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1 Enhanced catalytic activity in strained chemically exfoliated WS 2 nanosheets for hydrogen evolution Damien Voiry 1, Hisato Yamaguchi 1, Junwen Li 2, Rafael Silva 3, Diego C B Alves 1, Takeshi Fujita 4,5, Mingwei Chen 4,5, Tewodros Asefa 3,6, Vivek B Shenoy 2, Goki Eda 7,8, and Manish Chhowalla 1 1 Rutgers University, Materials Science and Engineering, 607 Taylor Road, Piscataway, New Jersey 08854, USA. 2 University of Pennsylvania, Materials Science and Engineering, 3231 Walnut St., Philadelphia, PA 19104, USA. 3 Rutgers University, Department of Chemistry and Chemical Biology, 610 Taylor Road, Piscataway, New Jersey 08854, USA 4 WPI Advanced Institute for Materials Research, Tohoku University, Sendai , Japan. 5 JST, PRESTO, Honcho Kawaguchi, Saitama , Japan 6 Rutgers University, Department of Chemical and Biochemical Engineering, 98 Brett Road, Piscataway, New Jersey 08854, USA. 7 National University of Singapore, Physics Department and Graphene Research Centre, 2 Science Drive 3, Singapore National University of Singapore, Chemistry Department, 3 Science Drive 3, Singapore **To whom correspondence should be addressed: manish1@rci.rutgers.edu Supplementary Information Materials Synthesis Bulk WS 2 was intercalated with lithium by reacting WS 2 powder (0.3 g, Alfa Aesar) with n-butyllithium in hexane (1.6 M, 4 ml, Sigma-Aldrich) at 100 under argon. After 2 days, NATURE MATERIALS 1

2 the suspension was filtered over a 450µm pore size membrane (Millipore) and washed 3 times with 50 ml of hexane (Sigma-Aldrich) giving a black powder of intercalated Li x WS 2. Exfoliation in water was achieved immediately after intercalation. Dissolution starts spontaneously but the solution was ultra-sonicated to facilitate the exfoliation of the WS 2 crystals. The solutions were then centrifuged several times to remove lithium cations as well as the unexfoliated materials. Finally the solution was sonicated with a sonicator horn at 25 W (40% amplitude) for 6 min. Electrode Preparation The electrodes for HER measurements for the 1T phase were prepared by simply drop casting the as-exfoliated solution onto the glass carbon electrodes. For 2H HER measurements, films of 1T WS 2 were prepared by vacuum filtering 0.5 ml of the solution over a 3.5 cm diameter membrane with 25 nm pores (equivalent to 6.5 µg/cm 2 ). Films were delaminated on water and transferred on silicon wafer covered with a 300-nm oxide overlayer and annealed at 300 C under vacuum with a 70 sccm flow of a N 2 /H 2 mixture. Poly(methyl methacrylate) (PMMA) was then spin coated on the top of WS 2 and the silicon oxide layer was etched by a 1M NaOH solution. The delaminated films (PMMA/WS 2 ) were finally washed in water and transferred on the glassy carbon electrode and the PMMA layer was removed in acetone. No chemical modification/degradation (such as oxidation) was observed during this process as confirmed by XPS. Platinum nanoparticles (1%) on carbon (Sigma-Aldrich) were 2 NATURE MATERIALS

3 dispersed in ethanol at 2 mg/ml. 10 µl was deposited on the working electrode (equivalent to 0.28 mg/cm 2 ) and then was covered by 7 µl of the 5% Nafion solution. Materials Characterization AFM data were obtained with a Digital Instruments Nanoscope IV in tapping mode with standard cantilevers with spring constant of 40 N/m and tip curvature <10 nm. The TEM images were taken in a JEOL 2000X at 200 kv. HAADF STEM imaging was performed using JEOL JEM-2100F TEM/STEM with double spherical aberration (Cs) correctors (CEOS GmbH, Heidelberg, Germany). The lens aberrations were optimized by evaluating the Zemlin tableau of an amorphous carbon. The acceleration voltage was set to 120 kv and the collecting angle was between 100 and 267 mrad. Figure S1: Schematics of WS 2 monolayer structure as viewed down the c-axis for corresponding STEM-HAADF in Figure 2b and 2c in the main MS. The left image represents the distorted 1T superlattice structure while right image is the 2H structure. The orange circles represent tungsten atoms while the light and dark green circles NATURE MATERIALS 3

