Introduction

MoS2 is a promising candidate to replace Pt for electrocatalytic hydrogen evolution reaction (HER) due to its environmental friendly and low cost characteristics1,2,3. While increasing the conductivity via forming heterojunction bi-layer with a conductive substrate can promote the overall catalytic performance4,5,6, the performance of pristine MoS2 is restricted by the density of active sites7,8,9,10. The pursuit to maximize MoS2 utility inspires researchers to explore various ways to rouse the activity of inert sulfurs in the MoS2 basal plane. For example, edge-site engineering9,11, phase transformation12,13, amorphization14,15, and in-plane doping/vacancy modifications16,17,18,19,20 have been reported. Notably, changing the local configurations18,21,22,23,24 by introducing atomic defects (doping or vacancy) is preferable as defected MoS2 exhibits better stability compared to transformed 1T′ phase25 and amorphous MoS210. However, the reported activity of in-plane sulfur enhanced by local configuration modification is still far from that of Pt-based catalysts26. This is because the large energy are required to break the in-plane Mo-S bonds. In fact, few types of atomic local configurations have been realized in the basal plane of MoS227,28,29,30, so the tuning ability of local configurations is quite limited so far16. Hence, in order to improve the intrinsic activity of in-plane sulfur atoms, it is essential to understand the intrinsic correlation and explore new methodologies to enrich stable and highly efficient local configurations.

Herein, we conducts both computational and experimental investigations in order to establish a correlation between local configuration and the electrocatalytic activity of monolayer MoS2. A group of stable local configurations with non-noble period-IV single atom or clusters (Co, Fe, V, and Cr) accompanying additional sulfur vacancy in the in-plane domain of MoS2 have been attained. Given the correlation between binding strength and local configurations electronegativity, the activity of in-plane sulfur can be regulated by electron transfer capacity of local configurations. The peculiar triangular-shape Co atom cluster surrounding one sulfur vacancy configuration (viz., 3CoMo−VS) is identified by both calculation and experiments to be most efficient to activate the inert sulfur sites. Correspondingly, a distinct enhancement in HER activity is achieved (η10: 75 mV and Tafel: 57 mV dec−1), exhibiting the highest intrinsic HER activity among MoS2 materials. The microcell HER measurements show a volcano-like relationship between content of specific local configuration and activity, which corroborates the optimized concentration of 3CoMo−VS. Therefore, as demonstrated in the present work, it is possible to further activate the in-plane sulfur sites by rational engineering of the local configurations. This result may provide a route to unleash the electrocatalytic potential of TMD materials for efficient hydrogen generation in acidic solutions.

Results

Design efficient and stable local configurations

The activation of the basal plane in TMDs have been extensively studied to achieve the stable structure and enhance their catalytic activity31,32,33. Sulfur vacancy (Vs) on the surface is an electron donor and can induce a localized gap state in MoS2. Below a critical carrier density, the transport of donor states is governed by nearest-neighbor hopping at high temperatures and variable-range hopping (VRH) at low temperatures23,34,35,36. Regional charge states around a defect structure are suggested to make an important contribution to regulating the catalytic activity. Based on the above analysis, we believe that it is reasonable to monitor the defects induced Bader charge fluctuation, and the H adsorption to define the active sites through DFT computational screening.

