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The Role of Intrinsic Defects in Electrocatalytic Activity of Monolayer VS Basal Planes for the Hydrogen Evolution Reaction 2

Yang Zhang, Xiaoshuang Chen, Yan Huang, Chong Zhang, Feng Li, and Haibo Shu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b11987 • Publication Date (Web): 04 Jan 2017 Downloaded from http://pubs.acs.org on January 4, 2017

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The Journal of Physical Chemistry

The Role of Intrinsic Defects in Electrocatalytic Activity of Monolayer VS2 Basal Planes for the Hydrogen Evolution Reaction Yang Zhang, †, ‡ Xiaoshuang Chen ‡,*, Yan Huang,‡ Chong Zhang,§ Feng Li,§ Haibo Shu,§,* †

National Synchrotron Radiation Laboratory, University of Science and Technology of China, 230029 Hefei, China ‡ National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Science, 200083 Shanghai, China § College of Optical and Electronic Technology, China Jiliang University, 310018 Hangzhou, China ABSTRACT: Two-dimensional VS2 nanomaterials have emerged as highly efficient and inexpensive electrocatalysts for the hydrogen evolution reaction (HER), and the further improvement of their HER performance depends on the understanding of the catalytic mechanism and activity in various pristine and defective structures. Here structural stability, electronic properties, and HER activity of monolayer VS2 nanosheets with various intrinsic point defects are studied by using first-principles calculations. Compared to the most studied 2H-phase MoS2 basal plane, both 2H- and 1T-phase VS2 basal planes exhibit superior catalytic activity due to their metallic properties. With the introduction of intrinsic point defects onto VS2 basal planes, we find that there are four types of stable defects in 2H phase (i.e., Sad, Svac, Vad, and VS) and three types of stable defects in 1T phase (i.e., Sad, Svac, and Vad), respectively. Moreover, the formation of Svac, Vad, and VS structures in 2H phase and Vad in 1T phase can enhance the HER activity of basal planes, which implies that the synthesis of VS2 nanosheets at the V-rich condition facilitates to achieve high HER performance. The HER activity of pristine and defective VS2 structures can be well understood by a Fermi-abundance model that is also suitable to describe a broad class of electrocatalytic HER systems. This work provides a deep insight into the HER activity of single-layer VS2 and the guidance for synthesizing highly active electrocatalysts in transition-metal dichalcogenides.

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1. INTRODUCTION Electrochemical water splitting through the hydrogen evolution reaction (HER) is a sustainable method to generate molecular hydrogen (H2),1-3 which has been proposed as one of the most promising clean energy solutions. Employing appropriate electrocatalysts is critical for the HER because they can accelerate the conversion from proton-electron pairs to H2 at low overpotentials (η).4 Platinum (Pt)based materials are still regarded as highly efficient catalysts due to their outstanding HER performance with high exchange current density and small Tafel slope.5 However, the high cost and scarcity of Ptbased electrocatalysts have limited their widespread use.6,7 Thus, the development of cost-effective and efficient catalysts with earth-abundant elements is strongly desirable. Recently, two-dimensional (2D) transition metal dichalcogenides (TMDs), such as MoS2 and WS2,8-12 have emerged as an alternative to Pt-based catalysts for the HER. The HER active sites have been identified from the exposed metallic edges of MoS2 and WS2 nanosheets but their less conducting basal planes are catalytically inert,13-15 which becomes a main limitation for the further improvement of HER performance. In order to explore efficient methods to achieve highly active TMDs-based catalysts, considerable efforts have been made during the past few years. Two feasible schemes have been proposed: (i) increasing the concentration of exposed edges and enhancing the conductivity of basal plane in typical semiconducting TMD materials (e.g., MoS2),16-20 (ii) finding metallic TMD materials that facilitates the HER on their basal planes.21 As a typical layered TMD material, vanadium disulfide (VS2) is an analogous of MoS2 in structure,22 in which sandwich-like S-V-S layers are interacted by van der Waals forces. Unlike semiconducting MoS2, the single-layer VS2 in 2H phase exhibits metallic characteristic2325