4 represent S atoms in the upper and lower layers, respectively. In the 2H structure, the two layers of S atoms overlap in position and only those in the upper layer are shown. The stress tensor map was calculated using the peak pair analysis (PPA) approach outlined in Ref. 44 in the main text. The image analysis was conducted using DigitalMicrograph software. A more detailed stress tensor map for the distorted 1T superlattice obtained from the high resolution STEM analysis is shown in Figure S1. Figure S2: Stress tensor map of distorted 1T superlattice phase calculated from peak pair analysis of the high resolution TEM results. The lighter regions represent tensile stress while the darker regions represent regions of compressive stress. The image is 7.45 nm x 7.45 nm. It should be noted that out-of-plane displacement of the atoms is assumed to be negligibly small compared to the lateral displacement. Raman spectra were measured using an InVia Raman microscope (Renishaw) at excitation laser wavelength of 514 nm. X-Ray photoelectron spectroscopy (XPS) experiments were performed with a Thermo Scientific K-Alpha spectrometer. All spectra were taken using Al Kα micro focused monochromatized source ( ev) with a 4 NATURE MATERIALS

5 resolution of 0.6 ev and a 400 µm spot size. The WS 2 thin films were measured on silicon dioxide wafer and Si2p3 was taken as a reference at ev. Raman and XPS Analysis Raman shift of as-deposited and annealed WS 2 films are shown in Figure S3a. Spectrum of bulk 2H WS 2 is also provided for comparison. Two prominent peaks corresponding to the in-plane E 1 2g and out-of-plane A 1g modes of 2H WS 2 are observed for all three samples. However, the as-exfoliated samples exhibit small peaks in the lower frequency region, similar to what occurs in chemically exfoliated MoS 2, that correspond to the distorted 1T phase Raman active modes that are not allowed in the 2H phase. The fraction of each phase was quantified using XPS. The W peaks at ~ 31 and 36eV correspond to the 4f7/2 and 4f5/2 components of the 2H-WS 2 phase. Deconvolution of these peaks reveals that they are shifted to slightly lower energies compared to the 2H phase, as indicated by the curve fits in Figure S3b. In the as-exfoliated films, the two primary peaks correspond to the 1T phase. The contribution of this phase decreases upon annealing at 300 C, where the spectrum matches closely the bulk 2H phase WS 2. Similar peak shifts are found in the sulfur peaks, indicating the presence of 1T phase. The quantification of the structure using XPS reveals that the ~80% of the as-exfoliated WS 2 sheets consist of the metallic 1T phase, in contrast with similar analysis of as-exfoliated MoS 2 which contains only 50% 1T component (Ref 31 in the MS). Upon annealing, the concentration of the 1T phase decreases and the nanosheets consist primarily (~80%) of the 2H phase. The large fraction of 1T phase is also confirmed by electrical NATURE MATERIALS 5

6 measurements that show that the as-exfoliated WS 2 nanosheets are electrically conducting while the annealed material is semi-conducting. Figure S3: a, Raman spectra of WS 2 samples deposited on silicon dioxide. The J 1, J 2, and J 3 weak peaks in the shaded regions are only active in the as-exfoliated 1T WS 2 phase. The spectrum for WS 2 nanosheets annealed at 300 o C resembles that of 2H bulk phase that is also shown. b, XPS spectra showing the W5p and W4f core level peak regions. W4f peaks were deconvoluted with the 2H (light red) and 1T (light green) components. Based on the deconvolutions, the 2H-1T content from the samples can be determined. As deposited WS 2 platelets are composed of ~ 80 % 1T phase whereas after annealing at 300 o C 80% of the material is converted to 2H. Structural Evolution of Chemically Exfoliated WS 2 Nanosheets The as-exfoliated WS 2 nanosheets predominantly exhibit distorted 1T structure. This has been verified with extensive TEM, Raman and XPS analysis. Raman and XPS were used to monitor the evolution of the WS 2 phase from the distorted 1T to 2H. It can be seen from Figure S4a that the contribution of the 1T phase decreases with temperature while 6 NATURE MATERIALS

