Tuning orbital orientation endows molybdenum disulfide with exceptional alkaline hydrogen evolution capability

Molybdenum disulfide is naturally inert for alkaline hydrogen evolution catalysis, due to its unfavorable water adsorption and dissociation feature originated from the unsuitable orbital orientation. Herein, we successfully endow molybdenum disulfide with exceptional alkaline hydrogen evolution capability by carbon-induced orbital modulation. The prepared carbon doped molybdenum disulfide displays an unprecedented overpotential of 45 mV at 10 mA cm−2, which is substantially lower than 228 mV of the molybdenum disulfide and also represents the best alkaline hydrogen evolution catalytic activity among the ever-reported molybdenum disulfide catalysts. Fine structural analysis indicates the electronic and coordination structures of molybdenum disulfide have been significantly changed with carbon incorporation. Moreover, theoretical calculation further reveals carbon doping could create empty 2p orbitals perpendicular to the basal plane, enabling energetically favorable water adsorption and dissociation. The concept of orbital modulation could offer a unique approach for the rational design of hydrogen evolution catalysts and beyond.

S ustainable hydrogen production in an economical way is the key to building new hydrogen-based energy system 1 . Water electrolysis driven by renewable energy sources such as solar, wind, or geothermal energy has been regarded as the most promising way for sustainable hydrogen production 2,3 . Despite the fact that water electrolysis is first discovered in acidic condition, alkaline electrolysis is more preferred in industrial plants, due to the robustness of electrode materials, long lifetime, and cheap electrolyzer construction 4 . Electrocatalysts, as the heart of the electrolyzers, significantly affect the cell efficiency 5 . Unfortunately, precious platinum-based materials till now are still the state-of-the-art hydrogen evolution reaction (HER) catalysts in both acidic and alkaline conditions 6,7 . In this regard, developing non-noble metal-based HER catalysts to replace Pt has been one of the focal points over the past decades [8][9][10][11][12][13][14] .
Molybdenum disulfide (MoS 2 ), a typical cost-effective layered transition metal dichalcogenide [15][16][17][18] , has been proved both theoretically and experimentally to be highly active for HER catalysis in acidic condition [16][17][18][19][20][21][22][23][24][25][26] . The edged Mo and S atoms with a free energy of H adsorption close to zero are commonly believed to be the catalytic sites 19,[27][28][29][30] . Unfortunately, MoS 2 is found to be inactive in alkaline condition 7,31,32 , while the alkaline catalysis is more practically viable. The inert alkaline electrolysis is mainly attributed to the sluggish water adsorption and dissociation dynamics, which is, in essence, determined by the intrinsic structural feature of MoS 2 19,[33][34][35] . As the dominated orbital compositions of the conduction band in MoS 2 , both the Mo 4d z2 orbitals in the central sublayer and the S 3p x,y orbitals in the outermost sublayers possess unfavorable charge interaction with water molecule due to the steric effect (d z2 ) and unsuitable orbital orientation (3p x,y ) in the basal plane, which essentially hinder the water adsorption and dissociation on MoS 2 (Fig. 1). Although improving the conductivity of MoS 2 31,36,37 or surface modification with water adsorption components 19,33,34 has shown enhanced alkaline electrolysis, the overall performance of MoS 2 is still far from being satisfactory for practical alkaline electrolysis and studies on this issue are also very limited. Moreover, the understanding of the alkaline catalytic essences especially at atomic levels is also absent. Therefore, rationally tailoring the catalytic sites to endow MoS 2 with efficient alkaline HER catalytic activity is highly desirable but extremely challenging as well.