which makes it potentially suitable for the HER electrocatalysts.26 Motivated by unique electronic

properties of VS2, a variety of methods have been developed to fabricate high-quality VS2 monolayer and nanosheets.26-28 The synthesized VS2 nanomaterials were found to have the 2H phase in monolayer structures and the 1T phase in their bulk-like structures,29 respectively. From these experimental and theoretical studies,19,20 the phase transition from 2H to 1T can leads to the significant improvement for the HER activity of MoS2 nanostructures. Despite the large potential as the HER electrocatalysts, there are few studies about the electrocatalytic activity of 2D-VS2 with both two phases. On the other hand, engineering intrinsic defects is an important way to tune electronic properties of 2D-TMD materials, consequently leading to the change in their HER activity. For example, sulphur (S) vacancies are a universal intrinsic defect in 2D-MS2 (M = Mo, W, and Sn) nanomaterials, and the inert basal plane of these materials can be activated by introducing the S vacancies.30-32 In addition to the vacancy defects, other types of intrinsic point defects, such as antisites, holes, substitution atoms, and adadtoms, have also been identified in experiment.33,34 However, how the intrinsic defects affect the catalytic activity of 2D-VS2 remains unclear. In this work, we present a systematic investigation on the 2 Environment ACS Paragon Plus

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geometry and stability of various potential intrinsic defects in monolayer VS2 basal plane with both 2H and 1T phases, and explore their HER activity by using density-functional theory (DFT) calculations. Our calculated results show that there are four types of stable defects in 2H phase (i.e., Sad, Svac, Vad, and VS) and three types of stable defects in 1T phase (i.e., Sad, Svac, and Vad) in allowed chemical potential ranges, respectively. We find that not all stable intrinsic defects contribute to the improvement of HER activity in VS2 basal planes, and highly active VS2 catalysts are easily achieved at the V-rich condition. Based on the analysis of electronic structures, we propose a Fermi-abundance model to understand the defect dependence of HER activity in monolayer VS2. 2. COMPUTATIONAL DETAILS The single-layer VS2 in 2H and 1T phases are shown in Figure 1a. The optimized lattice constants are a=b= 3.166 Å for 2H-VS2 and a=b= 3.174 Å for 1T-VS2, which is in good agreement with previous theoretical studies.25,29 Based on the optimized single-layer VS2 sheets, the defect models are created by introducing intrinsic point defects onto the 2D-VS2 supercell which has the in-plane lattice constants of 16.452 Å×15.830 Å in 2H phase and 16.491 Å×15.870 Å in 1T phase, respectively. Here we consider ten possible point defects in 2H-VS2, including of monosulfur vacancy (Svac), disulfur vacancy (S2vac), S adatom (Sad), S substitution at the Mo site (SV), disulfur substitution at the Mo site (S2V), V vacancy (Vvac), V adatom (Vad), one S atom replaced by one V atom (VS), two S atoms replaced by one V atom (VS2), and two S atoms replaced by two V atoms (V2S2), and six point defects in 1T-VS2, including of Svac, Sad, SV, Vvac, Vad, and VS, respectively. For the Sad and Vad structures, the optimal adsorption site is obtained by the energy comparison of various possible configurations. The optimized atomic models of various defective structures have been presented in Figures S1 and S2 of Supporting Information (SI). To evaluate the stability of various defective structures, their formation energies have been calculated by the following equation, E f = ED − ET + ∆ni ∑ µi i

(1)

where ED and ET are total energies of monolayer VS2 with and without intrinsic defects, respectively. µi is the chemical potential of atomic species i (i = V and S), and ∆ni is the difference of the number of V and S atoms between perfect and defective structures. To maintain thermodynamic equilibrium (µVS2 = µV +2µS) of VS2, the allowable value of µS is µS(bulk) –∆Hf/2 < µS < µS(bulk), where the upper (lower) limit corresponds to S-rich (V-rich) condition and ∆Hf is the heat of formation. Here ∆Hf is defined as ∆Hf = EVS2 – EV – ES, where EVS2, EV, and ES are the energies of VS2 monolayer, V atom in bulk, S atom in bulk, respectively. The computed ∆Hf is 1.30 eV and 1.29 eV for 2H- and 1T-phase VS2, respectively. The catalyst-supported HER is a multistep electrochemical process. The first step is the hydrogen adsorption onto a VS2 catalyst (i.e., Volmer reaction), which is described by H+ + e- + * H*, where 3 Environment ACS Paragon Plus