To study the TM and synergistic effect of Vs on sulfur sites, we have considered six configurations including TM atoms (TM: Co, V, Fe, and Cr; TM amounts from 1 to 3) with or without Vs (structures see in Supplementary Fig. 1 and Supplementary Note 1) that are set as models to screen stable catalytic structures through DFT calculations. The hydrogen adsorption free energy (ΔGH) is an effective descriptor to predict the activity for various catalyst systems37. The ideal value of ΔGH is 0 eV, which corresponds to a thermoneutral state of the adsorbed atomic hydrogen and efficient proton/electron transfer and hydrogen release1. The correspondingly calculated ΔGH of monolayer MoS2 with varied local configurations are further exhibited in Supplementary Fig. 2 and Supplementary Table 1, indicating the stronger H* adsorption on atomically structured MoS2 than on intact MoS2. In addition to intrinsic activity (ΔGH), structural stability affecting the final electrochemical durability of catalysts should be considered. Based on the formation energies of all possible configurations (Supplementary Fig. 3), the 3CoMo−Vs, 3FeMo−Vs, 1VMo and 1CrMo are identified as the most stable structures in the different possible TM-introduced MoS2 (Fig. 1a). Together with the activity (value of ΔGH), the 3CoMo−Vs is expected to be the potential structure with both good stability and high activity. The predicted HER activity of MoS2 with different local configurations following the trend 3CoMo−Vs > 1VMo > 3FeMo−Vs > 1CrMo (Fig. 1b). This trend remains the same with solvation correction, as demonstrated by our calculations with the implicit solvation model (Supplementary Fig. 4). The hydrogen adsorption free energy (ΔGH) on basal plane of intact MoS2 is far away from the optimal value. After tuning by local configurations, the ΔGH value of −0.085 eV comparable to that of Pt38, is achieved due to the much stronger bonding strength in S atoms with the assistance of 3CoMo−Vs, which surpasses predicted activity of edge sites8. As expected, different configurations induce varied activity; all the structures with co-existence of Vs and TMMo atoms synergistically tunes the ΔGH when compared to single one (Supplementary Table 1). In addition, the monolayers are used instead of porous 3D materials, minimizing the double layer effect induced by porosity. It is supported by CV curves in non-Faradaic region (blue rectangular in Supplementary Fig. 5) with nearly no hysteresis loop.

Fig. 1: DFT calculations to predict effect of local configurations to HER activity of MoS2.
figure 1

a The most stable structures of MoS2 with 3CoMo−Vs, 3FeMo−Vs, 1VMo, and 1CrMo configurations and the S bonding with H is marked as red circles. b The free energy diagram of corresponding configurations and pristine MoS2. c The correlation between change of Bader charge of local configuration around sulfur atoms and hydrogen adsorption free energy (ΔGH). The dashed line is linearly fitted with R2 = 0.95. The Bader charge changes of d Co atoms, e S1 and next-neighbor S atoms, and f the next-neighbor Mo atoms when 3CoMo−Vs is introduced in the MoS2.

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It is important to reveal the underlying mechanism of enhanced catalytic activity due to the local configuration. The above analysis indicates that the defects (TM substitution and S-vacancy) and H adsorption could induce charge fluctuation of the regional structure due to electron delocalization of MoS2. In principle, the catalytic activity depends on the charge transfer capacity before and after H adsorption. To identify the effective catalytic structure, we show the nearest and the next-neighbor atoms which possibly induce a charge fluctuation in HER (Supplementary Fig. 6 and Supplementary Note 2). First, the nearest metals (nMo and doped (3–n)TM, n = 0, 1, 2) and the adsorption S1 atom have relatively large change in charge (Fig. 1d–f, Supplementary Figs. 7–10). As a result, we consider (3–n)TM–S–nMo as the first-order catalytic structure that is comprised of TM substitutes, adsorption S atom, and the nearest Mo atoms. In contrat, the change in charge for the next-neighbor S and Mo atoms is relatively small. So they are considered as the second-order structure as the distance from the adsorption site is large. As a result, it is reasonable to assume the charge regulation of the second-order catalytic structure has a negligible effect on that of the first-order one. The radial distributions of charge distribution are presented in Supplementary Figs. 7–10. Therefore, in our study, we calculate the total charge difference of adsorption S atom and the nearest metals to depict the charge transfer capacity to S–H bonds. The amount of charge transfer of local configuration (namely, atoms to induce the charge transfer includes: nearest nMo, doped (3–n)TM, n = 0, 1, 2 and adsorption S1 atom) is linearly correlated with ΔGH. This result indicates a charge regulation effect by the local configuration on HER activity (Fig. 1c). The linear correlation indicates that charge transfer capacity induced by varied local configurations are mainly delocalized in the first-order catalytic structure instead of on individual sulfur atoms. We found that, a charge difference around 0.07e− (which corresponds to ΔGH = 0 eV) should correspond to a high HER catalytic activity.

