Chemical and Electronic Repair Mechanism ofDefects in MoS2 Monolayers

Anja Forster,†,‡,¶ Sibylle Gemming,‡,§,‖ Gotthard Seifert,‡,¶,⊥ and DavidTomanek∗,†

†Physics and Astronomy Department, Michigan State University, East Lansing, Michigan48824, USA

‡Center for Advancing Electronics Dresden (cfaed), 01062 Dresden, Germany¶Theoretical Chemistry, Technische Universitat Dresden, 01062 Dresden, Germany§Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials

Research, Bautzner Landstrasse 400, 01328 Dresden, Germany‖Institute of Physics, Technische Universitat Chemnitz, 09107 Chemnitz, Germany

⊥National University of Science and Technology, MISIS, Moscow, Russia

E-mail: tomanek@pa.msu.edu

Abstract

Using ab initio density functional theory cal-culations, we characterize changes in the elec-tronic structure of MoS2 monolayers introducedby missing or additional adsorbed sulfur atoms.We furthermore identify the chemical and elec-tronic function of substances that have beenreported to reduce the adverse effect of sul-fur vacancies in quenching photoluminescenceand reducing electronic conductance. We findthat thiol-group containing molecules adsorbedat vacancy sites may re-insert missing sulfuratoms. In presence of additional adsorbed sul-fur atoms, thiols may form disulfides on theMoS2 surface to mitigate the adverse effect ofdefects.

Keywords

transition metal dichalcogenides, 2D materials,ab initio calculations, electronic structure, de-fects

There is growing interest in two-dimensional(2D) transition metal dichalcogenide (TMD)

semiconductors, both for fundamental reasonsand as potential components in flexible, low-power electronic circuitry and for sensor appli-cations.1–3 Molybdenum disulfide, MoS2, is aprominent representative of this class of TMDs.A free-standing, perfect 2D MoS2 monolayerpossesses a direct band gap of 1.88 eV at the K-point in the Brillouin zone.4,5 Most commonlyused production methods for MoS2 monolay-ers are chemical vapor deposition (CVD) andmechanical exfoliation of the layered bulk ma-terial,6–8 as well as sputter growth atomiclayer deposition9 (ALD) of the precursor MoO3

and subsequent conversion to the disulfide un-der reducing conditions and at high tempera-tures.10,11 A direct ALD process using H2S andMoCl5

12 or Mo(CO)613 is another possibility to

obtain MoS2 monolayers. The CVD techniqueis probably best suited for mass production, butthe synthesized MoS2 layers lack in atomic per-fection. The most common defects in these lay-ers are sulfur and molybdenum vacancies, aswell as additional adsorbed sulfur atoms.14–19

Eliminating or at least reducing the adverse ef-fect of such defects is imperative to improvethe optoelectronic and transport properties ofTMDs.

1

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710.

0319

1v1

[ph

ysic

s.ch

em-p

h] 9

Oct

201

7

Figure 1

V A (a) (b)

A V

Mo S

Figure 1: (Color online) (a) Perspective and (b)top view of the optimized geometry of an MoS2

monolayer containing a sulfur monovacancy (V)and a sulfur adatom (A).

In search of ways to mitigate the adverse ef-fect of defects, different methods have beensuggested, including exposure of MoS2 to su-peracids20 or thiols.21,22 In the related MoSe2system, Se vacancies could be filled by S atomsfrom an adjacent MoS2 layer.23 In the presentstudy, we focus on the reactions of thiols withdefective MoS2 monolayers.

First, we characterize changes in the elec-tronic structure of MoS2 monolayers introducedby missing or additional adsorbed sulfur atomsusing ab initio density functional theory (DFT)calculations. We provide microscopic informa-tion about the chemical and electronic functionof thiols as a theoretical background for theunderstanding of the successful use of thiols,which have been reported to reduce the adverseeffect of sulfur vacancies in quenching photolu-minescence and to improve the electronic con-ductance of defective MoS2. We found that ad-sorbed thiols may re-insert missing sulfur atomsat vacancy sites. We also found that in presenceof sulfur adatoms, thiols will form disulfides onthe MoS2 surface, which both mitigate the ad-verse effect of defects.

In Figure 1 we display the structure of adefective MoS2 monolayer with a sulfur mono-vacancy (V) and an additional sulfur adatom(A), since these defects are known to sig-nificantly affect the electronic properties ofMoS2.

24 The formation energy of the sulfur va-cancy is 2.71 eV and that of the sulfur adatomis 1.07 eV. Consequently, the recombination en-ergy of a sulfur vacancy and a sulfur adatom is−1.89 eV. In spite of the large energy gain, nospontaneous healing will occur in a system with

both defect types present due to the high acti-vation barrier of ≈1.5 eV for this reaction. Thelisted defect formation energies are in agree-ment with a study reporting the effect of vari-ous defect types on the electronic structure ofMoS2,

25 and also with a study of vacancy de-fects.26

Defects affect drastically the electronic struc-ture in the vicinity of the Fermi level. Settingapart the inadequacy of DFT-PBE calculationsfor quantitative predictions of band gaps, weshould note that in our computational approachwith (large) supercells and periodic boundaryconditions, also defects form a periodic array.In spite of their large separation, defect statesevolve into narrow bands that may affect theband structure of a pristine MoS2 monolayer.The effect of a sulfur monovacancy, as well asthat of a sulfur adatom, on the density of states(DOS) of an MoS2 monolayer around the bandgap region is shown in Figure 2.