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the prefix of * denotes the adsorption site of the catalyst. The subsequent step is the release of H2 molecules from the catalyst following either the Heyrovsky (H* + H+ + e- H2 + *) or Tafer (2H* H2 + 2*) reaction. To insight into the HER pathway and activity, the change of Gibbs free energies for the H adsorption (∆GH) on various VS2 catalysts have been calculated in the acid solution using the standard hydrogen electrode (CHE) model as follows,35 ∆GH = ∆EH + ∆EZPE – T∆S

(2)

where ∆EH is the adsorption energy for adding one H atom onto VS2 catalysts and is defined as ∆EH = EVS2+nH – EVS2+(n-1)H – 1/2H2, ∆EZPE and ∆S are zero-point energies (ZPE) and entropy differences between the adsorbed system and gas phase, respectively and T is temperature which refers to the room temperature (T = 298.15 K). EZPE is defined as EZPE = 1/ 2∑ hωi , where ω is the vibration frequency i=N

and N is the number of H independent freedom degree in adsorbed system or H2 gas molecule. The ∆S term is defined as ∆S = 1/2SH2 – SH*, where SH* is the vibration entropy of adsorbed H and defined as

S H * = k B ∑ ln(1 − e− hωi / kBT ) , where kB and T are Boltzmann constant and temperature respectively,36,37 i=N

and SH2 is the vibration entropy of H2 gas molecule obtained from the standard thermodynamic database.38 The detailed data of various energies and entropies have been listed in Table S1 of SI. All DFT calculations are performed using the projector augmented wave (PAW) method39 as implemented in the Vienna ab initio Simulation Package (VASP).38 The electronic exchange-correlation energy is treated by generalized-gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE).41,42 The kinetic energy cutoff for the plane-wave expansion is set to 400 eV. The k-point sampling in the Brillouin zone is implemented by the Monkhorst-Pack scheme with the grids of 16×16×1 and 4×4×1for VS2 primitive cells and supercells, respectively. For the geometry optimization, the convergence criteria of electronic energy and forces acting on each atom are 10-3 eV and 10-2 eV/Å, respectively. In the calculation of electronic structures, the DFT-GGA method can lead to the underestimation of band gap, thus the GGA+U method have been considered as a comparison. We have investigated the Hubbard parameter Ueff = U – J from 0 eV to 4 eV to compute electronic structure of pristine and defective VS2 structures. The climbing-image nudged elastic band (cNEB) method43 is employed to search transition states for the transition of VS2 monolayer from 2H to 1T phase. In the calculation, the number of image is set to 6 and the spring constant is -5. Simulated scan tunneling microscopy (STM) images are obtained using the Tersoff-Hamann approximation based on calculated charge densities, and the STM tip height is set to ~ 1.8 Å in the simulation.


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Figure 1 (a) Atomic structures and barrier (in eV) of phase transition from 2H to 1T phase in monolayer VS2. (b), (c) spin-polarized band structures of 2H- and 1T-phase VS2 monolayers. The solid and dash lines denote spin-up and spindown bands, respectively.