To essentially manipulate the intrinsic properties of MoS 2 for alkaline HER catalysis, tuning the orbital orientation of the MoS 2 layer to promote water adsorption and dissociation dynamics is the key. Considering carbon with smaller atomic radius and less electrons owns more empty and lower-energy 2p valence orbitals than sulfur, partially substituting S with carbon in MoS 2 could generate sp 2 hybrid sites in the outermost sublayers of MoS 2 , which consequently vacate one p orbital perpendicular to the basal plane for water adsorption and activation. Herein, we successfully endow MoS 2 nanosheets with exceptional alkaline HER activities by carbon-induced surface orbital orientation modulation. Carbon is in-situ incorporated into MoS 2 through a unique incomplete sulfurization of Mo 2 C. The prepared carbon doped MoS 2 (C-MoS 2 ) nanosheets display an unprecedented overpotential of 45 mV at 10 mA cm −2 in alkaline condition, which represents the best alkaline HER activity among the ever-reported MoS 2 -based catalysts. X-ray photoelectron spectroscopy (XPS) and X-ray absorption spectroscopy (XAS) systematically reveal the structural and electronic evolution of MoS 2 after carbon doping. Moreover, density functional theory (DFT) analysis indicates carbon doping can generate empty p orbitals perpendicular to the basal plane of MoS 2 for water adsorption and dissociation, which is essential for the alkaline HER catalysis. More importantly, the capability to endow materials with the properties which are not readily available in nature by rational orbital modulation offers a new vision for the design of HER catalysts and beyond.

Results
Synthesis and structural characterization of C-MoS 2 . C-MoS 2 and MoS 2 were synthesized via a controlled sulfurization of Mo 2 C, which is illustrated in Fig. 2a. Mo 2 C as the precursor was obtained by a previously developed method (details, see Methods) 38 . Then, the as-synthesized Mo 2 C was controllably sulfurized to C-MoS 2 and MoS 2 in a home-built tube furnace with sulfur powder as the sulfur source and argon as the carrier gas (details, see Methods). The synthesized Mo 2 C, C-MoS 2 , and MoS 2 were further characterized by field-emission scanning electron microscopy (SEM), X-ray diffraction (XRD), Raman spectrum, and transmission electron microscopy (TEM), respectively. SEM images in Supplementary Fig. 1 indicate the carbon fibers of the carbon cloth (CC) substrate are uniformly coated with porous Mo 2 C thin film, which becomes rougher after sulfurization treatment. XRD patterns ( Fig. 2b) clearly reveal the Mo 2 C (JCPDS No. 00-035-0787) can be well converted to hexagonal MoS 2 (JCPDS No. 01-073-1508) after controlled sulfurization treatment. The sharp diffraction feature of MoS 2 with deep sulfurization suggests improved crystallinity. In addition, the sulfurization process can also be revealed by Raman spectroscopy (Supplementary Fig. 2). The fingerprint bands of Mo 2 C located at 662.5, 816.4, and 991.8 cm −1 disappear after sulfurization treatment 39 ; meanwhile, new bands centered at around 376 and 402 cm −1 emerge, which can be assigned to the in-plane (E 2g ) and out-plane (A 1g ) Mo-S phonon mode vibration of MoS 2 , respectively 40 . Moreover, the wavenumbers of E 2g and A 1g of C-MoS 2 display a positive shift relative to the MoS 2 , probably due to the susceptibility of electron-phonon coupling induced by carbon doping 41,42 . Taken together, all these results illustrate sulfurization treatment can well control the conversion from Mo 2 C to MoS 2 .