As seen in Figure 2c, sulfur monovacanciesintroduce defect states within the band gapand their superlattice shifts the DOS down by0.16 eV with respect to the pristine lattice. Thedefect states are localized around the vacancyas seen in Figure 2a. The effect of a superlat-tice of sulfur adatoms, addressed in Figure 2band 2d, is to reduce the DFT band gap from1.88 eV to 1.72 eV, in agreement with publishedresults.24,25

Defect sites play an important role as catalyti-cally active centers13 and as sites for functional-ization reactions of 2D MoS2.

27 Sulfur vacanciesin particular are considered to be important nu-cleation sites for a functionalization with thiolmolecules R-SH. The likely possibility of an ad-sorbed thiol group transferring a sulfur atom tothe vacancy and thus repairing the defect is par-ticularly appealing. In this case, the detachedhydrogen atom may reconnect with the remain-ing R to form R-H and fill vacancy site of MoS2

with sulfur, as

R-SH + MoSV2 → R-H + MoS2, (1)

where MoSV2 denotes the MoS2 layer with a sul-

fur vacancy.An alternative reaction has been proposed to

2

Figure 2

(a) (b) Sulfur Monovacancy Sulfur Adatom

DO

S

(c) D

OS

(d)

Figure 2: (Color online) Ball-and-stick modelsof (a) a sulfur vacancy defect and (b) a sul-fur adatom defect in an MoS2 monolayer. Den-sity of states (DOS) of MoS2 with (c) a vacancyand (d) an adatom defect. The DOS and theposition of the Fermi level are shown by solidblue lines in defective lattices and by dottedblue lines in the corresponding pristine latticesin (c) and (d). The DOS has been convolutedby a Gaussian with a full-width at half maxi-mum of 0.1 eV. The energy range of interest inthe gap of the pristine lattice is highlighted inred. The local density of states (LDOS), repre-senting the charge density associated with thishighlighted energy range, is represented by anisosurface and superposed to the structure of avacancy defect in (a) and an adatom defect in(b). The isosurface value in the LDOS plots is0.003 e/bohr3.

benefit from the STM tip current in an STMstudy.22 In the first step of reaction (2), simi-lar to reaction (1), a hydrogen atom is removedfrom the thiol as its sulfur atom fills the pre-vious vacancy, determining the reaction bar-rier for both reactions (1) and (2a). The re-moved hydrogen atom will then form H2 anddesorb from the MoS2 surface. The rest R isstill bound to the sulfur atom, adsorbed at thesulfur vacancy site. The final assumption of theproposed mechanism22 is that the R-groups areremoved with the support of the STM tip, as

represented in reaction (2b).

R-SH + MoSV2 →

1

2H2 + R-S-MoSV

2 (2a)

R-S-MoSV2

STM−−−→ R•+ MoS2 (2b)

There is evidence in the literature supportingboth reaction (1) (References [21], [28], [29])and reaction (2) (Reference [22]).

The authors of Reference [30] propose yetanother reaction (3a). Instead of the thiolmolecules repairing the sulfur vacancy, theyform an adsorbed R-SS-R disulfide at thesurface of MoS2 while releasing a hydrogenmolecule. We also considered the possibil-ity that instead of desorbing, the hydrogenmolecule will fill the vacancy defect as describedin reaction (3b),

2 R-SH + MoS2 → R-SS-R + H2 + MoS2 (3a)

2 R-SH + MoSV2 → R-SS-R + H2-MoSV

2 (3b)

Based on a previous study31 and the obser-vation of H2S as well as H3C=CH3 duringthe reaction of C2H5SH with bulk MoS2 inReference [28], we also considered a sulfur atomadsorbed on the MoS2 surface, identified asMoSA

2 , as the driving force for the observeddisulfide formation.