7 the contribution from the 2H phase increases, as indicated by the fitting the W 4f7/2 and 4f5/2 peaks in XPS. The 1T phase contribution in Figure S4a is indicated by the light green curve fits while the light red curve fits represent the 2H phase. The ratio of the two phases as a function of the annealing temperature is summarized in Figure S4b. The transition from 1T to 2H occurs at a transition temperature of around 200 o C, similar to what has been reported previously (See Ref 39 in the main text). It can be seen that the as-exfoliated samples consist of ~80% 1T phase while the annealed samples consist of ~ 80% 2H phase. Figure S4: (a) XPS spectra of chemically exfoliated WS 2 nanosheets as a function of annealing temperature. The light green curve fits represent 1T contribution while the light red curve fits represent the 2H phase contribution. (b) Summary of 1T phase concentration and thin film sheet resistance (see below for details) as a function of annealing temperature. The Raman spectra were also monitored as a function of the annealing temperature, as shown in Figure S5. The spectra reveal that the intensities of the Raman active modes NATURE MATERIALS 7

8 from the 1T phase decrease with annealing temperature while the peaks corresponding to the 2H phase become sharper. Spectrum of bulk 2H WS 2 is also shown for comparison. Figure S5: Raman spectra of chemically exfoliated WS 2 nanosheets as a function of annealing temperature. Electrical Properties Electrical and photoluminescence (PL) measurements were performed in order to monitor the structural evolution during annealing. The current voltage (I-V) characteristics of thin films of chemically exfoliated WS 2 are shown in Figure S6a. The as-exfoliated material exhibited linear I-V characteristics and low sheet resistance 430k /sq. reflecting its more conducting nature. Annealing leads to an increase in sheet resistance, especially above 200 o C, consistent with the onset of transition from 1T to 2H phase. The resistance as a 8 NATURE MATERIALS

9 function of the annealing temperature (as well as the phase concentration) is shown in Figure S4b. The transition to predominantly 2H phase was also corroborated by photoluminescence measurements as shown in Figure S6b. Excitation by 514nm laser of a monolayered film gave rise to PL at 2.01eV, which is in agreement with the direct band gap of 2H WS 2 monolayer. Very weak or no PL was observed in partially annealed WS 2 nanosheets or fully annealed films with thicknesses substantially higher than a monolayer, as indicated in Figure S6b. These results are similar to our findings on MoS 2 (See Ref 31 in the main text). Figure S6: (a) DC current versus voltage measurements as a function of annealing temperature on WS 2 thin films composed of chemically exfoliated nanosheets. (b) PL of thick and thin WS 2 films annealed at 300 o C. The PL is only observed for the thin films, which exhibit direct band gap. The inset shows the Raman peaks for a thick and thin WS 2 films. NATURE MATERIALS 9

10 1T and strain relationship: We have correlated the strain values to the 1T phase concentration by measuring the stress tensor maps in the TEM. We found that the strain is directly correlated with annealing (i.e. decrease in 1T concentration). Our analysis suggests that 1T concentrations of ~80%, ~50%, ~25%, and 0% would correspond to strains of ~ 3%, ~1%, ~ 0.3%, and 0%. Figure S7: Stress tensor maps of WS 2 nanosheets. Left most image represents assynthesized films containing maximum amount of 1T phase concentration. The images represent decreasing 1T phase concentration with the right one representing 100% 2H phase showing no strain. Additional HER properties: The key step in HER is the adsorption of the proton on the active site. To assess this, we have varied the ph. We found that WS 2 is active over a wide range of ph although the activity decreases after ph=1 due to the strong diminution of the quantity of protons available. Similar behavior has been reported in the case of amorphous molybdenum sulfide with a strong decrease of the current density observed when increasing the ph from 1 to 2 (Ref 16). Although the direct interpretation of the HER mechanism from the 10 NATURE MATERIALS