Furthermore, TEM was employed to acquire the microstructural features of Mo 2 C, C-MoS 2 , and MoS 2 , as shown in Supplementary Fig. 3 and Fig. 2c. The high-resolution TEM (HRTEM) images exhibit well-resolved lattice fringes, where the interplanar spacing of 0.23 nm is assigned to the (101) plane of Mo 2 C and 0.62 nm is assigned to the (002) plane of MoS 2 , respectively. Interestingly, both C-MoS 2 and MoS 2 prepared by sulfurization treatment are composed of ultrathin layered MoS 2 nanosheets. It is also worth mentioning that no obvious carbon coating is observed on the surfaces of Mo 2 C, C-MoS 2 , and Chemical states and coordination structures of C-MoS 2 . Given that EDX spectroscopy only provides composition information that is not convincing enough to prove carbon doping into MoS 2 , XPS, and XAS are further used to probe localized electronic states and coordination structures of C-MoS 2 . Figure 3a shows the XPS Mo 3d spectra of Mo 2 C, MoS 2 , and C-MoS 2 , respectively. Obviously, the typical characteristics of Mo-C bonds are observed at 231.1 and 228.0 eV in Mo 2 C, while a pair of new peaks located at 232.6 and 229.5 eV appear after deep sulfurization, which can be assigned to the Mo 3d 3/2 and Mo 3d 5/2 of Mo-S bond in MoS 2 , respectively 43 . Strikingly, the Mo 3d profiles in C-MoS 2 exhibit obvious shoulders at the lower binding energy region, suggesting the existence of multiple chemical states of Mo. The Mo 3d spectrum of C-MoS 2 can be further deconvoluted into two pairs of peaks corresponding to the chemical states of S-Mo-S and S-Mo-C, which indicates carbon has been substitutionally doped into the MoS 2 lattices (The fitting parameters are summarized in Supplementary Table 1). Meanwhile, the C 1s spectra of C-MoS 2 and Mo 2 C ( Supplementary Fig. 4, the fitting parameters in Supplementary Table 2) also support the existence of Mo-C bonds in C-MoS 2 . In addition, the slight shift of S 2 s position suggests the chemical environments around S atoms also slightly changes after carbon doping, which could be originated from the electronegativity difference between C and S. To probe the evolution of localized coordination environment in MoS 2 induced by carbon doping, X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) are performed. Figure 3b shows the Mo K-edge XANES spectra of Mo 2 C, C-MoS 2 , MoS 2 , and Mo foil, in which Mo foil is used as the reference. Apparently, the Mo foil possesses the smallest energy of absorption edge. Moreover, the enlarged Mo Kedge XANES curves (inset, Fig. 3b) reveal that the near-edge absorption energy of C-MoS 2 located between MoS 2 and Mo 2 C indicates the average electron density around Mo in C-MoS 2 is higher than MoS 2 but lower than Mo 2 C, which is consistent to the XPS Mo 3d spectra and also suggests the existence of Mo-C bonds in C-MoS 2 . In addition, Mo K-edge extended XAFS oscillation functions k 2 χ(k) of MoS 2 , C-MoS 2 , Mo 2 C, and MoS 2 mixed with small amounts of Mo 2 C (denoted as Mo 2 C + MoS 2 ) are presented in Supplementary Fig. 5a, respectively. Clearly, the oscillation of C-MoS 2 is very similar to MoS 2 , but quite different from Mo 2 C and Mo 2 C + MoS 2 , convincingly indicating the C-MoS 2 possesses similar structure to MoS 2 and there is no obvious Mo 2 C remaining in C-MoS 2 . Moreover, the XPS depth profiling analysis also does not show obvious existence of Mo 2 C ( Supplementary Fig. 5b). Figure  The detailed fitting parameters are summarized in Supplementary  Table 4. Although we cannot exclude the existence of Mo 2 C clusters in C-MoS 2 that is beyond the detection limits of the currently used characterization techniques, our experimental results clearly reveal that carbon is most probably doped into the lattices of MoS 2 in the form of Mo-C bond.
Alkaline hydrogen evolution catalysis of C-MoS 2 . The alkaline HER catalysis is evaluated in 1.0 M KOH solution using a typical three-electrode system with the studied materials as the working electrodes, Hg/HgO as the reference electrode and graphite rod as the counter electrode. Figure 4a shows the linear sweep voltammetry (LSV) curves of CC, Mo 2 C, C-MoS 2 , MoS 2 , and Pt/C with a scan rate of 5 mV s −1 , in which the blank CC and benchmark Pt/C are used as control samples. Impressively, C-MoS 2 delivers higher current density and lower current onset potential than CC, MoS 2 , and Mo 2 C, indicating carbon doping can substantially improve the catalytic performance toward HER in alkaline condition. Carbon doping enables the overpotential of C-MoS 2 at 10 mA cm −2 to be as