In this case, the reaction to form the disul-fide R-SS-R is divided into the following twosteps. In reaction (4a), one thiol reacts withthe adatom to R-S-S-H and, in the follow-upreaction (4b) with a second thiol, to R-S-S-R.An alternative reaction with a sulfur vacancyfollowing reaction (4a) is also possible. Similarto reaction (1), the SH-group of R-S-S-H cancure the vacancy defect, leading to the reduc-tion of R-S-S-H to the thiol R-S-H in Reaction(4c),

R-SH + MoSA2 → R-SS-H + MoS2 (4a)

R-SH + R-S-S-H→ H2S+R-SS-R (4b)

R-SS-H + MoSV2 → R-SH + MoS2 (4c)

To better understand the above reactionmechanisms (1) – (4), we performed DFT calcu-lations to compare the energy associated withthe pathways of these reactions. For the sake

3

Figure 3

Mo

S

H

C

Reaction 2a Reaction 1

Product

Vacancy healing process

+ ½H2

educt transition state product

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0Ea=0.22eV

ER=-3.09eV

En

erg

y [

ev]

Reaction coordinate

Reaction 1

Reaction 2a

ER=-0.90eV

Figure 3: (Color online) Reaction scheme forthe sulfur vacancy healing process caused by ex-posure of MoS2 with vacancies to CH3SH. ER

denotes the reaction energy and Ea the activa-tion barrier. The same initial state can lead totwo different final states via the same transi-tion state. The favorable reaction (1), shown indark blue, leads to a free CH4 molecule. Theenergetics of reaction (2a) is displayed in lightorange.

of easy understanding, we consider the smallmethanethiol molecule CH3SH as a representa-tive of thiols.

We limit our study of vacancy repair processesto reactions with MoS2 monolayers that containone sulfur monovacancy per unit cell. We ana-lyze which reactions with thiols are favorable torepair vacancy and adatom defects. Our resultsalso unveil the likely cause of apparent contra-

dictions in the interpretation of experimentalresults obtained by different researchers.

Results/Discussion

Vacancy Repair

The majority of published results indicate thatthiol molecules interacting with sulfur-deficientMoS2 may fill in sulfur atoms at the vacancydefect sites. Reaction pathways for the twovacancy-healing reactions (1) and (2a), whichhave been proposed in the literature,22,28,29 aresketched in Figure 3. We note that reaction (1)has been studied in greater detail for a differ-ent thiol21 and agrees with our findings for themodel compound H3C-SH.

We find that reactions (1) and (2a) are bothexothermic and require crossing only a low ac-tivation barrier of 0.22 eV, since they share thesame transition state shown in Figure 3. Thelarger energy gain ER = −3.09 eV in reaction(1) in comparison to −0.90 eV in reaction (2a)suggests that the former reaction is thermody-namically preferred.

Figure 4a shows the DOS and partial densi-ties of states (PDOS), projected on individualatoms, of the product of reaction (1). Figure 4bprovides the corresponding information for re-action (2a), and Figure 4c provides a detailedview of the PDOS for the CH3-group and theconnected sulfur atom. In both cases, the de-fect states associated with sulfur monovacancieshave been removed. In the final state of reac-tion (1) the DOS is completely restored to theundamaged state of the semiconductor. For re-action (2a), on the other hand, the Fermi levelis shifted to the lower edge of the conductionband due to the CH3-group. Therefore, onlythe preferred repair reaction (1) leads to bothan electronic and a chemical repair of MoS2.

Disulfide Formation

A different reaction scenario (3a) has been pro-posed in Reference [30], suggesting that disul-fides are formed when thiols interact withMoS2. We investigated the MoS2 surface bothin its pristine state and in presence of sulfur

4

Figure 4

(a) Product of Reaction 1

(b) Product of Reaction 2a

total

S

Mo

C

S(C)

H

(c) CH3 adsorbed on MoS2 in the product of Reaction 2a

Figure 4: (Color online) Electronic structure ofproducts of the vacancy healing process shownin Figure 3. The total density of states (DOS)and partial densities of states (PDOS) of theproducts of reactions (a) (1) and (b) (2a). (c)PDOS of the CH3-molecule bonded to a sulfuratom in an MoS2 monolayer. The PDOS of thesulfur atom connected to C in CH3, S(C), isshown by the brown line. All DOS and PDOSfunctions have been convoluted by a Gaussianwith a full-width at half maximum of 0.1 eV.The position of the Fermi level is shown by solidblue lines in defective lattices and by dottedblue lines in the corresponding pristine lattices.

vacancies to clarify the differences in the cat-alytic potential for disulfide formation. Fig-ure 5 illustrates reaction (3a) on pristine MoS2

and reaction (3b) on a sulfur-deficient MoS2

substrate. The schematic reaction profile in-dicates that both reactions involve significantactivation barriers. As seen in Figure 5, reac-tion (3a) is endothermic with a reaction energyof ER=0.39 eV and involves a high activationbarrier of 2.91 eV. Reaction (3b) near a sulfurmonovacancy is only slightly endothermic, witha reaction energy ER=0.02 eV, and involves asomewhat lower activation barrier of 2.13 eV.Thus, reaction (3b) is energetically more favor-

Figure 5

Product 3a

Disulfide formation process

Educt 3a (pristine MoS2)

Product 3b

Educt 3b (S monovacancy)

+ ½H2

Mo

S

H

C

educt transition state product

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Ea=2.13eV ER=0.39eV

Energ

y [e

V]