Realization and characterizations of local configurations

In light of the superior activity induced by the predicted local configurations, we employ the chemical vapor deposition (CVD) method to synthesize several monolayer MoS2 samples with various in-plane local configurations (Methods). The optical images of Co, Fe, Cr, and V-containing MoS2 monolayers are shown in Supplementary Fig. 11a–d. Raman spectra confirm that all the as-prepared samples preserve the lattice structure of MoS2 (Supplementary Fig. 12), as seen from the characteristic A1g mode at ~401 cm−1 and the E2g1 mode at ~381 cm−1 observed in pristine MoS2 monolayer39. In addition, the Raman mappings indicate homogenous elemental distribution (Supplementary Fig. 13). Atomic force microscopy (AFM) measurements further confirm that the as-prepared MoS2 domains are monolayers (Fig. 2a–d) with a thickness ranging between 0.7 and 0.9 nm. As for the the system with small doping concentration, the peak-shift is ascribed to the dopant induced Fermi level movement40. However, the shifts of X-ray photoelectron spectra in both Mo 3d and S 2p are very small (below 0.3 eV, see Supplementary Fig. 14), likely due to the low dopant concentrations. Therefore the minor peak shift cannot justify if the dopants incorporate into the MoS2 lattice. More evidence is provided by the high-resolution spectra of TM 2p (Supplementary Fig. 15), which show clearly the formation of metal-sulfur bonds in all samples and support the substitutional dopants within the MoS2 lattice.

Fig. 2: Imaging of MoS2 monolayers with various local configurations.
figure 2

AFM images of a 3CoMo−Vs, b 3FeMo−Vs, c 1VMo, and d 1CrMo samples, illustrating the monolayer nature of the as-synthesized MoS2. e–h Atomic resolution STEM images of the TM-containing MoS2 samples with i–l corresponding electron energy loss spectrum on single TM. The images confirm that, while Co and Fe atoms prefer to form triangular clusters where three TM atoms connect a central sulfur vacancy (3TMMo−Vs, highlighted by green circles), V and Cr only form substitutional single atom without sulfur vacancy (1TMMo, highlighted by white dashed circles), in good consistence with the theoretical prediction.

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The annular dark-field (ADF) scanning transmission electron microscopy (STEM) imaging and electron energy loss spectroscopy (EELS) are used to further confirm the local atomic configurations. Figure 2e–h show the atomic structure of the Co-, Fe-, V-, and Cr-containing MoS2 monolayers, respectively. All four images show the lattice of MoS2 with Mo and S atoms alternating in bright and dim spots periodically. The TM atoms, which occupy the metal sites, show lower image contrast than typical Mo atoms but similar to S2 columns due to the nature of the STEM imaging27. The line intensity profile of the single isolated dopant site and comparison to the STEM simulation (Supplementary Fig. 16) confirm that the TM atoms successfully doped into the lattice rather than the adatoms on the surface of MoS2. A more careful inspection reveals two main types of local configurations as predicted by previous theoretical calculations: one TM atom substitutes the Mo site forming an isolated single TM site, as marked by the white circles in all four TM-containing MoS2 monolayers (Fig. 2g, h, k, l); three TM atoms forming a triangular cluster with a connecting central sulfur vacancy, named as 3TMMo−Vs, as highlighted by green circles in Co and Fe-containing system (Fig. 2e, f, i, j). However, we find the 3TMMo−Vs are the dominating configuration in the Co- and Fe-containing MoS2 monolayers. The single isolated TM sites account for very small ratio (<10%) compared to the 3TMMo−Vs (Supplementary Figs. 17, 20c, and 21c; Supplementary Notes 3, 6, and 7), which corroborates that the latter are the dominating causes towards the HER activity.

