Introduction

There are various clean and renewable energy resources that are alternatives to fossil fuels, such as solar, wind, tide, and biomass energy. However, they suffer from intermittent availability, and thus, efficient energy conversion and storage systems are necessary for these alternatives1,2. Hydrogen has been considered a promising candidate for energy storage. It is clean and renewable with an energy storage density much higher than that of batteries, which makes it suitable for application in large-scale production facilities3,4. A hydrogen evolution reaction (HER) in water involves proton reduction and concomitant evolution of hydrogen molecule; it is an endothermic reaction with an additional kinetic energy barrier in intermediate processes. In this regard, catalysis to lower the kinetic energy barrier is crucial for efficient hydrogen production5,6. Although noble metals like Pt and Pd show high catalytic performance, they cannot be used in large-scale industrial applications owing to their scarcity5,7,8. Therefore, the development of low-cost and high-performance HER electrocatalysts has emerged an urgent issue for renewable and clean energy. In addition, HER is important for a variety of electrochemical processes either than energy storage, such as hydrogen fuel cells, electrodeposition, and the corrosion of metals in acids9,10.

Two-dimensional (2D) materials have emerged as potential HER catalysts owing to their large surface areas and earth-abundant elements. To date, several 2D systems, such as graphene and transition metal dichalcogenides (TMDs), have been studied for HER electrocatalysis11,12,13,14,15,16, and the results showed that the HER performance can be improved by intrinsic defects, doping, surface functionalization, strain engineering, phase regulation, and grain boundaries17,18,19,20,21,22,23,24. Recently, the 2D transitional-metal carbide/nitride monolayer (MXene) such as Mo2C was experimentally discovered as a new type of 2D material25,26,27. The chemical formula of MXene is Mn+1Xn, where M is a transition metal and X is C or N. In contrast to TMDs, MXene is intrinsically a metal in the 1T and 2H phases and has a high density of states near the Fermi level. These features are a prerequisite for excellent HER activity, and several theoretical and experimental studies for the electrocatalytic properties of MXene have been performed28,29,30,31,32,33,34,35,36,37. For example, the basal planes of Mo2C can be catalytically activated by functionalization with –O, –H, –OH, and –F groups in contrast to 2H-MoS233. Among these functional groups, the highest HER performance was observed for the samples functionalized with the –O group33,34. The catalytic activity of the Mo2C 2H phase can be enhanced by Co doping owing to the increase in the density of states at the Fermi level35, and Mo2C co-doped with N and S also shows a high HER performance36,37. Despite all the efforts such as surface functionalization and doping, more theoretical understandings of the HER processes and guides to improve the HER activity are still required to apply the 2D Mo2C to the electrocatalytic applications.

2D materials in electrocatalytic cells are placed on a metal substrate, which acts as an electrode. Because 2D systems are atomically thin unlike bulk materials, the substrate inevitably affects their surface chemistry. The effect may be considered insignificant because the catalytic reactions occur directly on the 2D materials, not on the substrate. However, this is not true: one famous counterintuitive example is the strong modification of chemical reactions in ultrathin oxide films on metal substrates, where the electron tunneling from the substrate plays a crucial role38,39,40. As such, it may be possible to optimize HER activity using substrates. Although there have been significant studies on chemically modifying MXenes and their HER electrocatalytic properties, the substrate effect on these materials is not yet understood. In this study, using density functional theory (DFT) calculations, we investigated the substrate effect on the HER activity of MXene. Here, we focus on Mo2C as a typical example of MXene and consider several metal substrates such as Ag, Au, Cu, and graphene. Based on the Sabatier principle, we estimated the catalytic HER activity using the calculated reaction free energy for hydrogen adsorption. Our results showed that the HER activity of the isolated Mo2C monolayer is higher than those of the isolated Ag and Au metal catalysts, but is comparable to that of the Cu catalyst. While the substrate effects of the Au and graphene were not significant, the HER activities of Mo2C on the Ag and Cu substrates were improved to be better than that of Cu. These improvements are caused by the modification of the effective charge of Mo atoms and consequent reduction of the Coulomb attraction between Mo2C and hydrogen. The results suggest that the substrate can be used for fine-tuning HER activity in two-dimensional electrocatalysis.