Reaction coordinate

Reaction 3a Reaction 3b

Ea=2.91eV

ER=0.02eV

Figure 5: (Color online) Reaction scheme of thedisulfide formation process involving exposureof an MoS2 monolayer to two CH3SH molecules.ER denotes the reaction energy and Ea the ac-tivation barrier. Reaction (3a), shown in darkpurple, occurs on pristine MoS2. Reaction (3b),shown in light green, occurs on a sulfur-deficientMoS2 substrate.

able than reaction (3a).The near-neutral reaction energy of reaction

(3b) can be explained by the Kubas interac-tion of transition metal η2-H2-complexes.32,33 Itmeans that the excess H2 molecule in the prod-uct of reaction (3b), which is attached to anMo atom at the sulfur vacancy site and indi-cated by a circle in Figure 5, still retains the H-H bond character. According to Reference [34],the Kubas interaction energy is in the range of0.2 − 0.4 eV, in agreement with the reactionenergy difference of 0.37 eV between reactions(3a) and (3b).

The Kubas interaction also reduces the reac-tion barrier and degree of endothermicity con-siderably. Nevertheless, reactions (3a) and (3b)are not competitive in comparison with the

5

Figure 6

(a) Product of Reaction 3a

(b) Product of Reaction 3b

total

S

Mo

C

H

(c) Atoms of the Kubas complex of Reaction 3b

S inC2H6S2

Figure 6: (Color online) Electronic structureof products of the disulfide formation processshown in Figure 5. The total density of states(DOS) and partial densities of states (PDOS)of the products of reactions (a) (3a) and (b)(3b). (c) PDOS of the 3 Mo atoms and theH2 molecule attached to the vacancy that formthe Kubas complex in the product of reaction(3b). All DOS and PDOS functions have beenconvoluted by a Gaussian with a full-width athalf maximum of 0.1 eV. The position of theFermi level is shown by solid blue lines in de-fective lattices and by dotted blue lines in thecorresponding pristine lattices.

strongly exothermic reaction (1) with ER =−3.09 eV in thermodynamic equilibrium.

The PDOS functions characterizing the prod-ucts of reactions (3a) and (3b), visualized inFigure 5, are shown in Figure 6. The productof reaction (3b) still contains a defect state inthe gap region, indicating that the chemisorbedH2 molecule is incapable of electronically re-pairing the effect of the sulfur vacancy. Thisis seen in the PDOS of the Mo atoms of theKubas complex surrounding the vacancy defectin Figure 6c. The product of reaction (3a), onthe other hand, shows no indication of a defect

Product 4b Product 4c

Product 4a

+ Sulfur vacancy

Adatom healing process

Figure 7

+ ½H2S

Mo

S

H

C

+

educt transition

state

interm.

state

transition

state

prodcut-4

-3

-2

-1

0

1

2

ER=-2.81eV

ER=-0.18eV

Ea~3.00eV

ER=-0.86eV

En

erg

y [

eV

]

Reaction coordinate

Reaction 4a

Reaction 4b

Reaction 4c

Ea=1.00eV

Figure 7: (Color online) Reaction scheme ofthe adatom healing process that starts with re-action (4a) and leads to disulfide formation inpresence of extra sulfur atoms on MoS2, shownin dark red. Subsequent ligand exchange reac-tion (4b) is shown in brown. Alternative subse-quent vacancy repair reaction (4c) is shown inlight blue. ER denotes the reaction energy andEa the activation barrier.

state, since the vacancy-free MoS2 monolayer isnot affected much by the physisorbed disulfide,as seen in the PDOS of Figure 6a.

We can thus conclude that the disul-fide formation reaction (3a), suggested inReference [30], is endothermic. The alterna-tive reaction (3b) on a sulfur-deficient MoS2

substrate displays a lower activation barrierand an end-product stabilized by the Kubasinteraction, but is still weakly endothermic andthus unlikely. In the following, we propose analternative pathway towards disulfide forma-tion.

6

Figure 8

(a) Sulfur adatom on MoS2

(b) Product of Reaction 4a

(c) Product of Reaction 4c

total

S

Mo

C

SadS in C2H6S2S in CH3SH

H

Figure 8: (Color online) Electronic structure ofproducts of the adatom healing process shownin Figure 7. The total density of states (DOS)and partial densities of states (PDOS) of (a)MoS2 with a sulfur adatom (without CH3SH),(b) the product of reaction (4a), and (c) theproduct of reaction (4c). All DOS and PDOSfunctions have been convoluted by a Gaussianwith a full-width at half maximum of 0.1 eV.The position of the Fermi level is shown by solidblue lines in defective lattices and by dottedblue lines in the corresponding pristine lattices.

Adatom Repair

The postulated alternative reaction requires ex-tra sulfur atoms adsorbed on the MoS2 surface,which act as nucleation sites for the disulfideformation. The reaction leading to the forma-tion of disulfide R-SS-R in presence of sulfuradatoms consists of two steps, described by re-actions (4a) and (4b), as well as the alternativereaction (4c) following reaction (4a), as shownin Figure 7.