11 Tafel slope is limited to well-defined systems such as Pt, the dramatic increase of the Tafel slope can be interpreted as decrease in hydrogen adsorption of WS 2 as ph increases. Figure S8: Variation of current density versus the overpotential (RHE) as a function of the ph. The highest current density is obtained for the lowest ph, consistent with the solution having the highest proton concentration. The inset shows that the Tafel slope also increases with ph indicating that the rate limiting proton adsorption step is strongly influenced by the proton concentration. Overpotential = E (RHE) ( x ph). Active sites measurements: The density of active sites was measured using underpotential deposition (UPD) of copper using the method described by Green et al. in Ref 28 in the MS. Green et al. have NATURE MATERIALS 11

12 demonstrated that the surface activity of platinum or ruthenium can be determined by measuring the charges exchanged during copper stripping after deposition at the underpotenial regions. By comparing the charges exchanged during hydrogen adsorption and copper stripping in sulfuric acid in absence and presence of cupric sulfate (CuSO 4 ) at various potentials, they found that when shifting the potential toward underpotential regions, the charge ratio Q Cu /Q H decreases and reaches a plateau for Q Cu /Q H equal to 2. This ratio of 2 is expected when monolayer cupper is deposited at the same site as hydrogen since copper stripping involves 2 electrons versus one for hydrogen adsorption. At higher potentials the ratio decreases indicating that less copper is deposited compared to the quantity of adsorbed hydrogen. We found that exfoliated WS 2 has the ability to reduce copper at higher potentials (underpotential deposition, UPD) than its thermodynamic potential (overpotential deposition, OPD) and the method of Green et al. was applied to quantify the number of active sites. Figure S9: Cycling voltammetry of the exfoliated WS 2 in presence of cupric sulfate reveals the presence of overpotential stripping and deposition signal (I A and Ic respectively) and broad peaks (II A and II C ) corresponding to the underpotential regions 12 NATURE MATERIALS

13 between 300 mv and 650 mv vs. RHE. Under the same condition bulk WS 2 shows a small UPD signal close to the OPD potential between 250 and 300 mv vs. RHE whereas glassy carbon does not exhibit any underpotential deposition signal, as shown. Experimentally, the charges associated with the copper stripping were measured in three steps. In a 0.1 M of H 2 SO 4 and 2mM of CuSO 4 solution, the electrode surface was thoroughly electrochemically cleaned prior to performing any deposition by applying a potential of 673 mv vs. RHE for 120 seconds. Then the potential was lowered and kept constant for 100s to deposit copper after which it was progressively increased to 673 mv vs. RHE to oxidize the copper. The current associated with the copper stripping was measured. Hydrogen adsorption was measured the same way using a 0.1 M H 2 SO 4 solution in absence of copper ions. The results agree perfectly with the observations reported by Green et al. and the Q Cu /Q H reaches at plateau of 2 after 525 mv vs. RHE (See Figure S9). This indicates that at this potential the same quantity of copper as hydrogen is deposited on the surface of the electrode at the active sites. From the quantity of charges generated during the Cu stripping at a potential of deposition of 573 mv vs. RHE, it can be calculated that 3.21 x mol of Cu (Q Cu /96500/2) have been deposited. From this, an active site density ranging from 4.5 x sites/cm x sites/cm 2 (n Cu /A electrode ) is obtained for hydrogen adsorption on 1T WS 2 nanosheets. Similar analyses on the annealed samples reveal lower active site density of 1.5 x sites/cm 2. The current exchange density was calculated using the method described previously in Ref. 4. From the Tafel plot, we measured the current density to be 6.2 x 10-6 NATURE MATERIALS 13

14 A/cm 2 geometric. From the measured site density of 4.5 x cm -2, the exchange current density per site is equal to 1.37 x A/sites. This value was then multiplied by the density of sites in case of platinum (1.5 x cm -2 ) for a direct comparison. Based on this method, the exchange current density of strained chemically exfoliated WS 2 was found to be 2 x 10-5 A/cm 2. Q Cu /Q H Potential (V vs. RHE) As-Deposited Figure S10: Q Cu /Q H reaches at plateau of 2 after 525 mv vs. RHE indicating that at this potential the same quantity of copper as hydrogen is deposited on the surface of the electrode at the active sites. Experimental details for the active sites measurements: Electrodes for active site measurements were prepared in the exact same manner as for HER experiments. 14 NATURE MATERIALS

