Highly Efficient and Stable Hydrogen Production in All pH Range by Two-Dimensional Structured Metal-Doped Tungsten Semicarbides

Transition-metal-doped tungsten semicarbide nanosheets (M-doped W2C NSs, M=Fe, Co, and Ni) have been synthesized through carburization of the mixture of tungsten trioxide, polyvinylpyrrolidone, and metal dopant. The nanosheets grow directly on the W mesh and have the lateral dimension of several hundreds of nm to a few μm with a thickness of few tens nm. It is demonstrated that the M-doped W2C NSs exhibit superior electrocatalytic activity for hydrogen evolution reaction (HER). Impressively, the Ni-doped W2C NSs (2 at% Ni) with the optimized HER activity show extremely low onset overpotentials of 4, 9, and 19 mV and modest Tafel slopes of 39, 51, and 87 mV dec−1 in acidic (pH=0), neutral (pH=7.2), and basic (pH=14) solutions, respectively, which is close to the commercial Pt/C catalyst. Density functional theory (DFT) calculations also demonstrate that the Gibbs free energy for H adsorption of Ni-W2C is much closer to the optimal value ∆GH⁎ = -0.073 eV as compared to -0.16 eV of W2C. Furthermore, nearly 100% Faradaic efficiency and long-term stability are obtained in those environments. This realization of highly tolerant metal semicarbide catalyst performing on par with commercial Pt/C in all range of pH offers a key step towards industrially electrochemical water splitting.


Introduction
Hydrogen generated by the electrolysis of water has become an increasingly attractive energy carrier due to its high energy density [1][2][3][4]. Electrocatalysts used for the hydrogen evolution reaction (HER) are important and key components for water splitting [5,6]. It is well known that noble metals, such as Pt, are the most efficient HER electrocatalyst due to its fast reaction kinetics and low overpotential to drive the HER reaction [7,8]. However, its high cost and low natural abundance hamper its wide applications [9][10][11][12]. Therefore, alternative electrocatalysts with low cost, good stability, and high catalytic activity are highly desirable.
In recent years, various nonnoble metal materials, such as phosphides [13,14], sulfides [15][16][17][18][19], phosphosulfides [20], and carbides [21,22], were prepared and tested as alternatives for Pt in the HER. Among the aforementioned materials, early transition metal carbides, especially tungsten carbides [23][24][25] with similar d-band electronic density-of-state to that of Pt, could be considered as effective nonnoble metal HER electrocatalysts [26,27]. For the past decades, many efforts have been devoted to the synthesis of highly active tungsten carbides (WC) HER electrocatalyst because of the above-mentioned electronic structure and other unique properties, such as high electrical conductivity, high resistance to carbon monoxide and bisulfide poisoning, and excellent corrosion tolerance over the wide range of pH and potential [28]. Unfortunately, all reported tungsten carbides (WC) exhibited poor performance towards HER. Therefore, 2 Research tungsten carbide has only been used as a catalyst support instead of carbon for Pt [24,29].
On the other hand, tungsten semicarbide (W 2 C) is metalterminated and theoretically predicted to have higher HER activity due to larger 5d-orbital electron population [30]. However, it has not been demonstrated experimentally, since the formation of W 2 C is not favorable below 1,250 ∘ C [31]. Even at high temperature, a mixture of WC and W 2 C phases often forms because the metastable W 2 C phase is readily transformed into stable WC phase in the presence of carbon [32]. Up to date, it has been reported that W 2 C possesses the onset overpotential of 50 mV, which is far higher than the Pt/C benchmark (∼0 mV) [33]. It may be arisen from the lack of reliable synthetic approaches. High temperature reduction (usually > 1500 ∘ C) of W or W-containing precursors by gaseous carbon source results in coking of catalyst surface and uncontrollable sintering. Consequently, it leads to lower electrochemical active surface area and then poor catalytic performance. Moreover, the morphology control and catalytic tuning should also be taken into account. As known, two-dimensional (2D) nanostructures offer good electron transfer platform, superior electron mobility, high surface area, and more surface active sites, which has not been demonstrated for W 2 C up to date. Therefore, it is urgent to explore an appropriate method for selective synthesis of W 2 C with desired 2D nanostructures and tunable electrocatalytic properties toward HER.