Results and discussion

It is well known that the catalytic activity of a material is strongly correlated with the reactant–material bond strength: a volcano-shaped graph is formed when the activity is plotted with the bond strength41,42,43. This is explained by the Sabatier principle, which states that catalytic activity is high when the bond strength is neither too strong nor too weak. If the bond strength is too weak, the surface cannot activate the catalytic reaction. If the bond strength is too strong, the product fails to dissociate; the optimal bond strength balances the two extremes. HER also involves complicate processes, and several factors such as reaction path and solvation could affect the HER activity. Based on the Sabatier principle, however, the HER activity can be simply quantified by the reaction free energy in hydrogen adsorption (ΔG)28,44, as defined in Method. Previous experiments have shown that an electrocatalyst with a ΔG close to the optimal value exhibits a high exchange current density, which is a measure of the electrocatalytic activity, and the exchange current density exponentially decreases as ΔG deviates from the optimal value41,44,45. ΔG has been a reasonable descriptor of the HER activity for a wide variety of metals and alloys and has been applied in the design of highly efficient catalysts46,47. Parsons suggested that the optimum value was approximately ΔG = 041. Recent theoretical and experimental results have reported that the optimal ΔG (approximately − 0.4 eV) is slightly smaller than zero in alkaline electrolytes45.

Before we discuss the Mo2C monolayers, we consider the HER activity of metal substrates such as Ag, Au, Cu, Pt, and graphene. For the substrates, only the (001) surface was considered. Figure 2a shows the ΔG of the metal substrates with respect to the coverage of the hydrogen absorbed on the surfaces. The coverage is defined as the ratio of the number of absorbed H atoms to the total number of possible absorption sites. The Pt substrate had the smallest ΔG for each H coverage, and the ΔG for each H coverage increased in the order of Cu, Ag, Au, and graphene. The ranges of the ΔG were from − 0.37 to − 0.02 eV, from 0.14 to 0.30 eV, from 0.41 to 0.53 eV, from 0.50 to 0.97 eV, and from 0.89 to 1.53 eV, for Pt, Cu, Ag, Au, and graphene, respectively. These results are in good agreement with previous findings44,45. In the graphene substrate, ΔG abruptly decreases to − 0.79 and − 0.54 eV at the two high coverages of 0.75 and 1.0, respectively. This is related to the qualitative change in the C π-bonding network accompanied by the metal-to-insulator transition48,49,50,51. In this regard, we distinguish the two results (open violate circle) from the others in low coverages in Fig. 2, because an insulator cannot be an electrocatalyst. Although the ΔG of both Pt and Cu were close to zero, the experiments clearly show that Pt is the better HER catalyst compared to Cu44,45. The results indicate that the optimal ΔG is close to, but smaller than zero. Therefore, in the following, we set the optimal value to the average ΔG of Pt (− 0.18 eV), which is represented by the horizontal lines in Fig. 2a,b. This indicates as the ΔG approaches the optimal value, the catalysis of HER activity increases.

Next, we consider the HER activity, i.e., ΔG, of Mo2C. To date, many studies have considered the Mo2C 1T phase, despite it being less stable than the 2H phase52,53. Here, we focused on the 2H phase. As shown in Fig. 1a, Mo2C has three absorption sites for hydrogen atoms, such as the top of a hexagonal center (TH), a C atom (TC), and a Mo atom (TM) (see Fig. 1a). We placed a H atom on each site and optimized the atomic structures. The H atom is the most stable at the TH site. The TC site is metastable, and its energy is higher by 0.20 eV than that of the TH site. The TM site is unstable, and the H atom moves to the stable TH site during ionic relaxation. In high H coverages, the TH sites of H atoms also have lower energies than the other sites. In this regard, we calculated the ΔG of the TH sites, and the results are shown in Fig. 2a,b. For the isolated Mo2C monolayer, ΔG varies from − 0.71 eV for low hydrogen coverage (0.0625) to − 0.37 eV for full hydrogen coverage (1.0). To check the calculational accuracy in our systems, we have also compared the PBE functional results with the RPBE functional ones, and as shown in Fig. 2b, the two results are in good agreement within 0.03 eV. In this regard, we conclude that, in the systems that we considered, the PBE functional also provides reasonable results with the same accuracy level of the RPBE functional.

Figure 1
figure 1

Atomic structures of (a) Mo2C and (b) Mo2C on a metal substrate. The pink, brown, and blue balls represent Mo, C, and substrate atoms, respectively. In (a), hydrogen absorption sites are denoted by TH, TC, and TM, which are on-top of a hexagonal center, C atom, and Mo atom, respectively.