15 Active site measurements were performed using two 0.1 M H 2 SO 4 solutions: one containing only sulfuric acid, the second one containing the cupric sulfate at 2 mm. Solutions were degassed with Ar prior the measurements and the measurement were done under an Ar blanket. Cyclic voltamperometric were performed with a scan rate of 2 mv/s and a saturated calomel electrode was used as the reference. Before each measurement, electrodes were cleaned at 673 mv for 120 s and the potential of deposition was maintained constant for 100 s. Stripping currents were measured by progressively increasing the potential from the deposition potential up to 673 mv with a scan rate of 2 mv/s. Discounting the presence of Lithium impurities: We have ruled out any possibility of Li in our exfoliated samples by performing highly sensitive Rutherford backscattering spectroscopy (RBS) analysis. The results shown in Figure S11 clearly demonstrate that Li is not present in our samples. NATURE MATERIALS 15

16 Figure S11: RBS results from an exfoliated WS2 nanosheet film showing no Li is present (red curve). A curve from a Li intercalated sample is also shown to demonstrate that Li can be detected with this technique. Curves are normalized to the W peak. Stability of 1T Phase as a function of long term stressing: To assess the electrochemical stability of the metastable 1T electrodes, we performed over 10,000 cycles to monitor the overpotential. We also stressed the electrodes by monitoring the current density for more than 100 hours at an applied cathodic potential of 0.3V. The variation in the current density, percent change in the overpotential, and the change in 1T concentration as a function of the electrode operation time are shown in the 16 NATURE MATERIALS

17 main MS. Below we provide the XPS and Raman data showing that spectroscopically the 1T phase remains substantially stable during operation. Figure S12: (a) W XPS peaks as a function of catalytic activity time. The fits represent ratio of 1T phase which was found to remain ~ 80% +/- 5%. (b) Raman spectra showing negligible change in 1T features at different catalyst operation times. In addition to the long term testing, we also measured the concentration of 1T phase in samples stored in our laboratory for over the past year to investigate whether the 1T phase relaxes to the 2H phase. NATURE MATERIALS 17

18 100 1T content (at. %) Days Films Solutions Figure S13: 1T phase concentration as a function of the number of days after exfoliation. It can be seen that the 1T phase remains stable with time. Impedance Measurements: Impedance measurements were performed on electrodes consisting of 1T and 2H films, bulk WS 2 powder as well as glassy carbon reference. 18 NATURE MATERIALS

19 Figure S14: Impedance spectra for glassy carbon electrode alone. Comparison between Pt and carbon counter electrode: Platinum contamination is a major risk in electrocatalysis since platinum would artificially increases the activity of WS 2. Figure S15 shows the polarization curves obtained from as-deposited WS 2 using platinum and carbon counter electrode. No difference is noticeable and this rules out any Pt contamination during the measurements (Figure S15). NATURE MATERIALS 19

20 Figure S15: Polarization curves for as-deposited WS 2 when using Pt or Carbon as counter electrode. Calculation of Turn Over Frequency: The exchange current densities (i 0 ) of the different samples were determined from the Tafel plots. The linear fit of the Tafel plot for the as-deposited sample gives an exchange current density of 6.2 x 10-5 A/cm 2. Turn-over frequencies were calculated from the density of active sites, which were explicitly measured using the method described above. This results in a density of active sites of ~4.5 x cm -2. Turn-over frequencies were then calculated using the following relation (See Ref 5 in the main text): TOF (s -1 ) = (i, A/cm 2 ) / ((4.5 x sites/cm 2 )*(1.602 x C/e-) (2 e - /H 2 )) Replacing the current density (i, A/cm 2 ) by the exchange current density determined from the Tafel plot gives a turn-over frequency of 0.043s NATURE MATERIALS