Herein, we report a simple strategy to prepare metaldoped W 2 C nanosheets (NSs) on tungsten (W) substrates at a lower synthetic temperature (900 ∘ C) through the hydrothermal reactions followed by a carburization process. The Mdoped W 2 C NSs (M=Fe, Co, and Ni) grown directly on the W mesh, with the lateral size of several hundreds of nm to a few m and the thickness of a few tens of nm, can be used as binder-free electrodes. This offers an efficient pathway for electron transport and the vertically aligned 2D nanostructure provides high surface area for HER. Among the M-doped W 2 C NSs, the Ni-doped W 2 C NSs (2 at% Ni) electrocatalyst exhibits close-to-Pt HER performance with low onset overpotentials of 4, 9, and 19 mV and small Tafel slopes of 39, 51, and 87 mV dec −1 in acidic (pH=0), neutral (pH=7.2), and basic (pH=14) conditions, respectively. Moreover, it gives ∼100% Faradaic yield and exhibits excellent stability towards the HER in those solutions. This outstanding performance can be attributed to its optimal |ûG H * | value (close to zero) based on the density functional theory (DFT) calculations. This phase-pure W 2 C, with high electric conductivity, excellent tolerance, and the advantages of 2D nanostructure, would be of great interest to a wide range of research areas (i.e., electrocatalysis, Li-O 2 batteries, supercapacitor, and chemical and biological sensing), where electrical conductivity is one of the key parameters for high performance applications.

Results and Discussion
Scheme 1 (Supporting Information) illustrates the synthesis of M-doped W 2 C NSs. First, vertical growths of WO 3 NSs were carried out on a W substrate by hydrothermal treatment of aqueous solution of Na 2 WO 4 ⋅2H 2 O and NaCl (pH ∼ 2) at 180 ∘ C (Step 1). The as-obtained WO 3 NSs were then immersed into a mixture of aqueous MCl 2 (MCl 2 =FeCl 2 , CoCl 2 , and NiCl 2 ) dopant and polyvinylpyrrolidone (PVP) precursor, followed by heat treatment at 180 ∘ C to obtain the WO 3 /PVP/M mixture (Step 2). Finally, the as-prepared WO 3 /PVP/M mixture was carburized at 900 ∘ C under the H 2 /Ar environment to obtain the M-doped W 2 C NSs (Step 3).
In Figure 1(a), the X-ray diffraction (XRD) peaks located at 40.2, 58.2, and 73.2 ∘ correspond to the W substrate (JCPDS No. 04-0806). After growth of WO 3 NSs on the W substrate, all the XRD peaks ( Figure S1, Supporting Information) can be indexed to the hexagonal WO 3 (JCPDS No. 33-1387) and W (JCPDS No. 04-0806). After carburization, the XRD peaks (Figure 1(a)) match those of W 2 C (JCPDS No. 35-0776) with space group of P-3m1 (a = 0.30387 nm and c = 0.46528 nm) and W (JCPDS No. 04-0806). Moreover, M-doped W 2 C (M=Fe, Co, and Ni) samples with varied dopant content have also been prepared. The amount of metal dopants was determined by the inductively coupled plasma-optical emission spectroscopy (ICP-OES, Table S1, Supporting Information). Due to the difference in ionic sizes and ionic charges we can only dope up to 4 at% of M into W 2 C lattice and 2 at% M-doped W 2 C (namely, 2% M-W 2 C, M=Fe, Co, and Ni) was mainly used for detail characterizations. It is notable that the (110) peak of W (40.2 ∘ ) overlaps with the (101) peak of W 2 C (39.6 ∘ ). Therefore, to obtain accurate lattice constants for 2% M-W 2 C, the nanosheets were scrapped off from the W mesh and dropped cast onto Cu substrate; and the XRD peaks were calibrated with the crystalline Cu (JCPDS No. 04-0836) as an internal standard (Figure 1(b)). The XRD patterns of M-W 2 C (M=Fe, Co, and Ni) with varied doping content (0-4%) reveal that the diffraction peaks of (100), (002), and (101) at 34.5 ∘ , 38.0 ∘ , and 39.6 ∘ , respectively, slightly shift to the higher angles as compared to those of pure W 2 C (Figures 2(a)-2(d); Figures S2a-S2d and S3a-S3d in Supporting Information). It is worth noting that Cu as the internal reference did not show any detectable peak shift in the XRD measurements; hence, this kind of peak shift indicates the decrease of lattice parameters (i.e., a and c as shown in Figure S4 in Supporting Information) after M (M=Fe, Co, and Ni) was doped into the W 2 C lattice. To specify, the Rietveld refinement method [34] was performed to determine the changes of lattice parameters and the unit cell volumes with respect to the amount of dopant. The lattice parameters and consequently the unit cell volume decrease with the increased dopant content, implying that smaller Ni, Co, or Fe atoms have substituted for the W atoms randomly in the crystal structure (Figures 2(e)-2(g); Figures S2e-S2g and S3e-S3g in Supporting Information). Such observation is expected as the Ni, Co, and Fe atoms have smaller radii as compared to W [35].
