increase of Q s- and Q p-derived states as going from S to Te. Therefore, the topologies of HOMO and LUMO curves relate to the cluster geometry and are essentially independent of the chemical composition of the pGMC. The HOMO-LUMO energy differences


11


3.3.3

75

Hirshfeld Charge

E 2D - E 1D (meV/f.u.)

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

In order to obtain more detailed knowledge of the charge transfer effects acting upon the pGMCs, we have performed Hirshfeld charge analysis, 62 distinguishing the atoms in core and edge according to their coordination, and the results are shown in Figure 9. Mo and Q atoms with three- and six-fold coordinations, respectively, are termed core, whereas atoms with other coordinations are termed edge. The cationic and anionic character of the Mo and Q atoms, respectively, and the magnitudes of charge transfer are in agreement with the trends expected based on the values of Pauling electronegativity, which are 1.8, 2.6, 2.4, and 2.1 for Mo, S, Se and Te, respectively. 63 The more intense charge transfer effects as the chalcogen radius decreases indicates stronger Coulomb binding, as seen in the higher magnitude of binding energies. Furthermore, it is observed that the more intense charge transfer effects take place on edge atoms, and that the core values tend to the ones of the 1T0 monolayers, as expected given the absence of edges in periodic monolayers.

4

0 -75 -150

MoS2 MoSe2 MoTe2

-225 6

8

10

12

14

16


Figure 10: Energy differences per formula unit for 1T0 (indicated as 2D in the figure) and 1D clusters for the MoQ2 (Q = S, Se, Te) pGMCs as a function of the cluster size. The dashed line is set to zero in order to show the clusters sizes where core energy of the 1T0 nanoflakes stabilizes this dimensionality compared to 1D morphologies. difference between the energy of a 1T0 nanoflake and the 1D nanoflake of same n. The results of this energy analysis are shown in 10. For n ≤ 13, the core energies depend on the nanoflake geometry. However, as the nanoflake size grows, the core energy tends to grow in modulus, indicating that the 2D dimensionality tends to be more favorable as the clusters grow. The magnitude of the core energy also increases as the chalcogen radius decreases, which can be correlated with the increase of charge transfer effects. From Figure 9, we can see that edge atoms are more charged than the core atoms. Therefore, the stability of the edges is decreased due to repulsive electrostatic interactions, and the presence of a core in 1T0 nanoflakes is a stabilizing factor because it reduces the intensity of these repulsive electrostatic effects due to smaller edges and larger distances between edges. Because of the larger charge transfer effects, the destabilizing factor of the edges increases when the chalcogen radius decreases and therefore the 1D → 1T0 transition occurs in smaller cluster sizes for the smaller chalcogen radii. Beyond this charge effect, the appearance of distorted Mo octahedra in the core allows the lowering of DOS near HOMO. Thus, the stabilization of 1T0 nanoflakes can be

Atomistic Insights into Mo-based Nanoflakes

To obtain more insights into the MoQ2 nanoflakes, we divided the total energy of the nanoflakes, Etot , into core and edge energies, Ecore and Eedge , respectively Etot = Eedge + Ecore .

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From our calculations and analyses, the formation of the 2D MoQ2 nanoflakes can be separated into two steps, namely, (i) the formation of a 1D structure with an energetically preferred edge configuration; and (ii) competition between 1D morphologies and 1T0 nanoflakes which maintain the edge configuration defined in (i). Therefore, if we consider the 1D nanoflakes as being formed only of edge atoms, we can obtain an estimation of the core energy of 1T0 nanoflakes as the


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summarized as a combination of electrostatic effects of edge atoms and Peierls distortion.

5

Biofuels Agency) through the R&D levy regulation. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. The authors also acknowledge the National Laboratory for Scientific Computing (LNCC/MCTI, Brazil) for providing HPC resources of the SDumont supercomputer, which have contributed to the research results reported within this paper. URL: http://sdumont.lncc.br. Authors thank also the infrastructure provided to our computer cluster by the Department of Information Technology − Campus São Carlos. Research developed with the help of HPC resources provided by the Information Technology Superintendence of the University of São Paulo. R. Besse acknowledges financial support (Ph.D. fellowship) from FAPESP, Grant No. 2017/09077-7.

Conclusions

The evolution of the energetic, electronic, and structural properties of the (MoQ2 )n nanoflakes, where Q = S, Se, Te, and n = 1 – 16, have been studied using spin-polarized DFT calculations as implemented in the FHIaims package. For the purpose of generating the initial set of (MoQ2 )n configurations, we employed the well known tree-growth scheme combined with the Euclidean similarity distance algorithm (TG-ESD). Furthermore, we incremented the configuration data base by adding structures obtained from the 2H and 1T0 monolayers, which helps to improve the quality of configuration set. We found two structure types for the pGMCs nanoflakes: a 1D elongated motif, which is favored for smaller cluster sizes, followed by 1T0 2D nanoflakes, preferred for greater cluster sizes. These two structural configurations are more stable than 2H nanoflakes due to their shared Q-passivated edge configuration, which provides less intense electron lonepair interactions, opposed to the zigzag and armchair edges from 2H nanoflakes. The 1D → 1T0 energetic transition among the pGMCs is driven by the charge transfer effects in the edges and the Peierls distortion stabilization associated with the core atoms of the 1T0 nanoflakes, therefore making the core energy of the 2D pGMCs the second driving factor for the transition of energetic preference that we observed. Thus,our study points a pathway for understanding the stabilization factors for MoQ2 , Q = S, Se, Te nanoclusters, providing insights of their fundamental chemistry and potential hints for the design of new MoQ2 based materials.

Supporting Information Available: Additional supporting data and analyses are summarized in the Supporting Information, which includes: total energy convergence tests as a function of the number of NAOs, investigation of the edge Q dimers in the 2H nanoflakes after optimization, the wave-like distortion of the MoS2 1D nanoflakes, the PDOS for all the pGMCs, and the orbital isosurfaces for examples of 1D and 1T0 pGMcs. Furthermore, we provide technical details on the definitions of the calculated structural and energetic properties. Finally, we report the atomic coordinates, (x, y, z), for all calculated configurations along with the their respective number of formula units, total energies, and relative total energies. This material is available free of charge via the Internet at http://pubs.acs.org/.

References

Acknowledgement The authors gratefully acknowledge support from FAPESP (São Paulo Research Foundation, Grant Number 2017/11631-2), Shell and the strategic importance of the support given by ANP (Brazil’s National Oil, Natural Gas and

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