21 Turn-over frequencies at the different potentials are calculated the same way using the current density (i, A/cm 2 ) instead of the exchange current, i 0. Computational approach The density functional calculations were carried out by using the Vienna ab initio simulation package (VASP), with exchange-correlation functional described by Perdew- Burke-Ernzerhof generalized gradient approximation (PBE-GGA) and interaction between core electrons and valence electrons by the frozen-core projector-augmented wave (PAW) method. An energy cutoff of 600 ev was used for plane wave basis expansion. The fully relaxed lattice constants are a = 3.18 Å, b = 3.18 Å and a = 3.19 Å, b = 6.54 Å for 2H-WS 2 and distorted 1T-WS 2, respectively. W-W bond length in 2H- WS 2 is 3.18 Å. In the distorted 1T-WS 2 the W-W can have bond lengths of 2.77 Å and 3.19 Å. These values compare well with our experimental measurements. The hydrogen adsorption energies have been calculated with a 4x2x1 supercell shown in Figure S16 for 1T-WS 2. Usually denser k points are required to achieve convergence for metals. However, the bands of 1T-WS 2 are rather flat as shown in Figure S17 such that we can sample the Brillouin zone by using Monkhorst-Pack 4x4x1 k-point grid. Denser sampling only gives rise to a total energy change less than 2.5 mev as shown in Figure S18 for the unit cell of 1T-WS 2. We also carried out spin-polarized calculations for different H coverage of 0% strain which only show total energy changes smaller than 1 mev with respect to the non-spin-polarized results as indicated in Figure S19. A vaccum region of greater than Å was added along the direction normal to the sheet plane to avoid the interaction between periodic supercells. We carried out relaxation for all supercells and NATURE MATERIALS 21

22 all atoms in the supercells were allowed to move until the force on each atom is less than 0.02 ev/å. Although the 2H-WS 2 is more stable with total energy ev lower than that of the distorted 1T-WS 2, there is a bigger energy barrier for the phase transformation. The nudged elastic band [citation: H. Jonsson, G. Mills, and K.W. Jacobsen, in Classical and Quantum Dynamics in Condensed Phase Simulations, edited by B. J. Berne, G. Ciccotti, and D. F. Coker (World Scientific, Singapore, 1998)] was applied to determine this energy barrier. Because of the lattice mismatch between 1T and 2H structures, we employ the lattice constants of 1T phase for both 1T and 2H structures and results are presented in Figure S20. The energy barrier is determined to be 0.92 ev. The tensile strain experienced by the 2H structure makes the stabilization energy reduce to 0.49 ev. We also carried out calculations with lattice constants of 2H phase. The energy barrier is 0.97 ev and the compressive strain experienced by the 1T structure increases the stabilization energy to 0.59 ev. The stability of hydrogen can be described by the differential hydrogen adsorption energy ΔE H, which is defined as ΔE H = E WS2 + nh - E WS2+(n-1)H E H2, Where E WS2+nH is the total energy for the WS 2 system with n hydrogen atoms absorbed on the surface, E WS2+(n-1)H is the total energy for (n-1) hydrogen atoms adsorbed on the surface and E H2 is the energy for a hydrogen molecule in the gas phase. The ΔE H obtained from the ground state calculations does not include the contributions from the 22 NATURE MATERIALS

23 vibrational motion and the entropy. The Gibbs free energy for hydrogen adsorption can be calculated by including these corrections: ΔG H = ΔE H + ΔE ZPE - TΔS H where ΔE H is the differential hydrogen adsorption energy, ΔE ZPE is the difference in zero point energy between the adsorbed hydrogen and hydrogen in the gas phase and ΔS H is the entropy difference between the adsorbed state and the gas phase. The contribution from the configurational entropy in the adsorbed state is small and is neglected. We can take the entropy of hydrogen adsorption as ΔS H = 1/2S H2 where S H2 is the entropy of molecule hydrogen in the gas phase at standard conditions[citation: NIST Chemistry WebBook, NIST Standard Reference Database Number 69, edited by Linstrom, P. J. & Mallard, W. G. (National Institute of Standards and Technology, Gaithersburg, MD, 2009), (1 bar of H 2, ph = 0 and T = 300 K). We have calculated the vibrational frequencies of H adsorbed on site 1 of the distorted 1T-WS 2 by using finite differences to determine the Hessian matrix. The calculated vibrational frequencies are 2521 cm -1, 668 cm -1 and 562 cm -1. With these values the Gibbs free energy is ΔG H = ΔE H eV. Our calculations show that vibrational frequencies do not exhibit sensitive dependence on strains studied in this paper, so we use the same value for all corrections. NATURE MATERIALS 23