3. RESULTS AND DISCUSSION We first investigate structural and electronic properties of prefer single-layer VS2, which can provide a reference for the study of defective structures. Figure 1a shows atomic structures and energetics of 2Hand 1T-phase VS2 monolayers. The 2H-VS2 monolayer indicates relatively higher stability than the 1T structure, which agrees well with previous studies.29 However, there is a very small energy difference (~0.04 eV) between 2H and 1T structures. Moreover, the calculated 2H-to-1T phase-transition barrier is 0.65 eV that is far lower than that of monolayer MoS2 (~1.80 eV).44 The result suggests the possibility of phase coexistence during the synthesis of single-layer VS2 using regular experimental methods, such as the chemical intercalation and chemical vapor deposition (CVD). The electronic band structures show that both 2H and 1T structures are metallic with ferromagnetic (FM) coupling (see Figures 1b and 1c), which is in good agreement with previous reports.23-25, 45 Therefore, the phase transition does not change the metallic characteristic of VS2. The calculated density of states (DOS) indicates that the magnetism of monolayer VS2 systems mainly originates from spin polarization of V-3d states (see Figures S3 and S4), resulting in that the magnetic moment of V atom is 0.5 µB in 2H phase and 4.5µB in 1T phase, respectively. Owing to the difference of FM coupling between 2H and 1T phases, there is a different distribution for electronic states around the Fermi level. The distribution of occupied states near Fermi level in 1T phase is larger than that of 2H phase. Such a difference may induce different HER activities in 2H- and 1T-phase VS2 basal planes, which will be discussed blow. It needs to be noted that the DFTGGA method underestimates the band gap. In order to confirm the metallic characteristic of 2H- and 5 Environment ACS Paragon Plus


1T-phase VS2 monolayers, their DOS are calculated using the GGA+U method. It can be found that both 2H- and 1T-phase VS2 monolayers are still metallic with the change of Ueff value from 0 eV to 4 eV (see Figure S5). Furthermore, we also examine electronic structure of defective VS2 structures (Svac), and calculated DOS shows that the Svac structure in both 2H and 1T phases can maintain its metallic characteristic with different Ueff values (see Figure S6). The above results suggest that metallic pristine and defective VS2 structures calculated by the DFT-GGA method are valid. To explore the defect effect on the HER activity of monolayer VS2 basal planes, it needs to firstly understand the stability of various intrinsic point defects on VS2 basal planes. The formation energies (Ef) of sixteen intrinsic point defects in 2H-VS2 as a function of S chemical potential difference (∆µS, ∆µS = µS–µS(bulk)) are plotted in Figure 2b. It can be found that Svac is the most stable point defect in the most of allowed ∆µS range, and Sad becomes the most stable defect under the S-rich regime, and Vad and VS indicate higher stability under the V-rich growth condition. The similar result has also been found in other transition-metal sulfides, such as MoS2 and SnS.33,46 For other intrinsic point defects, such as SV, S2V, S2vac,VS2, and V2S2, they present relatively larger formation energies. According to the defect concentration C ∝ exp(−E f / kBT ) , a large Ef value means that the defect is difficult to be formed on VS2 basal planes during the experimental synthesis. As shown in Figure 2b, the stability of intrinsic defects on 1T basal plane is very similar to the case of 2H phase: Svac is the most stable defect for most of allowed range of ∆µS, and Sad and Vad become the most stable intrinsic defect under the S-rich and Vrich conditions, respectively. 8

6

4

S2V SV

V2S2

(b)

VS2

6

SV

4

S2vac

Vvac

Ef (eV)

(a)

Ef (eV)

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Vvac

VS

2

2

VS 0

0

Svac

Vad -1.2 Mo-rich

Sad -2

-0.8

-0.4

∆µS (eV)

0.0 S-rich

Svac

Vad -1.2 Mo-rich

-0.8

-0.4

∆µS (eV)

Sad 0.0 S-rich

Figure 2 Formation energies of various intrinsic point defects on (a) 2H and (b) 1T VS2 basal planes as a function of S chemical potential difference ∆µS.

Figure 3 shows atomic structures and simulated STM images of these stable intrinsic point defects on VS2 basal planes. For the Svac structures, introducing an S vacancy (Svac) onto both 2H- and 1T-phase VS2 basal planes brings three nearest-neighboring V atoms with the dangling bonds (see Figure 3a,e). The coulomb repulsion effect induces the increase of atomic distance among these V atoms from ~3.15 6 Environment ACS Paragon Plus