On the other hand, Cr and V form predominantly isolated single TM sites in the MoS2 lattice. This is due to the different formation energy of the two types of local configurations with different TM atoms. The single atom EELS measurements on the TM in each image further confirm the chemical identity of the corresponding introduced element, as recognized by the sharp L edges of Co, Fe, V, and Cr, respectively, offering strong evidence of the presence of TM atoms and the consistence of the predicted local configurations. The reference EELS spectra taken away from the dopant site (Supplementary Fig. 18 and Supplementary Note 4) confirms the observed sharp peaks in the spectra of Fig. 2 are not an artifact during the collection at the dopant site.

Electrochemical test of MoS2 with local configurations

To verify the predicted HER activity of in-plane sulfur modulated by designed local configurations, the effects of 3CoMo−Vs, 3FeMo−Vs, 1CrMo, and 1VMo on HER catalytic activity are examined using a three-electrode electrochemical cell in an electrolyte containing 0.5 M H2SO4. Data are compared to pristine MoS2 and commercial Pt/C. Before LSV tests, electrochemical activation was implemented. Stable CVs of configured MoS2 samples after electrochemical activation process (black curves in Supplementary Fig. 19 and Supplementary Note 5) indicate no phase change during activation. Figure 3a shows linear-sweep voltammograms (LSV) in the cathodic direction after the correction of ohmic potential drop (i.e., iR), where the currents are normalized to the electrode geometric area. It is seen that the pristine MoS2 with an overpotential of 317 mV at 10 mA cm−2 (η10) shows an inferior HER activity than those of configured MoS2. The optical image of pristine MoS2 as shown in Supplementary Fig. 22 shows the similar edge length with that of configured MoS2, excluding the edge effect on different activity. Both the 3FeMo−Vs and the 1CrMo samples exhibit values of η10 over 200 mV. On the contrary, the 3CoMo−Vs and the 1VMo show significantly reduced η10 values down to below 150 mV. In particular, the 3CoMo−Vs has a lowest η10 value of only 75 mV. The first cycles of CV for HER were operated to verify the structural stability of introduced basal configurations after activation (Supplementary Fig. 19). The trend of activity shown in the first CVs of configured MoS2 exhibits the same as that of LSV curves. Note that the Co atoms in 3CoMo−Vs configuration has an over 90% occupancy among the total Co atoms. Hence, even though a minor content (<0.2 at%) of 1Co configuration is detected, we believe the 3CoMo−Vs configuration plays the dominating role in the catalyst activity. This is also in concise with the calculation that ΔGH of 3CoMo−Vs is closest to 0 eV (Supplementary Table 1). The corresponding Tafel plots show the same trend with that of η10 (Fig. 3b). The 3CoMo−Vs configuration sharply reduces the Tafel slope from 175 mV dec−1 in pristine MoS2 to 57 mV dec−1. And the 1VMo sample gives an acceptable value of 68 mV dec−1. In comparison, the 3FeMo−Vs and 1CrMo configurations have little effect to the Tafel slope. Therefore, the lowered Tafel slopes of the 3CoMo−Vs and 1VMo with a fast discharge process of protons41 (Supplementary Note 8), may reflect a strengthened capability to adsorb H. The Faradic efficiency was determined from the produced H2 characterized quantitatively by gas chromatography. As shown in Supplementary Fig. 23, the 3CoMo−Vs sample exhibits >98% efficiency over the time scale of the measurement, confirming the H2 as the dominating product during the whole electrolysis process. From the overall comparison (Fig. 3c), we can conclude that the 3CoMo−Vs configuration, with synergistic triangular Co clusters surrounding one Vs in the center, renders MoS2 monolayer the best HER catalytic performance among all the configured MoS2 samples16,42,43,44,45,46,47,48. Supplementary Table 2 provides an extensive comparison to other TMDs and non-noble metal catalysts in their electrocatalysis of HER. The performance of our MoS2 monolayer with 3CoMo−Vs configuration exceeds all the pure TMD monolayer catalysts, and also compete with other non-noble metal catalysts.