24 Figure S16 The supercell used in the calculations of hydrogen adsorption on the surface of the distorted 1T-WS 2. Gray and yellow spheres represent the W and S atoms, respectively. The numbers indicate the favorable sites of hydrogen binding. Figure S17: Electronic band structure of distorted 1T WS 2. The Fermi level is set to zero and is indicated by blue solid line. 24 NATURE MATERIALS

25 Figure S18: Convergence test of k-point sampling. The 4x4x1 k grids used in our calculations for 4x2x1 supercell is equivalent to the 16x8x1 k grids for 1T unit cell. Denser k grids such as 24x12x1 and 32x16x1 only lead to total energy change less than 2.5 mev. Figure S19: Energy difference between spin-polarized and non-spin-polarized calculations for unstrained 4x2x1 supercell shown in Figure X. (1) corresponds to one hydrogen at site 1 and (1,2), (1,3), (1,5), and (1,6) correspond to two hydrogen atoms with one at site 1 and the other one at site 2, 3, 5, and 6, respectively. NATURE MATERIALS 25

26 Figure S20: Phase transformation energy barrier and stabilization energy between 1T and 2H structures. The lattice constants of 1T-WS 2 were used for both 1T- and 2H-WS 2 in the calculations. With lattice constants of 2H-WS 2 for both 1T- and 2H-WS 2 the energy barrier and stabilization energy are determined to be 0.97 ev and 0.59 ev, respectively. We found that the hydrogen prefers to adsorb on the top of the S atoms which are indicated in Figure S16. We studied two different hydrogen adsorption coverages (1/16 and 2/16) for the distorted 1T-WS 2 and varied the tensile strain from 0% to 4%. The calculated Gibbs free energies are shown in Table I and Figure S21. The strain can strengthen the hydrogen binding on the surface. For small strain, the low coverage can effectively evolve hydrogen. With higher strain, the high coverage will also be able to turn over. We also analyzed the density of states of the distorted 1T-WS 2 under different strains and the results for 0% and 3% strains are depicted in Figure S22. Note that strain 26 NATURE MATERIALS

27 significantly increases the density of states near the Fermi level. This may account for the enhanced hydrogen binding and the catalytic performance. We also studied the hydrogen adsorption on the surface of 2H-WS 2 and a 4x4x1 supercell is employed. The size of this supercell is close to that used in the study of distorted 1T- WS 2. Our calculations show that even under 4% tension, the Gibbs free energy for 1/16 coverage is still as high as 1.93 ev. This indicates that the tensile strain in the range studied here can not make the surface of 2H-WS 2 have good catalytic activity. Table I: Calculated Gibbs free energy for H under strain ranging from 0.0% to 4.0%. The 1/16 coverage corresponds to one hydrogen at site 1 and the 2/16 coverage correspond to two hydrogen atoms with one at site 1 and the other one at site 2, 3, 5, and 6, respectively. Strain ΔG H (ev) 1 ΔG H (ev) 1, 2 ΔG H (ev) 1, 3 ΔG H (ev) 1, 5 ΔG H (ev) 1, 6 0.0% % % % % NATURE MATERIALS 27

28 Figure S21: Calculated Gibbs free energy for H under strain ranging from 0.0% to 4.0%. (1) corresponds to 1/16 coverage with one hydrogen at site 1 and (1,2), (1,3), (1,5), and (1,6) show the Gibbs free energies of the 2/16 coverage corresponding to two hydrogen atoms with one at site 1 and the other one at site 2, 3, 5, and 6, respectively. 28 NATURE MATERIALS

29 Figure S22: Density of states of the distorted 1T-WS 2 without or with 3% strain. The Fermi level is set to be zero and is indicated by the vertical line. NATURE MATERIALS 29