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Å to ~3.86 Å. The simulated STM images display that there are bright spots at the sites of three nearestneighboring V atoms approaching the S vacancy in 2H phase (see Figure 3a), but there is a dark region around the S vacancy in 1T phase (see Figure 3e). The difference of STM images means that the S vacancy should have different effects on the HER activity of VS2 basal plane in two phases. For the Sad structures, the S adatom prefers to occupy at the top of V atom and bonds with one V atom and two S atoms in 2H phase (see Figure 3b), while the S adatom prefers to situate at the top of S atom, forming SS dimer in 1T phase (see Figure 3f). The simulated STM images indicate a highly bright spot at the site of S adatom in both 2H and 1T phases due to the localization of unpaired electrons at the defect, implying that the S adatom has a high activity to trap H atoms during the HER. In the Vad structures, the V adatom prefers to adsorb at the hollow site regardless of the crystal phase. It is seen from Figures 3c,g that simulated STM images present a triangle-like bright spot in both 2H and 1T phases, which arises from unpaired electrons of V adatom delocalized to its adjacent V atoms. For the VS structure (see Figure 3d), the V substitution atom causes a local structural distortion in 2H basal plane, leading to the elongation of V-V bonds and the constriction of V-S bonds. Hence, the simulated STM image displays a high bright spot at the site of V substitution atom and the dark region at its nearest-neighboring V atoms. The above results reflect that these intrinsic defects lead to a significant change in electronic states of VS2 basal planes at the vicinity of Fermi level, which may have a significant effect on their HER activity.

Figure 3 Side and top views of atomic structures and simulated STM images of stable intrinsic point defects on (a)-(d) 2H and (e)-(g) 1T VS2 basal planes. The simulated STM images are obtained at a voltage of -1.0 V using the TersoffHamann approximation.



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Now we turn to investigate the HER activity of perfect and defective VS2 basal planes. The change of Gibbs free energy for hydrogen adsorption (∆GH) is an important parameter to measure the intrinsic catalytic activity of a catalyst. An ideal catalyst should be able to facilitate HER with zero for ∆GH (∆GH = 0). Generally, the ideal case cannot be achieved due to the binding interaction of H with the catalyst. Therefore, a catalyst with lower ∆GH would have better HER performance. Based on this principle, the free-energy diagram through either Volmer-Heyrovsky or Volmer-Tafel pathway has been firstly calculated to reveal the HER mechanism on VS2 basal planes. As is shown in Figure 4a (VolmerHeyrovsky pathway), the free energy change (∆GH) on both 2H- and 1T-phase pristine basal planes is the first Volmer step, which serves as the rate-limiting step for the overall HER at equilibrium potential. In contrast, as shown in Figure 4b (Volmer-Tafel pathway), the ∆GH of the Tafel step on two pristine basal planes is larger than that of the Volmer step, and the overall ∆GH of the Volmer-Tafel pathway is also greater than that of the Volmer-Heyrovsky pathway. Therefore, the Volmer-Heyrovsky pathway should be energetically favorable for the HER of VS2-based catalysts and the ∆GH of the Volmer step is thus used to evaluate the HER activity of VS2 catalysts. The result is similar to the case of heteroatomdoped graphene HER electrocatalysts.47 It is seen from Figure 4a that the calculated ∆GH of pristine VS2 basal plane in 2H and 1T phases is 0.26 eV and -0.16 eV respectively, which is far lower than that of monolayer MoS2 basal plane (∆GH =1.89 ~1.92 eV)25,48 and closes to that of Pt (∆GH =-0.09 eV).49 The lower ∆GH of VS2 basal planes originate from their metallic electronic structures which facilitate to the charge transfer from the catalytic surfaces to the H adatoms. The result suggests a large potential of monolayer VS2 as the highly efficient HER electrocatalysts.

Figure 4 Schematic illustration and the corresponding free-energy diagram of the HER following (a) the VolmerHeyrovsky pathway and (b) the Volmer-Tafel pathway on 2H- and 1T-phase pristine VS2 basal planes.