The X-ray photon-electron spectroscopy (XPS) was also used to characterize the 2% M-W 2 C (M=Fe, Co, and Ni) (Figure 1(c)). The two strong peaks at 853.3 eV and 869.9 eV with two corresponding satellite peaks in the Ni 2p XPS spectrum can be assigned to the Ni 2+ in Ni-C bond, which are  the characteristic of Ni-doping in metal carbide materials [36,37]. In the fine Co 2p XPS spectrum, peaks at binding energies of 778.4 eV and 793.4 eV and their satellites correspond to Co 2p 3/2 and Co 2p 1/2 , indicating the presence of Co 2+ and Co 3+ in Co-C bond [37]. The peaks at 707.0 eV and 720.1 eV in the Fe 2p XPS spectrum are attributed to Fe 3+ in Fe-C bond [37,38]. All these results suggest that the Fe, Co, and Ni have been successfully doped into W 2 C.
The scanning electron microscopy (SEM) images of W 2 C and 2% M-W 2 C (M=Fe, Co, and Ni) samples (Figures 3(a) and 3(b) and Figures S5a and S5b in Supporting Information) clearly show that the individual nanosheets were densely grown on the W mesh. The thickness of the whole nanosheet film on W mesh is ∼1.0 m ( Figure S6, Supporting Information). The obtained W 2 C and 2% M-W 2 C nanosheets were then scraped off from the W mesh for the atomic force microscopy (AFM), transmission electron microscopy (TEM), and high-resolution (HR) TEM measurements. The AFM result confirmed that the thickness of the nanosheet is several tens of nm ( Figure S7, Supporting Information). As shown in the TEM images (Figures 3(c) and 3(d)), the shape of the NSs is irregular and the lateral dimension of the nanosheets is from several hundreds of nm to a few m. The HRTEM image of W 2 C nanosheet shows a lattice spacing of 0.260 nm (Figure 3(e)), corresponding to the dspacing of (010) atomic planes of the W 2 C phase, whereas those lattice fringes for 2% M-W 2 C (M=Fe, Co, and Ni) are slightly higher at 0.261 nm (Figure 3 The HER electrocatalytic properties of M-W 2 C NSs (M=Fe, Co, and Ni) were studied using conventional 3electrode setup in solutions with different pH values. Linear sweep voltammetry technique was performed at 2 mV s −1 to lower the capacitive current. All the measurements were carried out at room temperature (25 ∘ C) unless otherwise stated. For comparison, the W substrate, pure W 2 C NSs, and commercial Pt/C were also examined. We started the evaluations of the samples in H 2 -saturated 0.5 M H 2 SO 4 (pH=0) solution ( Figure 4). Firstly, it should be noted that the W substrate exhibits nearly negligible HER activity even at -0.3 V vs. RHE ( Figure S9, Supporting Information). For three types of doped samples (M-W 2 C, M=Ni, Co, and Fe), 2 at% of metal doping leads to an optimal HER catalytic activity in all prepared samples ( Figure S10, Supporting Information). Compared to W substrate, the W 2 C nanosheets afford a much smaller onset overpotential, which could be further reduced by chemically doping metal M (M=Fe, Co, and Ni) into W 2 C lattice (Figure 4(a)). As summarized in Table  S2 in Supporting Information, the pure W 2 C, 2% Fe-W 2 C, 2% Co-W 2 C, and 2% Ni-W 2 C NSs electrocatalysts exhibit onset overpotentials of 122, 78, 45, and 4 mV, respectively, in 0.5 M H 2 SO 4 solution (pH=0). In addition, the operating overpotentials required to drive a cathodic current density of 10 mA cm −2 ( 10 ) are 274, 197, 157, and 57 mV for pure W 2 C, 2% Fe-W 2 C, 2% Co-W 2 C, and 2% Ni-W 2 C NSs, respectively (Figure 4(b)). Clearly, the 2% Ni-W 2 C electrocatalyst demonstrates the lowest