Fig. 3: HER properties of samples with different local configuration types.
figure 3

a Polarization curves of pristine MoS2, MoS2 with 3CoMo−Vs, 3FeMo−Vs, 1VMo, 1CrMo configurations and Pt/C. The currents are normalized to the projected geometric area of the electrode. b The corresponding Tafel plots of the polarization curves in a. c Comparison of η10-Tafel slope for HER catalysts in 0.5 M H2SO4. MoS2 with 3CoMo−Vs configuration exhibits top performance. The data are taken from refs. 16,42,43,44,45,46,47,48. d TOFs of MoS2 with varied configuration types. e Electrochemical impedance spectroscopy (EIS) Nyquist plots for sample 3CoMo−Vs, 3FeMo−Vs, 1VMo, and 1CrMo. f Long-test stability test for the 3CoMo−Vs electrode at a current density of 10 mA cm−2. .

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The turnover frequency (TOF) per sulfur is calculated in order to correlate the intrinsic activity per sulfur atom with the local configuration (Supplementary Note 9). Each sulfur site tuned by 3CoMo−Vs or 1VMo possesses much higher efficiency than that in 3FeMo−Vs and 1CrMo samples with increased value of TOFs. Compared to other configurations, the 3CoMo−Vs and 1VMo samples demonstrate the most appropriate tuning on the charge transfer capacity of local configuration.

Electrochemical impedance spectroscopy with fitted circuit models (Supplementary Fig. 24) shows significantly decreased charge-transfer resistances (Rct) for the 3CoMo−Vs (30.3 Ω) and the 1VMo (47.9 Ω) samples, as compared to those of 3FeMo−Vs (91.5 Ω) and 1CrMo (100.3 Ω), indicating a facilitated charge transfer between the S and protons in electrolyte (Fig. 3e). In addition, the 3CoMo−Vs sample exhibits an extraordinary long-term operation durability with small changes in potential (Fig. 3f and Supplementary Fig. 25). Hence, we may conclude that the 3CoMo−Vs configuration is efficient for HER during the whole cycling process.

Microcell measurements

In addition to the effect of local configuration type, it is expected that the concentration of such local configurations can also influence the amount of active sulfur sites. In order to prove the concentration effect, the on-chip electrochemical micro-devices are fabricated from a set of 3CoMo−Vs samples with local probe test, as shown in Fig. 4. Figure 4a, b show the three-electrode setup for the electrochemical measurements (more details are shown in Supplementary Fig. 26). In the first step, a controlled linear I–V scan is done on the PMMA layer (Supplementary Fig. 27) to measure the electrochemical blocking reliability of the PMMA layer. The MoS2 samples with different 3CoMo−Vs concentrations (determined from STEM measurements, see Supplementary Fig. 21 and Supplementary Table 3) are applied for the microcell experiments. The obtained results are Fig. 4c–e. We can clearly see that an optimal Co concentration, corresponding to η10 < 100 mV, should be around 3.8 at%, which translates to the 3CoMo−Vs concentration of ~1.2 at%. The excessive increase in 3CoMo−Vs concentration results in performance decline. Possible reasons for this are deteriorated surface stability16 and superfluous lattice distortion18. This concentration effect also corroborates the key contribution of 3CoMo−Vs rather than 1CoMo to the HER catalyst activity enhancement. In addition, the microcell HER measurements are implemented on 3CoMo−Vs, 3FeMo−Vs, 1VMo, and 1CrMo samples with similar defect concentrations (Supplementary Fig. 28), showing the similar trend with that of three-electrode measurements (Fig. 3a).

Fig. 4: Microcell HER measurements of the 3CoMo−Vs samples.
figure 4

a, b Schematic illustration of the microreactor device fabricated on 3CoMo−Vs structured MoS2 monolayer. c LSV curves of the samples with Co concentrations of 1.6, 3.1, 3.8, 5.8, and 7.0 at%. d The corresponding Tafel plots of the polarization curves in panel c. e The changing trends of Tafel slopes and η10 with varied Co concentration. The optimal Co concentration is determined to be ~3.8 at%, corresponding to the concentration of 3CoMo−Vs around 1.2 at%.