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Based on the Volmer-Heyrovsky pathway, the free-energy diagrams of various defective VS2 structures in 2H and 1T phases have been compared. For the comparison, the data of pristine VS2 and Pt catalysts have been provided here. We find that the introduction of most of intrinsic point defects more or less increases the surface activity of VS2 basal planes except for 1T-Vad and 1T-Svac structures (see Figure 5a), resulting in calculated ∆GH more negative. For example, the calculated ∆GH of Vad, VS, Svac, and Sad structures in 2H phase is 0.17, 0.46, 0.55, and 0.73 eV lower than that of pristine 2H basal plane, respectively. Similarly, the calculated ∆GH of 1T-Sad structure is 0.41 eV lower than that of the pristine structure (see Figure 5b). Overall, the defective structures formed under V-rich condition, such as Vad and VS in 2H phase and Vad in 1T phase, have the relatively smaller absolute values of ∆GH (< 0.26 eV). Therefore, the V-rich growth condition should facilitate the synthesized VS2 catalysts with high HER activity. We find that the formation of Svac defect in 2H and 1T basal phases leads to different change trends for the ∆GH relative to the pristine ones. As shown in Figures 5a and 5b, the ∆GH shows the reduction of ~0.55 eV in 2H basal plane but has the increase of ~0.42 eV in 1T basal plane with the formation of Svac defect. In addition, introducing Sad defect onto VS2 basal planes can induce the significant reduction of ∆GH (> 0.4 eV) in both 2H and 1T phase, which is related to the high activity of S adatom to trap H atom. These results agree well with the prediction from the simulated STM images. 0.4

(b)

Pristine 0.2 +

0.0

H +e

-

Vad

-0.2

Pt VS

-0.4

Svac

-0.6

Sad

0.4

Svac

0.2 1/2 H2

+

∆GH (eV)

(a)

∆GH (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


0.0

H +e

-

Pt

-0.2

Vad

1/2 H2

Pristine

-0.4 Sad -0.6

Reaction coordinate

Reaction coordinate

Figure 5 Calculated free-energy diagrams for the hydrogen evolution on pristine and defective VS2 basal planes in (2) 2H phase and (b) 1T phase. For the comparison, ∆GH of Pt has also been included here.

In order to understand the inherent mechanism of HER activity, electronic structures of pristine and defective VS2 structures in 2H and 1T phases have been calculated. In the HER process, the adsorption and desorption of H are strongly related to its binding strength on a catalyst that substantially depends on electronic structures of the catalyst. The previous studies have demonstrated that the d-band center (εd)50,51 is an efficient descriptor for the activity of transition-metal-based materials and it is defined as, +∞

εd

∫ = ∫

ED ( E ) dE

−∞ +∞ −∞

D ( E ) dE


(3)


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where D(E) is d states of transition metal in catalysts. Figure 6a indicates ∆GH of various VS2 catalysts as a function of εd. However, we find that ∆GH does not display a regular trend with εd. In other words, the d-band center is not suitable to describe the HER activity of VS2 catalysts. Considering that closer the electronic state is to the Fermi level, the greater its contribution to bonding interaction. Therefore, the reactivity of a catalyst should be determined by both its density of states (D(E)) and a weight factor (w(E)) that quantifies the contribution of every electronic state to the surface reaction.52 For the HER, the activity of an electrocatalyst relies on the abundance of occupied states near the Fermi level because the reaction refers to the charge transfer from the catalyst to the H adatoms. The magnitude of occupied states near the Fermi level (FA) is obtained by the sum of the weight contribution of occupied states as follows (see Figure 6b), FA = ∫

EF

−∞

(4)

D( E ) w( E )dE

where EF is the energy of Fermi level. From previous studies, the derivative of the Fermi-Dirac function, 52 − fT′(E − EF ) , has been validated as a good weight function. The Fermi-Dirac function is defined as,

fT ( E − E F ) =

1 exp[( E − EF ) / kT ] + 1

(5)

Figure 6 (a) ∆GH of pristine and defective VS2 structures as a function of d-band center (εd). (b) The abundance of occupied states (FA) is defined as a weight sum of occupied states of density, E D( E ) w( E )dE , where w(E) is the weight

∫

F

−∞

function that is applied by using the derivative of the Fermi-Dirac function, − fT′(E − EF ) . (c) ∆GH of pristine and defective VS2 structures as a function of DF using kT = 0.4 eV. The overlapped shadow region indicates the optimal range for highly active HER catalysts.