In reaction (4a), a CH3SH molecule in-teracts with the reactive sulfur adatom tomethylhydro-disulfide (CH3SSH), releasing−0.86 eV due to the formation of a stable

disulfide bond. The estimated activation bar-rier for this reaction is close to 1 eV, which isconsiderably lower than the values for the cor-responding reactions (3a) and (3b) in absenceof an extra sulfur adatom.

Electronic structure changes during theadatom healing process are displayed in Fig-ure 8. The DOS of the product of reaction (4a),shown in Figure 8b, shows no defect-relatedstates in the band gap, indicating chemical andelectronic repair of the sulfur adatom defectthat is seen in Figure 8a.

In the subsequent reaction (4b), shown inFigure 7, a second CH3SH molecule interactswith the methylhydro-disulfide CH3SSH, lead-ing to the exchange of the hydrogen atom with amethyl group and formation of hydrogen sulfide(H2S) as a side product. This reaction is mildlyexothermic, with an overall reaction energy of−0.18 eV. Even though the combined reaction(4a) and (4b) for the formation of CH3SSCH3

is strongly exothermic with a net energy gain of−1.05 eV, the activation barrier for the ligandexchange in reaction (4b) is prohibitively highwith Ea≈ + 3 eV, which essentially suppressesthe formation of CH3SSCH3 following reaction(4a).

Therefore, we investigated reaction (4c) as analternative follow-up process to reaction (4a).In reaction (4c), the CH3SSH molecule inter-acts with a nearby sulfur vacancy defect. Thisreaction is similar to the vacancy healing reac-tion (1) and consequently is strongly exother-mic with a reaction energy of −2.81 eV. Reac-tion (4c) is barrier-free and thus occurs spon-taneously. As seen in in Figure 8c, describingthe product of reaction (4c), the defect-relatedstate above EF has been removed from theDOS. This means that following the adatom re-pair and disulfide formation reaction (4a), reac-tion (4c) will take place in case that also sulfurvacancies are present. The two reactions willthus heal both vacancy and adatom defects.

Our above considerations offer an attrac-tive explanation why disulfide formationwas observed in Reference [30], but not inReferences [21], [22], [28] and [29]. Initially,reactions (1) and (4a) plus (4c) have takenplace in all samples that contained vacancies.

7

Vacancy healing as primary outcome of re-actions reported in References [21], [22], [28]and [29] could likely be achieved due to anabundance of vacancies in the samples used.We may speculate that the MoS2 sample ofReference [30] contained more sulfur adatomsthan sulfur vacancies. In that case, all vacancydefects could be repaired, but some adatomdefects were left unrepaired in the sample ofReference [30]. At this point, lack of vacancydefects would block reactions (1) and (4c). Theonly viable reaction was (4a), which repairedadatom defects, leaving a pristine MoS2 surfacebehind with disulfide as a by-product . Thisspeculative assumption is also consistent withthe observation that the electronic structure ofMoS2 has remained unaffected by the reactionleading to the formation of disulfide.30

Conclusions

We studied three different reaction paths ofthiols, represented by methanethiol (CH3SH),with a defective 2D MoS2 monolayer. Weshowed that the repair of sulfur monovacan-cies by adsorbed CH3SH is an exothermic re-action releasing up to 3 eV. In another possi-ble reaction between CH3SH and MoS2, lead-ing to the formation of disulfide, we found thatpresence of sulfur vacancies lowers the reactionbarrier due to the Kubas interaction at the de-fect site. The corresponding reaction involv-ing MoS2 with sulfur adatoms instead of vacan-cies, on the other hand, leads to disulfide forma-tion and releases about 0.9 eV. In the presenceof sulfur vacancies, the formed disulfides willimmediately reduce to thiols while simultane-ously healing the vacancy defect. We can there-fore conclude that, regardless of interim disul-fide formation, thiols always lead to a chemicalrepair of available sulfur vacancies by filling-inthe missing sulfur atoms and consequently elim-inating vacancy-related defect states in the gap.

Methods/Theoretical

To obtain insight into the reaction processes,we performed DFT calculations using the

SIESTA code.35 We used ab initio Troullier-Martins pseudopotentials38 and the Perdew-Burke-Ernzerhof (PBE) exchange-correlationfunctional36 throughout the study. Except forsulfur, all pseudopotentials used were obtainedfrom the on-line resource in Reference [39]. Thepseudopotential of sulfur has been generatedwithout core corrections using the ATM codein the SIESTA suite and the parameters listedin Reference [39]. All pseudopotentials weretested against atomic all-electron calculations.We used a double-ζ basis set including polariza-tion orbitals (DZP) to represent atoms in crys-tal lattices, 140 Ry as the mesh cutoff energyfor the Fourier transform of the charge density,and 0 K for the electronic temperature. Weused periodic boundary conditions with largesupercells spanned by the lattice vectors ~a1 =(12.84, 0.00, 0.00) A, ~a2 = (6.42, 11.12, 0.00) A,~a3 = (0.00, 0.00, 22.23) A to represent pristineand defective 2D MoS2 lattices. The unit cellsof defect-free MoS2 contained 16 molybdenumand 32 sulfur atoms, and were separated by avacuum region of ≈15 A normal to the layers.The Brillouin zone was sampled by a 4×4×1k-point grid37 and its equivalent in larger su-percells.