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Discussion

We have promoted the per-site electrochemical activity of in-plane sulfur sites of MoS2 monolayer via tuning H–S bonding strength, which can be understood by a hypothetical model of activating the inert sulfur atom into an open valence state. That activation can be correlated with the charge transfer capacity of local configuration. This is realized by forming various local configurations of transition metal atom or clusters (Co, Fe, V, and Cr) and compensative sulfur vacancy (Vs), which are confirmed by STEM images. In particular, the in-plane sulfur atoms modulated by 3CoMo−Vs configuration render the most active MoS2-based HER electrocatalyst in acidic medium to date (an overpotential η10 of 75 mV). The optimized 3CoMo−Vs configuration is also verified by the systematic DFT calculations. In addition, the suitable Co concentration for the HER performance is achieved by the in-situ probe measurements of microcell. Our work highlights the potency of local configuration engineering in boosting the in-plane electrocatalytic activity of MoS2, as well as possibly other 2D TMD monolayers.

Methods

Synthesis of configured and pristine MoS2

Pure MoS2 and configured MoS2 were synthesized by CVD method using MoO3 and sulfur (Sigma) as the precursor. For different TM-doped MoS2, V2O5, CrCl3, Fe2O3, and Co3O4 were used as the corresponding TM sources. The synthesis was conducted using a quartz-tube single-zone furnace (1-inch diameter) in a temperature range from 550 to 650 °C. Specifically, for the growth of pure MoS2, a quartz boat containing 10 mg MoO3 powder was put in the center of the tube, and the SiO2/Si substrate was placed on top of the quartz boat with the front side facing down. Another quartz boat containing 0.5 g sulfur powder was put upstream. The temperature ramped up to 700 °C in 15 min, and was maintained at the peak temperature for 5 min to 10 min. During the reaction, a constant 80 sccm Ar flow was used as the carrier gas. After the reaction, the furnace cooled down naturally to room temperature. For the 3CoMo−Vs, 3FeMo−Vs, 1VMo, and 1CrMo structured MoS2, the precursor loaded in the central boat contained mixed powder of V2O5, CrCl3, Fe2O3, Co3O4, respectively, with MoO3 (mole ratio of 2: 98). The carrier gas used for the structured MoS2 was mixed Ar/H2 with a flow of 80/5 sccm. The rest reaction conditions were the same as that for pure MoS2.

Structural characterizations

Room temperature Raman measurements were performed using a WITEC alpha 300 R Confocal Raman system with an excitation laser of 532 nm. The Raman system was pre-calibrated based on the Raman peak of crystalline Si at 520 cm−1. The laser power was kept below 1 mW to avoid sample heating. The TEM samples of the 3CoMo−Vs, 3FeMo−Vs, 1VMo, and 1CrMo structured MoS2 were prepared as follows. A layer of poly (methyl methacrylate) (PMMA) was spin-coated on the sample surface with a thickness of ~1 µm, and then baked in an electric oven at 180 °C for 3 min. Afterwards, the substrates were immersed in a NaOH solution (1 M) overnight to dissolve the SiO2 layer. After lift-off, the MoS2 samples were washed with DI water for several cycles. Then the monolayer samples were fished by a TEM grid (Quantifoil Mo grid). The obtained TEM specimen were dried naturally in ambient environment, and then dipped into high-purity acetone overnight to remove the PMMA layers. The STEM investigation was performed at room temperature on an aberration-corrected Nion UltraSTEM-100 and a JEOL 2100 F with a cold field-emission gun and an aberration corrector (the DELTA-corrector), both operating at 60 kV.

Electrochemical measurements

PMMA methylbenzene was uniformly spun on the SiO2/Si substrates deposited with monolayer MoS2. After baking at 100 °C for 5 min, the PMMA film covered substrates were immersed in a 5 M KOH solution. As a result of the etching effect by KOH, the monolayer MoS2 samples with the PMMA film were detached from the SiO2/Si substrate. Then, the obtained monolayer MoS2/PMMA films were washed in DI water and overlaid on the glassy carbon rotating disk electrode (RDE). After the thorough evaporation of DI water between the RDE electrode and the MoS2/PMMA films, the PMMA films were further removed by dipping into acetone. As a result, the glassy carbon RDE electrode covered by monolayer MoS2 were obtained45,46.