low as 45 mV, which is much better than the 200 mV of Mo 2 C and 228 mV of MoS 2 and even close to the catalytic activity of Pt/C (30 mV). Although the performance of C-MoS 2 is not the best among all kinds of the HER catalysts including non-precious and precious catalysts, C-MoS 2 represents the best alkaline HER activity among the ever-reported MoS 2 ( Fig. 4b and Supplementary  Fig. 8). With the increase of the sulfurization temperatures, the HER overpotentials display an inverse volcanoshaped feature. At the temperature below 500°C, Mo 2 C cannot be completely converted to MoS 2 and the corresponding catalytic activity is far less than that of the C-MoS 2 , further revealing C doping probably plays vital role in the HER catalysis. To probe the effects of carbon contents, we further study the carbon content dependent HER activities of C-MoS 2 ( Supplementary Fig. 9). Obviously, with the increase of carbon concentration, the catalytic activity of C-MoS 2 increases and reaches a maximum value. However, further increasing the C ratio will result in performance decay probably due to too much destroy of the layered structures of MoS 2 , suggesting moderate carbon doping in MoS 2 is essential for the HER catalysis. Additionally, Tafel slope can be used to probe the effects of carbon dopants on the rate-determining steps during HER process. Figure 4c displays the corresponding Tafel curves. The derived Tafel slope of MoS 2 is around 129 mV dec −1 , suggesting the alkaline HER catalysis on MoS 2 undergoes Volmer mechanism and water dissociation is the rate-determining step. Importantly, C-MoS 2 exhibits a substantially decreased Tafel slope of 46 mV dec −1 , clearly revealing the sluggish water dissociation behavior has been significantly improved after carbon doping. Meanwhile, the exchange current densities for Mo 2 C, MoS 2 , C-MoS 2 , and Pt/C derived by Tafel extrapolation are 0.12, 0.25, 0.87, and 1.28 mA cm −2 , respectively. Clearly, although the exchange current density of C-MoS 2 is a little smaller than that of Pt, it is still substantially larger than that of MoS 2 , also suggesting carbon doping can change the intrinsic catalytic activities of MoS 2 for alkaline HER catalysis. Considering surface area may also affect the HER catalytic performance, we further estimate the electrochemical surface areas of the studied materials by deriving the electrochemical double layer capacitance (C dl ) from the cyclic voltammetry studies (Supplementary Fig. 10) 11 . The C-MoS 2 is found to have a larger C dl of 54 mF cm −2 than MoS 2 (19 mF cm −2 ) and Mo 2 C (27 mF cm −2 ), indicating carbon doping treatment can also increase the surface area of C-MoS 2 . To eliminate the influence of surface area and reveal the intrinsic catalytic behavior, turnover frequency (TOF), a surface area independent figure of merit, is calculated to gain the intrinsic per-site activity, as shown in Fig. 4d. Impressively, the TOF values of C-MoS 2 are significantly larger than those of MoS 2 and Mo 2 C, clearly revealing carbon doping can essentially promote the per-site activity for HER catalysis. Additionally, electrochemical impedance spectroscopy (EIS) in Fig. 4e presents that C-MoS 2 possesses a smaller charge transfer resistance (R ct ) of 32.1 Ω than MoS 2 (83.7 Ω) and Mo 2 C (59.7 Ω), further suggesting carbon doping in MoS 2 can also substantially boost the interfacial electron-transfer kinetics. Besides carbon doping, the superior electrochemical behavior of C-MoS 2 is also attributed to the unique carbon doping strategy without involving carbon deposition on the catalyst surface. We also use a conventional post-doping method to introduce carbon and study their electrochemical performance, shown in Supplementary Fig. 11. TEM image clearly illustrates obvious carbon shell deposited on the surface of MoS 2 , which results in decreased catalytic performance probably due to the blocked active sites for catalysis ( Supplementary Fig. 12). Given that the MoS 2 is derived from Mo 2 C which may have tiny amounts of carbon remaining, MoS 2 with minimum carbon interference is also prepared by thermal sulfurization of ammonium molybdate ( Supplementary  Fig. 13). Electrochemical studies reveal that the HER performance of the newly prepared MoS 2 is far less than that of C-MoS 2 , also suggesting carbon dopants play vital roles in the HER catalysis of C-MoS 2 . Finally, the stability of C-MoS 2 is evaluated by polarization cycling and chronoamperometric test, both of which display superior catalytic stability for alkaline electrolysis (Fig. 4f).