The above input parameters were found toguarantee convergence. In particular, we foundthat using the larger triple-ζ polarized (TZP)instead of the DZP basis and increasing themesh cutoff energy affected our total energydifferences by typically less than 0.01 eV. Wefurthermore validated the ab initio pseudopo-tential approach used in the SIESTA code bycomparing to results of the all-electron SCM-Band code41 and found that energy differencesobtained using the two approaches differed typ-ically by less than 0.3 eV.

All geometries have been optimized usingthe conjugate gradient method,40 until noneof the residual Hellmann-Feynman forces ex-ceeded 10−2 eV/A. In addition to the defaultdensity matrix convergence, we also demandedthat the total energy should reach the toler-ance of .10−4 eV. To eliminate possible arti-facts associated with local minima, we verifiedinitial and final state geometries by perform-ing canonical molecular dynamics (MD) sim-

8

ulations using the NVT-Nose thermostat withT = 273.15 K and 1 fs time steps.

Due to the complexity of the reaction energyhypersurface and the large number of rele-vant degrees of freedom, approaches such asthe nudged elastic band, which are commonlyused to determine the reaction path includingtransition states, turned out to be extremelydemanding on computer resources. We fo-cussed on transition states only and initiatedour search by running canonical MD simula-tions starting from a set of educated guessesfor the geometry. Following the atomic tra-jectories, we could identify a saddle point inthe energy hypersurface, where all forces actingon atoms vanished, and postulated this pointin configurational space as a transition state.To confirm this postulate, we ran MD simula-tions starting at a slightly altered geometry ofthe postulated transition state. We concludedthat the postulated transition state is indeedthe real transition state once all trajectoriesreached either the initial (educt) or the final(product) state. The activation barrier was de-termined by the energy difference between theinitial and the transition state.

Author Information

Corresponding Author∗E-mail: tomanek@pa.msu.eduNotesThe authors declare no competing financial in-terest.

Acknowledgement We thank Jie Guanand Dan Liu for useful discussions and Gar-rett B. King for carefully checking the bib-liography. This study was supported by theNSF/AFOSR EFRI 2-DARE grant number#EFMA-1433459. Computational resourceshave been provided by the Michigan State Uni-versity High Performance Computing Centerand the Center of Information Services andHigh Performance Computing (ZIH) at TUDresden. AF, SG and GS acknowledge fund-ing from the Center for Advancing ElectronicsDresden (cfaed). AF especially acknowledgesthe cfaed Inspire Grant. SG acknowledges fund-

ing from the Initiative and Networking Funds ofthe President of the Helmholtz Association viathe W3 programme.

References

1. Li, H.; Yin, Z.; He, Q.; Li, H.; Huang, X.;Lu, G.; Fam, D. W. H.; Tok, A. I. Y.;Zhang, Q.; Zhang, H. Fabrication of Single-and Multilayer Mos2 Film-Based Field-Effect Transistors for Sensing NO at RoomTemperature. Small 2012, 8, 63–67.

2. Castellanos-Gomez, A.; van Leeuwen, R.;Buscema, M.; van der Zant, H. S.;Steele, G. A.; Venstra, W. J. Single-LayerMoS2 Mechanical Resonators. Adv. Mater.2013, 25, 6719–6723.

3. Chang, H.-Y.; Yang, S.; Lee, J.; Tao, L.;Hwang, W.-S.; Jena, D.; Lu, N.; Akin-wande, D. High-Performance, Highly Bend-able MoS2 Transistors with High-K Di-electrics for Flexible Low-Power Systems.ACS Nano 2013, 7, 5446–5452.

4. Ellis, J. K.; Lucero, M. J.; Scuseria, G. E.The Indirect to Direct Band Gap Transi-tion in Multilayered MoS2 as Predicted byScreened Hybrid Density Functional The-ory. Appl. Phys. Lett. 2011, 99, 261908.

5. Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.;Kim, J.; Chim, C.-Y.; Galli, G.; Wang, F.Emerging Photoluminescence in MonolayerMoS2. Nano Lett. 2010, 10, 1271–1275.

6. Pachauri, V.; Kern, K.; Balasubrama-nian, K. Chemically Exfoliated Large-AreaTwo-Dimensional Flakes of MolybdenumDisulfide for Device Applications. APLMater. 2013, 1, 032102.

7. Li, H.; Wu, J.; Yin, Z.; Zhang, H. Prepara-tion and Applications of Mechanically Ex-foliated Single-Layer and Multilayer MoS2

and WSe2 Nanosheets. Acc. Chem. Res.2014, 47, 1067–1075.