For the electrochemical measurements, a standard three-electrode cell consisting of the glassy carbon RDE as the working electrode, a graphite carbon counter electrode and a saturated calomel reference electrode (SCE) was used. The electrolyte solution was 0.5 M H2SO4. An electrochemical workstation (CHI760) coupled with a RDE system (AFMSRCE3529, Pine Research Instrumentation, USA) was used to control the cell. The potential versus the reversible hydrogen electrode (RHE) was calculated according to ERHE = ESCE + E°SCE (0.2412) + 0.059 × pH. Before HER test, the catalysts went through an electrochemical activation process by cyclic voltammetry scanning in the same electrolyte (0.5 M H2SO4) with a scan rate of 100 mV s−1 in the potential range of 0.1 to −0.29 V (vs. RHE). Linear sweep voltammetry (LSV) measurements were conducted with a scan rate of 2 mV s−1 under 1500 rpm. The current vs. potential plots were corrected by 90% ohmic compensation. The electrochemical impedance spectroscopy (EIS) were obtained in the same three-electrode configuration in the frequency range of 100 KHz to 0.1 Hz and at an applied current of 10 mA cm−2. For the stability assessment, polarization data were measured in the beginning and after 1000 CV sweeps (−0.2 and +0.2 V vs. RHE, scan rate: 50 mV s−1). In addition, the constant-current (10 mA cm−2) measurements were also implemented to evaluate the stability of potential.

The on-chip electrochemical measurements were carried out following the previous report11. Briefly, structured-MoS2 monolayers were transferred onto SiO2 (300 nm)/Si substrate with pre-made gold fingers by PMMA assisted wet transfer method. Monolayers were further patterned into domains by e-beam lithography and 5-s treatment in nitrogen plasma. Contacts between gold fingers and monolayers were made via e-beam lithography and gold deposition processes. Microcell reaction windows were made by e-beam lithography on 1-μm-thick spin-coated PMMA layer. During measurements, gold fingers connecting configured MoS2 monolayers, Ag/AgCl encapsulated by Luggin capillary and carbon rod were used as working, reference and counter electrodes respectively. In all, 5 μl of 0.5 M H2SO4 (degassed with Ar bubbling for 10 min) was used as electrolyte for each test. The scan rate for the LSV tests were 10 mV/s.

Computational methods

The density functional theory (DFT) calculations were perfomed using the Vienna Ab initio simulation package49,50. The generalized gradient approximation with the Perdew−Burke−Ernzerhof exchange−correlation fuctional and a 450-eV cutoff for the plane-wave basis set are employed51. The projector-augmented plane wave was adopted to describe the electron−ion interactions52. The em piracal dispersions of Grimme (DFT-D2) was applied to account for the long-range van der Waals interacions53. All calculations were spin-polarized and the convergence threshold was set to be 10−4 eV in energy and 0.01 eV/Å. The k-point sampling of the Brillouin zone was obtained using a 4 × 4 × 1 by the Monkhorst−Pack scheme. In addition, a 5 × 5 × 1 supercell was also used to confirm the sufficiency of 4 × 4 × 1 supercell (Supplementary Fig. 29). In the electronic structure calculation, denser k-points (8 × 8 × 1) were used for better accuracy. The vacuum slab of 15 Å was inserted in the z-direction for suface isolation to eliminate periodic interaction. The free energy of the adorbed state was calculated as

$$\Delta {{G}} = \Delta {{E}}_{{\mathrm{H}}^ \ast } + \Delta {{E}}_{{\mathrm{ZPE}}} - {{T}}\Delta {{S}},$$
(1)

where ∆EH* is the hydrogen chemisorption energy, and ∆EZPE is the difference of the zero point energy between the adsorbed state and the gas phase. Considering the fact the vibriation entropy of H* in the adsorbed state is very small, the entropy of 1/2 H2 adsorption can be approximated as ∆SH ≈ −1/2\({{S}}_{{\mathrm{H}}^2}^0\), where \({{S}}_{{\mathrm{H}}^2}^0\) is the entropy of H2 in the gas phase at the standard conditions.