XPS and XAFS are further employed to evaluate the C-MoS 2 after the stability test ( Supplementary Fig. 14). Impressively, there is no big difference in chemical and bonding states in C-MoS 2 before and after the durability test, suggesting the robustness of the C-MoS 2 for HER catalysis.

Discussion
To decipher the modulation essence of the carbon dopants in C-MoS 2 for alkaline HER catalysis at the atomic level, DFT calculations are further carried out. The C content used in the C-MoS 2 model is based on the area ratio of Mo-C and Mo-S states in the XPS Mo 3d of C-MoS 2 . In light of the charge balance after carbon doping, we also introduce sulfur vacancies (V s ) in the structural models. To equally distribute the positions of the C dopants and S vacancies, we considered seven different configurations, as shown in Supplementary Fig. 15. Supplementary  Fig. 16 shows one of the typical structures of C-MoS 2 , where the C dopants are pulled into the sublayer of MoS 2 , due to the formed stronger Mo-C bond with shorter bond length than the original Mo-S bond. Detailed bond length information is provided in Supplementary Fig. 17. The electron density difference images in Supplementary Figs 18 and 19 clearly reveal that the introduction of carbon can significantly break the unified surface electron distribution of MoS 2 . More importantly, the orbital analysis in Fig. 5a and b indicates the carbon dopants prefer to form the sp 2 hybrid orbitals (highlighted by red dash circle in Fig. 5a), which thus vacates an unhybridized 2p z orbital perpendicular to the basal plane (highlighted by red dash circle in Fig. 5b). This 2p z orbital orientation can maximize the head-on orbital overlapping to form sigma bonds, which can potentially offer active sites for water adsorption and activation. This orbital orientation is also consistently observed on the other structural configurations of C-MoS 2 , as shown in Supplementary Fig. 15 Fig. 20) indicates that carbon doping can well increase the electrical conductivity of the MoS 2 and thus could benefit the electron transportation and enhance the catalytic activity. Although conductivity is important for electrocatalysis, we reasonably believe the exceptional alkaline HER activity of C-MoS 2 is mainly stemmed from the C-induced orbital tuning for water adsorption and dissociation, considering 1-T MoS 2 with better conductivity does not exhibit such exceptional activity 49 . Moreover, the electrostatic potential mapping images ( Fig. 5c and Supplementary Fig. 21) and the electron density difference slices ( Supplementary Fig. 22) further reveal superior water adsorption on the basal plane of C-MoS 2 , which is confirmed by the apparent charge transfer and the formation of remarkable chemical bonding orbital between water and C-MoS 2 (Fig. 5c), while no apparent orbital bonding or charge interaction occurs on MoS 2 (Fig. 5d). We also consider the MoS 2 model with only sulfur vacancies. Structural analysis indicates sulfur vacancies indeed do not have obvious effects on the orbital orientation tuning (Supplementary Fig. 23a). The corresponding water adsorption energy on the defected MoS 2 (MoS 2 -Vs) is around −0.23 eV, which is only slightly higher than that on the MoS 2 . Meanwhile, we also experimentally prepare MoS 2 with sulfur vacancies via a typical hydrogen treatment and study their electrochemical properties. The overall performance of the hydrogen treated MoS 2 is still far less than that of C-MoS 2 ( Supplementary  Fig. 23b), suggesting the sulfur vacancy may not be the main factor for the exceptional alkaline HER activity of the C-MoS 2 .
Taken together, all the structural information consistently suggest that carbon doping can effectively manipulate the orbital orientation and create more active sites on the basal plane of MoS 2 for water adsorption and activation. Besides structural information, alkaline HER catalytic pathways on the basal plane of MoS 2 and C-MoS 2 are further studied. Figure 5e shows the relative energy profiles of water adsorption and dissociation on MoS 2 and C-MoS 2 , respectively. As expected, the basal plane of MoS 2 is almost inert for alkaline HER catalysis, with poor water adsorption and giant water dissociation energy barrier. Impressively, carbon doping enables the HER catalysis to proceed on a much lower potential energy surface. Specifically, C-MoS 2 owns more favorable adsorption energies (−0.53 eV for RC1 & −0.25 eV for RC2) and much lower transition state energy barrier (0.70 eV for TS1 & 1.15 eV for TS2). From the water adsorption/dissociation configurations on C-MoS 2 (Fig. 5e), H 2 O is adsorbed on the C site, while the nearby S sites assist water dissociation by attracting the H in water molecule. In addition, we also performed the catalytic pathway of Mo 2 C (001) (Supplementary Fig. 24). Obviously, the reaction on the Mo 2 C proceeds on a potential energy surface with much higher energy barrier than that on C-MoS 2 . Moreover, the generated hydrogen adsorbed intermediate (Sur-H) is so stable that the adsorbed hydrogen needs overcome 1.37 eV for H desorption from the carbon site of the surface, which could potentially impede the HER catalysis. The studies on the catalytic pathways clearly reveal carbon doping could intrinsically boost the water adsorption and dissociation kinetics and thus endow MoS 2 with exceptional alkaline catalysis by tuning the orbital orientations on the basal plane.