8. Varrla, E.; Backes, C.; Paton, K. R.; Har-vey, A.; Gholamvand, Z.; McCauley, J.;

9

Coleman, J. N. Large-Scale Production ofSize-Controlled MoS2 Nanosheets by ShearExfoliation. Chem. Mater. 2015, 27, 1129–1139.

9. Samassekou, H.; Alkabsh, A.; Wasala, M.;Eaton, M.; Walber, A.; Walker, A.;Pitkanen, O.; Kordas, K.; Talapatra, S.;Jayasekera, T.; Mazumdar, D. ViableRoute towards Large-Area 2D MoS2 UsingMagnetron Sputtering. 2D Materials 2017,4, 021002.

10. Kastl, C.; Chen, C. T.; Kuykendall, T.;Shevitski, B.; Darlington, T. P.; Bo-rys, N. J.; Krayev, A.; Schuck, P. J.;Aloni, S.; Schwartzberg, A. M. The Impor-tant Role of Water in Growth of MonolayerTransition Metal Dichalcogenides. 2D Ma-terials 2017, 4, 021024.

11. Keller, B. D.; Bertuch, A.; Provine, J.; Sun-daram, G.; Ferralis, N.; Grossman, J. C.Process Control of Atomic Layer Deposi-tion Molybdenum Oxide Nucleation andSulfidation to Large-Area MoS2 Monolay-ers. Chem. Mater. 2017, 29, 2024–2032.

12. Browning, R.; Padigi, P.; Solanki, R.;Tweet, D. J.; Schuele, P.; Evans, D. AtomicLayer Deposition of MoS2 Thin Films.Mater. Res. Express 2015, 2, 035006.

13. Kwon, D. H.; Jin, Z.; Shin, S.; Lee, W.-S.; Min, Y.-S. A Comprehensive Study onAtomic Layer Deposition of MolybdenumSulfide for Electrochemical Hydrogen Evo-lution. Nanoscale 2016, 8, 7180–7188.

14. Vancso, P.; Magda, G. Z.; Peto, J.; Noh, J.-Y.; Kim, Y.-S.; Hwang, C.; Biro, L. P.;Tapaszto, L. The Intrinsic Defect Struc-ture of Exfoliated MoS2 Single Layers Re-vealed by Scanning Tunneling Microscopy.Sci. Rep. 2016, 6 .

15. Addou, R.; McDonnell, S.; Barrera, D.;Guo, Z.; Azcatl, A.; Wang, J.; Zhu, H.;Hinkle, C. L.; Quevedo-Lopez, M.; Alsha-reef, H. N. Impurities and Electronic Prop-erty Variations of Natural MoS2 CrystalSurfaces. ACS Nano 2015, 9, 9124–9133.

16. Liu, K.-K.; Zhang, W.; Lee, Y.-H.; Lin, Y.-C.; Chang, M.-T.; Su, C.-Y.; Chang, C.-S.; Li, H.; Shi, Y.; Zhang, H. Growth ofLarge-Area and Highly Crystalline MoS2

Thin Layers on Insulating Substrates. NanoLett. 2012, 12, 1538–1544.

17. Lee, Y.-H.; Zhang, X.-Q.; Zhang, W.;Chang, M.-T.; Lin, C.-T.; Chang, K.-D.;Yu, Y.-C.; Wang, J. T.-W.; Chang, C.-S.; Li, L.-J. Synthesis of Large-Area MoS2

Atomic Layers with Chemical Vapor Depo-sition. Adv. Mater. 2012, 24, 2320–2325.

18. Zhan, Y.; Liu, Z.; Najmaei, S.;Ajayan, P. M.; Lou, J. Large-AreaVapor-Phase Growth and Characteriza-tion of MoS2 Atomic Layers on a SiO2

Substrate. Small 2012, 8, 966–971.

19. Hong, J.; Hu, Z.; Probert, M.; Li, K.;Lv, D.; Yang, X.; Gu, L.; Mao, N.; Feng, Q.;Xie, L.; Zhang, J.; Wu, D.; Zhang, Z.;Jin, C.; Ji, W.; Zhang, X.; Yuan, J.;Zhang, Z. Exploring Atomic Defects inMolybdenum Disulphide Monolayers. Nat.Commun. 2015, 6, 6293.

20. Amani, M.; Lien, D.-H.; Kiriya, D.;Xiao, J.; Azcatl, A.; Noh, J.; Mad-hvapathy, S. R.; Addou, R.; KC, S.;Dubey, M.; Cho, K.; Wallace, R.M.;Lee, S.-C.; He, J.-H.; Ager, J.W.;Zhang, X.; Yablonovitch, E.; Javey, A.Near-Unity Photoluminescence QuantumYield in MoS2. Science 2015, 350, 1065–1068.

21. Yu, Z.; Pan, Y.; Shen, Y.; Wang, Z.;Ong, Z.-Y.; Xu, T.; Xin, R.; Pan, L.;Wang, B.; Sun, L.; Wang, J.; Zhang, G.;Zhang, Y.W.; Shi, Y.; Wang, X. To-wards intrinsic charge transport in mono-layer molybdenum disulfide by defect andinterface engineering. Nat. Commun. 2014,5, 5290.