onset overpotential and 10 as compared to other control samples and approaches close to Pt (∼ 0 onset overpotential and 10 of 23 mV). The Tafel slopes Intensity (a.u.) Intensity (a.u.) Intensity (a.u.) Intensity (a.u.) 1 m  are 145, 102, 122, and 39 mV dec −1 for the pure W 2 C, 2% Fe-W 2 C, 2% Co-W 2 C, and 2% Ni-W 2 C NSs, respectively (Figure 4(c)). It means that the HER for pure W 2 C, 2% Fe-W 2 C, and 2% Co-W 2 C proceeds through the Volmer-Heyrovsky mechanism, in which the Volmer reaction is the rate-limiting step [39], whereas the HER for 2% Ni-W 2 C NSs follows the Volmer-Tafel reaction process, in which the recombination of adsorbed hydrogen atoms is the ratedetermining step [39]. Notably, the Tafel slope of 2% Ni-W 2 C NSs is close to the commercial 20% Pt/C electrocatalyst  (30 mV dec −1 ), suggesting that 2% Ni-W 2 C NS electrode might be used to replace the expensive Pt electrocatalyst for HER. The inherent activities toward HER were also evaluated by the exchange current density. The 2% Ni-W 2 C still performs well at 0.79 mA cm −2 , which is far higher than W 2 C (0.19 mA cm −2 ), 2% Fe-W 2 C (0.22 mA cm −2 ), and 2% Co-W 2 C (0.41 mA cm −2 ) and is just slightly below Pt/C (0.92 mA cm −2 ).
In light of the high electrocatalytic activity of 2% M-W 2 C NSs (M=Fe, Co, and Ni), the electrochemical effective surface area (ESCA), which is proportional to the measured double-layer capacitance (C dl ), was determined using cyclic voltammetry (Figures 5(a)-5(d)). The C dl values of the W 2 C, 2% Fe-W 2 C, 2% Co-W 2 C, and 2% Ni-W 2 C electrodes are 38, 54, 58, and 75 mF cm −2 , respectively ( Figure 5(e)). The 2to 2.5-fold higher ESCA of 2% M-W 2 C NSs as compared to the pure W 2 C indicates that the number of surface active sites significantly increased after the substitutional doping of transition metal atom (e.g., Fe, Co, or Ni) in W 2 C NSs. Importantly, after ECSA normalization, the HER activity of 2% Ni-W 2 C NSs is still the best ( Figure 5(f)). Hence, the enhancement seen in HER activity is attributed not only to the increase of ECSA but also to the high intrinsic activity of 2% M-W 2 C NSs, especially 2% Ni-W 2 C NSs. Electrochemical impedance spectroscopy (EIS) results ( Figure S11, Supporting Information) compare the charge transfer resistance (R ct ) of pure W 2 C and 2% M-W 2 C (M=Fe, Co, and Ni) electrodes. The obtained R ct values of pure W 2 C, 2% Fe-W 2 C, 2% Co-W 2 C, and 2% Ni-W 2 C are 43.8 Ω, 29.0 Ω, 25.7 Ω, and 12.6 Ω, respectively. The lowest R ct of 2% Ni-W 2 C could be attributed to the fast reaction rate for the proton reduction on the electrocatalyst surface.

Research
Due to the best performance of 2% Ni-W 2 C in acidic condition, it is necessary to evaluate its long-term durability. Continuous CV was performed between 0.2 and -0.3 V (vs. RHE) at a scan rate of 100 mV s −1 in 0.5 M H 2 SO 4 solution (Figure 4(d)). As can be seen, the polarization curves before and after 1000 CV cycles almost overlap with each other. Chronoamperometry measurement of 2% Ni-W 2 C NSs at overpotential of 180 mV also shows a stable current density of 108 mA cm −2 for 28 hours (Figure 4(d), inset). The post HER analysis, i.e., XRD, XPS, and SEM (Figures S12a, S13a, S14a, and Table S1 in Supporting Information), shows almost no change observed, revealing high structural and chemical stability. All these results suggest the remarkable stability and durability of the synthesized 2% Ni-W 2 C NSs in such HER process.