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Using the − fT′(E − EF ) as the weight function can ensure that reaches a maximum at EF and descends to zero with the increase of |E–EF|, as shown in Figure 6b. It can be found that the spreading of the w(E) is sensitive to the magnitude of kT that reaches the optimal value at 0.4 eV. Based on above analysis, we propose a Fermi-abundance (DF) model to describe the HER activity and it is defined as follows, EF

DF

∫ = ∫

ED( E ) fT′ ( E − EF )dE

−∞ EF −∞

(6)

D( E ) fT′ ( E − EF )dE

Considering that electronic states of perfect and defective VS2 near the Fermi level are mainly from V atoms, here D(E) refers to the projected DOS of V atoms in various VS2 structures (see Figures S7 and S8 in SI). Figure 6c shows that ∆GH of pristine and defective VS2 structures as a function of DF. The ∆GH values of various VS2 catalysts indicate an approximately linear trend in relation to their DF values, suggesting that DF can become a good descriptor for the HER activity. A smaller DF value represents the distribution of few occupied states at the vicinity of Fermi level, resulting in that the catalyst has a weak surface activity to capture H atoms (e.g., 1T-Svac). In contrast, the catalyst with a larger DF value will have a strong surface activity to trap H (e.g., 1T-Sad). The calculated DOS indicates that the 1T-Sad structure has greater occupied states than that of the 1T-Svac structure near the Fermi level (see Figure S8). However, a good catalyst should balance the H adsorption/desorption strength based on the Sabatier principle. Therefore, the DF values of the VS2 catalysts located in the range from -0.6 to -0.5 eV should have higher HER activity, such as 2H-Vad and 2H-VS structures. The result reflects that the HER activity of these VS2 catalysts is actually decided by the occupied states near the Fermi level. To examine the rationality of Fermi-abundance model, we also calculated the DF value of Pt(111) surface (see Figure S9). The DF of Pt(111) surface is -0.54, thus Pt(111) surface has a good HER activity. Such a result agrees well with theoretical and experimental reports on the HER activity of Pt catalysts.35,49 Therefore, the Fermi-abundance model should be of generality and be also used to describe the HER activity of other type of electrocatalysts.

4. CONCLUSIONS In summary, we have performed systematic DFT calculations to insight into the role of intrinsic point defects in HER activity of monolayer VS2 catalysts. The calculation of formation energies indicates that there are four types of stable intrinsic defects in 2H phase (i.e., Sad, Svac, Vad, and VS) and three types of stable intrinsic defects in 1T phase (i.e., Sad, Svac, and Vad), respectively. The calculated results of ∆GH suggest that the formation of Svac, Vad, and VS structures in 2H phase and the Vad structure in 1T phase can improve the HER activity of VS2 basal planes, which implies that the synthesis of VS2 should be maintained at the V-rich regime facilitating the catalysts with high HER performance. Based on the 11 Environment ACS Paragon Plus


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analysis of electronic structures, we find that the HER activity of pristine and defective VS2 structures can be well understood by a Fermi-abundance model, which is also applicable to describe a broad class of electrocatalysts for the HER. ASSOCIATED CONTENT Supporting Information Atomic structures of intrinsic point defects in 2H and 1T VS2 basal planes, DFT energies and entropies for calculating ∆GH of pristine and defective VS2 structures, electronic structure of 2H and 1T VS2 monolayers, DOS of pristine VS2 monolayers and Svac defective structures calculated using GGA+U method, projected DOS of V atoms in pristine and stable defective VS2 structures, and projected DOS of Pt(111) Surface. This material is available free of charge via the internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (Haibo Shu), Phone: 86-0571-86875622; [email protected] (Xiaoshuang Chen), Phone: 86-021-35052062. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT This work was supported in part by the National Natural Science Foundation of China (Grant no. 11404309, 51402275, 11334008, and 61290301) and the Fund of Shanghai Science and Technology Foundation (Grant no. 13JC1408800). Computational resources from the Shanghai Supercomputer Center are acknowledged.

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