22. Makarova, M.; Okawa, Y.; Aono, M. Selec-tive Adsorption of Thiol Molecules at Sul-fur Vacancies on MoS2 (0001), Followed by

10

Vacancy Repair via S–C Dissociation. J.Phys. Chem. C 2012, 116, 22411–22416.

23. Surrente, A.; Dumcenco, D.; Yang, Z.;Kuc, A.; Jing, Y.; Heine, T.; Kung, Y.-C.;Maude, D. K.; Kis, A.; Plochocka, P. De-fect Healing and Charge Transfer-MediatedValley Polarization in MoS2/MoSe2/MoS2

Trilayer van der Waals Heterostructures.Nano Lett. 2017, 17, 4130–4136.

24. Noh, J.-Y.; Kim, H.; Kim, Y.-S. Stabilityand Electronic Structures of Native Defectsin Single-Layer MoS2. Phys. Rev. B 2014,89, 205417.

25. Santosh, K.; Longo, R. C.; Addou, R.; Wal-lace, R. M.; Cho, K. Impact of IntrinsicAtomic Defects on the Electronic Struc-ture of MoS2 Monolayers. Nanotechnology2014, 25, 375703.

26. Ghorbani-Asl, M.; Enyashin, A. N.;Kuc, A.; Seifert, G.; Heine, T. Defect-Induced Conductivity Anisotropy in MoS2

Monolayers. Phys. Rev. B 2013, 88,245440.

27. Sim, D. M.; Kim, M.; Yim, S.; Choi, M.-J.; Choi, J.; Yoo, S.; Jung, Y. S. ControlledDoping of Vacancy-Containing Few-LayerMoS2 via Highly Stable Thiol-Based Molec-ular Chemisorption. ACS Nano 2015, 9,12115–12123.

28. Peterson, S. L.; Schulz, K. H. EthanethiolDecomposition Pathways on MoS2 (0001).Langmuir 1996, 12, 941–945.

29. Wiegenstein, C. G.; Schulz, K. H.Methanethiol Adsorption on DefectiveMoS2 (0001) Surfaces. Phys. Chem. B1999, 103, 6913–6918.

30. Chen, X.; Berner, N. C.; Backes, C.; Dues-berg, G. S.; McDonald, A. R. Functional-ization of Two-Dimensional MoS2: On theReaction Between MoS2 and Organic Thi-ols. Angew. Chem. Int. Ed. 2016, 55, 5803–5808.

31. Benziger, J. B.; Preston, R. E. Organosul-fur Chemistry on Tungsten (211) Sur-faces. 1. A Comparison of Methanethiol andMethanol. Phys. Chem. 1985, 89, 5002–5010.

32. Kubas, G. J. Five-Co-Ordinate Molyb-denum and Tungsten Complexes,[M(CO)3(PCy3)2], which ReversiblyAdd Dinitrogen, Dihydrogen, and OtherSmall Molecules. J. Chem. Soc., Chem.Commun. 1980, 61–62.

33. Gordon, J. C.; Kubas, G. J. Perspec-tives on How Nature Employs the Prin-ciples of Organometallic Chemistry inDihydrogen Activation in Hydrogenases.Organometallics 2010, 29, 4682.

34. Skipper, C. V. J.; Hamaed, A.; An-tonelli, D. M.; Kaltsoyannis, N. The KubasInteraction in M(II) (M = Ti, V, Cr)Hydrazine-Based Hydrogen Storage Mate-rials: A DFT Study. Dalton Trans. 2012,41, 8515–8523.

35. Soler, J. M.; Artacho, E.; Gale, J. D.;Garcıa, A.; Junquera, J.; Ordejon, P.;Sanchez-Portal, D. The SIESTA Methodfor Ab Initio Order-N Materials Simulation.J. Phys.: Condens. Matter 2002, 14, 2745.

36. Perdew, J. P.; Burke, K.; Ernzerhof, M.Generalized Gradient Approximation MadeSimple. Phys. Rev. Lett. 1996, 77, 3865.

37. Monkhorst, H. J.; Pack, J. D. Spe-cial Points for Brillouin-Zone Integrations.Phys. Rev. B 1976, 13, 5188.

38. Troullier, N.; Martins, J. L. Efficient Pseu-dopotentials for Plane-Wave Calculations.Phys. Rev. B 1991, 43, 1993–2006.

39. http://departments.icmab.es/leem/

siesta/Databases/Pseudopotentials/

periodictable-gga-abinit.html, ac-cessed on August 1, 2016.

40. Hestenes, M. R.; Stiefel, E. Methods ofConjugate Gradients for Solving LinearSystems. J. Res. Natl. Bur. Stand. 1952,49, 409–436.

11

41. BAND2017, SCM, Theoretical Chem-istry, Vrije Universiteit, Amsterdam, TheNetherlands, http://scm.com, accessed onJune 22, 2016.

12