An ideal HER electrocatalyst should not only have comparable activity/efficiency to Pt/C in 0.5 M H 2 SO 4 , but also acquire high catalytic activity and good stability over a wide pH range. Therefore, we further examine the electrochemical performance of the 2% M-W 2 C NSs (M=Fe, Co, and Ni) in neutral (1 M phosphate buffer, pH=7.2) and basic (1 M KOH, pH=14) solutions. In neutral condition, the reductive sweep of W 2 C reveals a high 10 of 334 mV for HER ( Figure 6(a)). In contrast, noticeable enhancement was obtained with lower 10 (242 mV, 188 mV, and 63 mV for 2% Fe-W 2 C, 2% Co-W 2 C, and 2% Ni-W 2 C, respectively) and sharply increased cathodic current. Interestingly, the 2% Ni-W 2 C still displays favorable performance, which is further shown by its modest onset overpotential and Tafel slope of 9 mV and 51 mV dec −1 , respectively ( Figure 6(b)), while the values for W 2 C, 2% Co-W 2 C, and 2% Fe-W 2 C are less attractive at 227 mV and 143 mV dec −1 ; 67 mV and 96 mV dec −1 ; 123 mV and 98 mV dec −1 , respectively. Similarly, HER catalytic activity in basic condition is presented in Figures 6(d) and 6(e). The onset overpotential and 10 for 2% Ni-W 2 C are 19 mV and 81 mV, respectively, surpassing the 2% Co-W 2 C (85 mV and 213 mV), 2% Fe-W 2 C (188 mV and 312 mV), and W 2 C (226 mV and 380 mV) by a great margin. The Tafel slope for 2% Ni-W 2 C in KOH solution is 87 mV dec −1 , which is slightly worse than that of the commercial 20% Pt/C (60 mV dec −1 ) and is much lower than those of 2% Co-W 2 C (130 mV dec −1 ), 2% Fe-W 2 C (102 mV dec −1 ), and W 2 C (133 mV dec −1 ). Furthermore, these values of 2% Ni-W 2 C are much better than the reported electrocatalysts (Tables S3-S7, Supporting Information).
The stability and durability of 2% Ni-W 2 C in PBS and KOH solution were also investigated by continuous CV and chronoamperometry method (Figures 6(c) and 6(f)). Less than 5% changes in current density are observed within 28 hours of electrolysis at 180 mV overpotential in both solutions. After 1000 CV scans, the reductive sweep voltammetry shows a slight negative shift compared to the initial one (Figures 6(c)-6(f), inset). In addition, the SEM results for 2% Ni-W 2 C after the durability test indicate no obvious changes in the 2D morphology (Figures S12b and S12c, Supporting Information). Similarly, the XRD patterns (Figures S13b and S13c, Supporting Information) of the 2% Ni-W 2 C NSs samples after chronoamperometry measurements for 28 h, specifically the diffraction peaks at 34.5 ∘ , 38.0 ∘ , and 39.6 ∘ corresponding to (100), (002), and (101) planes, respectively, resemble those of the W 2 C (JCPDS 35-0776) in acidic, neutral, and alkaline solutions. These detectable peaks indicate that the phases of the samples remain unchanged after long-term HER testing. Equally important, Figures S14b and S14c in Supporting Information show the binding energies of the 2% Ni-W 2 C NSs samples at 853.3 eV (Ni 2p 3/2 ) and 869.9 eV (Ni 2p 1/2 ) which are attributed to the Ni dopant in the W 2 C phase. These noticeable peaks imply that the chemical structures of Ni dopant in the W 2 C structure remain unchanged after durability test for 28 h in various pH solutions. On top of that, quantitative XPS analyses show almost no nickel leaching (Table S1, Supporting Information). Those results demonstrate that the 2% Ni-W 2 C possesses remarkable stability in HER under neutral and basic condition, suggesting the promise for implementing this new catalyst into realistic cathodic electrode for water splitting.
Faradaic efficiency tests in the pH solutions of 0, 7.2, and 14 were also conducted ( Figure S15, Supporting Information). For experimental amount of H 2 generated, headspace samples were taken for gas chromatography every 20 minutes while operating continuously at -80 mA cm −2 . The theoretical volume of H 2 evolved was calculated by Faraday's law with the assumption that all electrons passing through the circuit engage in proton reduction. The experimental and theoretical amounts of H 2 generated are in a good agreement, showing almost 100% current to hydrogen productivity.