In summary, we have demonstrated carbon doping can intrinsically endow MoS 2 with exceptional alkaline HER catalytic capability by tuning the orbital orientation. In comparison with the inert alkaline HER activity of MoS 2 , the prepared C-MoS 2 achieves an overpotential of 45 mV at 10 mA cm −2 , which is very close to the commercial Pt/C and also represents the best catalytic activity among the ever-reported MoS 2 for alkaline HER catalysis. XPS and XAS analysis reveal that the electronic and coordination structures of MoS 2 have been significantly changed after carbon doping. DFT studies further indicate that carbon-induced empty 2p orbitals perpendicular to the basal plane of MoS 2 enable energetically favorable water adsorption and dissociation, and thus promote the alkaline HER catalytic kinetics. The capability to intrinsically manipulate the catalytic activities by orbital modulation could offer a powerful platform to rationally design HER catalysts and beyond.  Synthesis of Mo 2 C. Typically, 3.708 g ammonium molybdate and 1.638 g CTAB were dissolved in 30 mL and 180 mL deionized water with ultrasonic assistance, respectively. Then, the two solutions were mixed homogeneously by magnetically stirring for 30 min, and further aged for another 24 h to obtain a uniform emulsion. A volume of 15 mL of the as-prepared emulsion was transferred into a 20 mL Teflon-lined stainless steel autoclave with the pretreated CC (CC, 2*3 cm 2 , pretreated with nitric acid and deionized water, respectively) as the growth substrate. After keeping the autoclave at 200°C for 20 h, the CC was taken out, cleaned by deionized water and dried at vacuum oven at 60°C overnight. Finally, Mo 2 C was obtained by annealing the prepared samples at 900°C for 6 h in a home-built tube furnace system under argon atmosphere.
Synthesis of C-MoS 2 and MoS 2 . C-MoS 2 and MoS 2 were prepared by a temperature-controlled sulfurization process. The as-prepared Mo 2 C was sulfurized in a tube furnace system for 2 h with powdered sulfur as the sulfur source and argon as the carrier gas (flowing rate at 20 sccm Structural characterizations. XRD measurements were performed on a Philips X'Pert Pro Super diffractometer using Cu Kα radiation (λ = 1.54178 Å). The fieldemission scanning (FE-SEM) images were collected using a FEI Sirion-200 SEM, while TEM and HRTEM images were acquired at a JEOL-2010 TEM with an acceleration voltage of 200 kV. Raman spectra were recorded on a Renishaw RM 3000 Micro-Raman system. XPS were performed at the photoemission end-station (BL10B) in the National Synchrotron Radiation Laboratory (NSRL), Hefei. To avoid the carbon interference for the binding energy calibration, all the samples were sprayed with tiny amount of Au as an external standard and the obtained binding energies were calibrated using the Au 4f energy (Au 4f 7/2 , binding energy of 84 eV). The XPS fitting was performed using the XPS PEAK41 software with Shirley background subtraction. The XPS database (NIST X-ray Photoelectron Spectroscopy Database, https://srdata.nist.gov/xps/intro.aspx) was used as a reference to assign the possible chemical states. During fitting, the peak intensity ratio and the full width at half maximum (FWHM) were well constrained in a reasonable range. XAS measurements were conducted at the beamline (BL14W1) of Shanghai National Synchrotron Radiation Facility (SSRF, China). The EXAFS data were disposed according to the standard procedures through the ATHENA module implemented in the IFEFFIT software packages 50 . The quantitative curve-fittings were conducted for the Fourier-transformed k 2 -weighted χ(k) in the R-space with a Fourier transform k-space range of 3.1-11 Å −1 by employing the module ARTE-MIS 4 of IFEFFIT. The backscattering amplitude F(k) and phase shift Φ(k) were calculated by FEFF8.0 code. While the curve-fitting, all the amplitude reduction factor S 0 2 was set to the best-fit value of 0.85 determined from fitting the data of MoS 2 . In order to fit the curves in the R-range of 1.1-3.4 Å, we considered Mo-C, Mo-Mo and Mo-S paths as the central-peripheral. For each path, the structural parameters, like coordination number (N), interatomic distance (R), and edgeenergy shift (ΔE 0 ) were opened to be varied. For the Mo-C, Mo-S, and Mo-Mo coordination, the common adjustable parameters of ΔE 0 and σ 2 were employed to reduce the number of free parameters.
