Metal Dichalcogenides Monolayers: Novel Catalysts for Electrochemical Hydrogen Production

Catalyst-driven electrolysis of water is considered as a “cleanest” way for hydrogen production. Finding cheap and abundant catalysts is critical to the large-scale implementation of the technology. Two-dimensional metal dichalcogenides nanostructures have attracted increasing attention because of their catalytic performances in water electrolysis. In this work, we systematically investigate the hydrogen evolution reduction of metal dichalcogenides monolayers based on density-functional-theory calculations. We find that metal disulfide monolayers show better catalytic performance on hydrogen production than other metal dichalcogenides. We show that their hydrogen evolution reduction strongly depends on the hydrogen coverage and the catalytic performance reduces with the increment of coverage because of hydrogenation-induced lower conductivity. We further show that the catalytic performance of vanadium disulfide monolayer is comparable to that of Pt at lower hydrogen coverage and the performance at higher coverage can be improved by hybridizing with conducting nanomaterials to enhance conductivity. These metal disulfide monolayers with lower overpotentials may apply to water electrolysis for hydrogen production.

metallic edges can promise the excellent HER activity. To date, a comprehensive study on the HER performances of MX 2 monolayers as well as its origin has not been available. In this work, the applications of MX 2 monolayers in electrolysis of water are systematically investigated based on the calculations of density-functional theory (DFT). We predict that the HER performances of MX 2 monolayers depend on M, X and H-coverage. We show that VS 2 is comparable to Pt for electrolysis of water at lower H-coverage and its catalytic activity can be further enhanced by improving conductivity.

Results and discussion
In our calculations, we focus on metallic/semimetallic 2H transitionmetal dichalcogenides, MX 2 (M 5 Nb, Ta, and V; X 5 S, Se, and Te) because 2H phase is more stable and high conductivity is essential to the electrolysis of water. The MX 2 unit cells with trigonal prismatic (2H) coordination are first optimized to obtain the lattice parameters. The optimized structures of MX 2 (M 5 Nb, and Ta; X 5 S, Se, and Te) (see Supporting Data, Table I) from our calculations are consistent with the reported experimental and theoretical data 46 . We see that the lattice parameters of NbX 2 are almost equivalent to those of TaX 2 , while are larger than those of VX 2 (Supporting Data, Table I). To investigate the HER performances of MX 2 monolayers at various hydrogen coverage on their surfaces, the geometries of MX 2 monolayers with one surface fully covered by hydrogen atoms (MX 2 -H) are relaxed to find out the effects of hydrogen coverage on their lattice parameters. The hydrogen atoms are adsorbed on the top of X atoms (Figure 1), where is the most stable position 37,47,48 . The optimized structures of MX 2 -H (Table II in Supporting Data & Figure 2) show that the lattice constants (a) are extended by 2.0 to 3.8%, 1.7 to 3.3%, and 3.4 to 4.5% for NbX 2 , TaX 2 , and VX 2 , respectively, where the extension increases as X changes for S to Se, further to Te ( Figure 2). The thicknesses (c) and the X-M bonds of the monolayers are reduced by the H-coverage on their surfaces ( Figure 2). The calculated bond lengths are about 1.4, 1.5 and 1.7 Å for S-H, Se-H, and Te-H bonding, respectively (Supporting Data, Table II).
According to the Sabatier principle, the optimal catalytic activity of material for HER can be achieved on a catalytic surface with intermediate binding energies (or free energies of adsorption) for reactive intermediates 15 , which can be quantified by analyzing the reaction free energy of hydrogen adsorption (DG H ) 13,15,37,49 . The optimum value is around DG H 5 0. To obtain the reaction free energy, we calculate DG H for various H coverage on MX 2 monolayers as following: where DE H is the hydrogen chemisorption energy defined as: atom is attached to one of the 6 X atoms ( Figure 1). For other Þ ), all of the possible H-adsorption configurations on the six X atoms are considered, where the adsorption energy is calculated by two methods -''average'' of all configurations and ''most stable'' configuration. We first consider the supercell (psupercell) based on monolayer pristine lattice parameters (from Table I    We also calculate the hydrogen adsorption energy in the supercell (h-supercell) constructed on the lattice parameters of fully H-covered monolayer (from Table II in Supporting Data). We see that the HER trend as a function of H-coverage ( Figure 5) is the same as that in p-supercell. The MS 2 monolayers still show the best HER performance at same H-coverage because their overpotentials are smaller than those of MSe 2 and MTe 2 monolayers ( Figure 5). For all of MX 2 monolayers, DG H in h-supercell is reduced because of the extended lattice constants (that is equivalent to the effect of strain in Ref. 37 (Figure 4b). After 25% H-coverage, VS 2 gives out the best HER performance because its overpotential is positive and lower than those of NbS 2 and TaS 2 (Figure 4b). By carefully comparing the energies of systems calculated from p-supercell and h-supercell, we find that the effect of H-coverage on lattice parameters is negligible when it is less than the 33% ( 2 6 coverage). Therefore, we combine the calculated DG H of MS 2 from p-supercell for H-coverage up to 1 6 and h-supercell for H-coverage from 2 6 to 6 6 into Figure 6. Clearly, we see that VS 2 monolayer shows the best HER performance in all of considered systems.
To investigate the possible origin of HER performance and the effects of H-coverage, the partial densities of states (PDOSs) of M, X, and H are calculated. The calculated PDOSs clearly show the change of conductivities of MS 2 monolayers with the H-coverage (Figure 7 and supporting data S1 , S5). We see that the pristine VS 2 monolayer is metallic, where the Fermi level is within the middle energy band and near to its bottom (Figure 7a). The middle energy states are dominated by V d electrons. With introducing H atoms to the monolayer's surface, the energy sates shift down to lower energy region, or under high H-coverage (Supporting data, S1 , S5). The analysis of PDOSs shows that the conductivities of the MX 2 monolayers are reduced by the H-coverage, especially after half H-coverage on the surfaces, leading to the decreases of their HER performances (Figures 3 , 6). This finding may also apply to the MX 2 nanostructures with metallic edges because their conductivities should be reduced when edges are fully saturated by hydrogen atoms 44 . This is different from Pt-related catalysts, whose conductivities have not been affected by the H-coverage on their surfaces 13,15,49 . How to improve the conductivities of MS 2 -based catalysts under high Hcoverage should be a challenge for their application in electrolysis of water. One of ways is to mix these MS 2 monolayers with high conducting nanostructures, such as graphene 33,50 .   For comparison, the HER performance of MoS 2 monolayer is calculated. We see that its overpotential (DG H ) (Supporting data, S6) is larger than those of MX 2 (M 5 Nb, Ta, and V; X 5 S, Se, and Te) monolayers considered in this work ( Figure 6). At lower and full H-coverage (  1  12  ,  1  6 , and 1), its overpotential is about 2.0 , 2.1 eV.
At moderate H-coverage, its overpotential is larger than 1.1 eV. The calculated densities of states show that pure and H-covered MoS 2 monolayers are intrinsic or n-type semiconductors (Supporting data, S7). These results confirm that the surface of MoS 2 monolayer is inert to electrolysis of water, and the most active sites are at the edges or defects of MoS 2 nanostructures [27][28][29] . However, our study show that the surfaces of MX 2 (M 5 Nb, Ta, and V; X 5 S, Se, and Te) monolayers, especially VS 2 , are very active, which further enhance their ability for electrolysis of water due to higher contacting area with water.