To understand the effect of the Ni dopant in W 2 C toward the HER activity, a systematic calculation on the electronic properties of pure W 2 C and Ni-W 2 C was carried out by employing DFT calculations (details of simulation method can be seen in the experimental section in Supporting Information). The proposed surface active sites of the Ni-W 2 C were then theoretically predicted by the HER free energy diagrams. The overall HER pathway can be described by a three-state diagram: (1) an initial state (H + + e − ), (2) an intermediate state (adsorbed H * ), and (3) a final state (1/2 H 2 product) [7]. As known, the optimal value of Gibbs free energy of H * adsorption, |ûG H * |, should be zero, leading to the optimal HER electrocatalytic activity. Negative ûG H * implies that the desorption of H * is to be the ratedetermining step (RDS), while positive ûG H * means that the formation of intermediate H * is the RDS [7]. As shown in Figure 7(a), there are three possible adsorption sites for hydrogen on W 2 C nanosheet, i.e., the top of W atom (T), two trigonal sites with superimposing with C (H1), and bottom W atoms (H2). Based on the calculations, H prefers to be adsorbed at the H2 sites with lowest free energy of -0.71 eV (Table S8, Supporting Information). With Ni doping, we firstly investigated the energy-preferable adsorption site out of 4 H2 sites in the configuration (sites 1-4 in Figure 7(a)). As shown in Figure 7(b), the H adsorbed on site 4, which is far away from the doping position, has the lowest free energy. This reveals that the H will be preferable to be adsorbed firstly on the sites away from the doping position. Therefore, at high hydrogen adsorption coverage, the sites far away from the doping position are preferably occupied by hydrogen  ( Figure 7(c)). In this case, the calculated |ûG H * | value is 0.073 eV, whereas the pristine W 2 C shows a much higher |ûG H * | value of 0.16 eV at high coverage (Figure 7(d)). These results indicate that the Ni incorporation would significantly enhance the hydrogen adsorption/desorption process, and thus, catalytic activity of W 2 C towards HER, which is in a good agreement with the experimental data.

Conclusion
In (1) All HER results were corrected for all ohmic (IR) losses throughout the system. To obtain the ohmic resistance, the electrochemical impedance spectroscopy (EIS) measurements were performed with frequency from 0.1 Hz to 100 kHz at an amplitude of 10 mV. The electrochemical surface area (ESCA) was estimated from the double-layer capacitance (C dl ) of the films. The C dl was determined with a simple cyclic voltammetry (CV) method. The CV was conducted in a potential window (0.192-0.242 V vs. RHE) at various scan rates of 5, 10, 20, 50, and 100 mV s −1 . Then capacitive current (j anodic -j cathodic ) at 0.22 V vs RHE was plotted against various scan rates, while the slope obtained was divided by two to obtain the C dl value. The Faradaic efficiency of the catalysts was determined by passing 80 mA cm −2 of current density through the water electrolysis system and the hydrogen gas generated was determined by analyzing 500 l of headspace samples via gas chromatography. The Faradaic efficiency is then defined as the ratio of the measured amount of H 2 to that of the theoretical amount of H 2 (based on Faraday's law).

Simulation Details and Methods.
All the calculations were performed by using density functional theory (DFT) as implemented in the Vienna ab initio package (VASP) [40]. The projector augmented wave (PAW) method [41] was used to describe electron-ion interaction, while the generalized gradient approximation using the Perdew-Burke-Ernzerhof (PBE) functional was used to describe the electron exchangecorrelation. A plane wave basis was set up to an energy cutoff of 520 eV. A 4 × 4 supercell of W 2 C monolayer was used to investigate the adsorption of hydrogen. A 30Å vacuum space was constructed to avoid the periodical image interactions between periodical interactions. The Brillouin zone was integrated using the Monkhorst-Pack scheme [42] with 3 × 3 × 1 k-grid. All the atomic positions and cell parameters were relaxed using a conjugate gradient minimization until the force on each atom is less than 0.01 eVÅ −1 . Gibbs free-energy of the H adsorption was calculated using equation (2): where û ZPE and û H are the zero-point energy and entropy difference of hydrogen in the adsorbed state and the gas phase, respectively. The hydrogen adsorption energy û H is calculated by the following expression: where + and +( −1) are the total energy of Ni-W 2 C nanosheet with n-th and (n-1)-th H atoms adsorption, respectively. H 2 is the energy of a gas-phase hydrogen molecule.

Research
The calculated frequency of H 2 gas is 4345 cm −1 . The contribution from the configurational entropy in the adsorbed state is small and neglected. So the entropy of hydrogen adsorption as △ = (1/2) 2 where 2 is the entropy of molecule hydrogen in the gas phase at standard conditions. With these values, the Gibbs free energy from equation (2) can be rewritten as

Data Availability
All data generated or analyzed during this study are included in this published article and its Supplementary Materials.

Conflicts of Interest
The authors declare no competing financial interests.