Electrochemical measurements. All the electrochemical characterizations were performed in a three-electrode system on CHI 760E electrochemical workstation. The studied materials grown on CC were used as working electrodes, while Hg/ HgO electrode and graphite rod were employed as the reference and counter electrodes, respectively. All the measurements were conducted in 1.0 M KOH electrolyte and the potentials vs. Hg/HgO were converted with respect to the reversible hydrogen electrode (RHE) using the equation E (vs. RHE) = E (vs. Hg/ HgO) + E 0 (Hg/HgO) + 0.059*pH in the 1.0 M KOH. LSV curves were collected with a scan rate of 5 mV s −1 and the LSV curves shown in the manuscript were corrected by IR compensation (E iR-corrected = E original -I * R s ). The chronoamperometry curve was performed for the durability test at the potential of −0.1 V vs. RHE. Electrochemical surface area (ECSA) was obtained by conducting cyclic voltammetry (CV) in the range of 0.1-0.2 V vs. RHE with various scan rates from 10 to 50 mV s −1 . The current density differences (Δj = j a − j c ) were plotted against scan rates, and the slopes can be used to derive C dl and the ECSA. EIS measurements were carried out at the potential of −0.1 V (vs. RHE) in the frequency range of 100,000-0.001 Hz with a perturbation of 5 mV. TOF values were calculated using a previously reported method, in which the number of active sites was estimated as the amount of surface sites (including C, Mo, and S atoms) 11 . The Faradic efficiency of C-MoS 2 was evaluated in a H-type cell with an anion exchange membrane as the separator and 20 mL 1.0 M KOH as the electrolyte in each compartment, with a gas chromatography (HA GC-9560) for the hydrogen gas detection. The gas production was detected by the gas chromatography and the Faradic efficiency was calculated using the formula: Faradic efficiency = 2 F × N H 2 / Q = 2 F × N H 2 /(It), where F is the Faradic constant, I is the current, t is the running time and N H 2 is the amount of H 2 production.
Density functional theory calculation. All the DFT calculations were carried out using the CASTEP program in Material Studio package of Accelrys Inc 51 . The exchange-correlation functional was employed by the Perdew-Burke-Ernzerhof (PBE) of generalized gradient approximation (GGA) with the ultrasoft pseudopotentials (USP). The van der Walls interactions was considered by the DFT dispersion correction (DFT-D). The number of plane wave was determined by an energy cutoff of 450 eV. The Brillouin zone was sampled by a 2 × 2 × 1 k-points grid for the structure optimizations and double k-points meshes were employed for the density of states (DOS) calculations, respectively. A complete linear synchronous transitions (LST) and quadratic synchronous transitions (QST) approach was used for the transition state searching. The convergence tolerances were set to 2.0 * 10 −6 eV per atom for energy, 0.002 Å for maximum displacement, and 0.05 eV Å −1 for maximum force. The surfaces were modeled by a periodic slab repeated in 6 * ffiffi ffi 2 p * 2 ffiffi ffi 2 p surface unit cell with a vacuum region of 13 Å between the slabs along the z axis.