Conclusions
The DFT-based first-principles calculations are carried out to investigate the hydrogen evolution reduction of MX 2 monolayers. We find that MS 2 monolayers are better than MSe 2 and MTe 2 monolayers in electrolysis of water, especially VS 2 , which shows the best HER performance because of its lower overpotential. We show that the HER performances of MX 2 monolayers strongly depend on the Hcoverage on their surfaces. With increasing H-coverage, the performance is reduced because of the reduction of conductivity. We also show that the strain may improve the HER performance at relatively low H-coverage. We further predict that their HER applications at high H-coverage can also be achieved by improving their conductivities, such as hybridization with metallic nanostructures. It is expected that the MS 2 monolayers, especially VS 2 , may find applications to electrolysis of water for hydrogen production.

Methods
The first-principles calculations are carried out to investigate the hydrogen evolution reduction of transition-metal dichalcogenide monolayers. Our calculations are based on the density functional theory (DFT) 51 and the Perdew-Burke-Eznerhof generalized gradient approximation (PBE-GGA) 52 . The projector augmented wave (PAW) scheme 53,54 as incorporated in the Vienna ab initio simulation package (VASP) 55 is used in the study. The Monkhorst and Pack scheme of k point sampling is used for integration over the first Brillouin zone 56 . A 15 3 15 3 1 grid for k-point sampling for geometry optimization of unit cells, and an energy cut-off of 450 eV are consistently used in our calculations. A sufficiently large supercell is used so that the monolayers in neighbouring cells in the vertical direction are separated by a vacuum region of at least 20 Å . Good convergence is obtained with these parameters and the total energy was converged to 2.0 3 10 25 eV/atom. The error bar (or uncertainty) of the DFT calculation is less than 5 meV. The thermodynamic processes via Tafel pathway are calculated 17 . The effect of solvent on the HER performance of VS 2 monolayer is investigated by including H 2 O molecules in the systems with various Hcoverage 18,21 .
The calculated thermodynamc processes of HER on VS 2 monolayer via Tafel channels and the effect of solvent on overpotentials are included in Supporting Data.