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Figure 2
figure 2

The variation of ΔG with respect to hydrogen coverage. In (a) and (b), the violate, dark yellow, red, green, and gray dotted lines are the results for the graphene, Au, Ag, Cu, and Pt catalysts, respectively, and the corresponding solid lines are the results for the Mo2C on each substrate. The horizontal gray line is the averaged ΔG for the Pt catalyst, which is the optimal ΔG. (b) We magnified the energy window from − 0.8 to 0.0 eV, which is the ΔG region of Mo2C. The black filled and open circles represent the PBE and RPBE functional results for the isolated Mo2C, respectively, and the black and red open boxes are the results for 1T Mo2C and 1T Mo2C on the Ag substrate, respectively. The red triangles are the results for the two layers of Mo2C on the Ag substrate.

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To directly compare the HER activity of Mo2C with those of the metal substrates, we plotted the volcano-shaped HER activity with the peak located at the optimal ΔG in Fig. 3. The ΔG of Cu, Ag, Au, and graphene were all positive and located on the right of the optimal value. The HER activity of the Cu substrate was expected to be higher than the other substrate except Pt. The results of the graphene substrate are not shown in Fig. 3 because it had very large ΔG values, that is, very low HER activity. As discussed above, the ΔG values of Mo2C were smaller than the optimal value; thus, the HER activity (black line) is shown on the left side of the optimal line in Fig. 3. The HER activity of Mo2C was expected to be higher than that of Ag and Au, but comparable to that of Cu. The HER activity of Mo2C was broader than that of Cu, and the HER activity was lower with low H coverage, but it was higher for high H coverage.

Figure 3
figure 3

The HER activity for the catalysts Pt (gray), Cu (green), Ag (red), and Au (dark yellow). The HER activity of the Mo2C on the corresponding substrates are shown. The vertical black line at − 0.18 eV represents the optimal value, and the activity of the catalysts are compared on the vertical line. A higher position on the line represents higher HER activity.

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The HER activity can be affected by the metal substrate of Mo2C. Figure 1b shows the atomic structure of Mo2C on a substrate: the Mo2C was placed on the (001) surface of the substrate. There was no strong bonding between the Mo2C and substrates, but a heterostructure was formed by a weak dispersive interaction. The atomic structures indicated that the physical properties of Mo2C were not significantly altered by the substrates. Using these structures, we calculated the ΔG of Mo2C on Cu, Ag, Au, and graphene substrates, and the results are shown in Fig. 2a,b. The ΔG values for all cases are distributed in the range from − 0.74 to − 0.35 eV, which is similar to the range of the isolated Mo2C case (− 0.71 ~ − 0.37 eV). These results indicate that Mo2C is dominant in determining ΔG because the H atoms directly bond to Mo2C, and the substrate effects are secondary. However, there are some ΔG differences that are attributable to the substrate. On the Cu and Ag substrates, the variation of ΔG was significantly reduced: while the ΔG for high coverages is similar to that of the Mo2C monolayer, the ΔG for low coverage increases from that of the Mo2C monolayer. This ΔG change results in the high HER activity for all H coverages. As shown in Fig. 3, the overall HER activity becomes better than that observed in the isolated Cu substrates, as the ΔG approaches the optimal value. Thus, the HER activity of 2D Mo2C can be adjusted by the substrate. For Mo2C on Au and graphene substrates, on the other hand, the changes in ΔG with H coverage are similar to those of the isolated Mo2C monolayer, which implies that the effects of the two substrates are negligible. Previous work suggested that HER activity can be improved in small Mo2C clusters on clean/nitrogen-doped graphene substrates54. Note that our results have only considered the pure 2D Mo2C fully covered on clean graphene surfaces, and in different structures such as the small Mo2C clusters in the previous work the substrate effect could be significant. We also considered the two Mo2C layers on the Ag substrate. As shown in Fig. 2b, the ΔG (red open triangle) decreases from ΔG of the Mo2C monolayer on the Ag substrate and approaches toward ΔG of the isolated Mo2C. As one may expected, this is because the substrate effect is reduced, when more Mo2C layers are stacked on the substrate.

While we have focused on the Mo2C 2H phase until now, the substrate can also tune the HER activity of the Mo2C 1T phase. As shown in Fig. 2b, ΔG of 1T Mo2C varies from − 0.53 eV (at the coverage 0.125) to − 0.41 eV (at the full coverage 1.0). On the Ag substrate, i.e., 1T Mo2C on the Ag substrate, ΔG is changed to the range from − 0.46 eV (at the coverage 0.5) to − 0.35 eV (at the low coverage 0.0625). Similar to the 2H Mo2C, the HER activity of 1T Mo2C can be also improved on the Ag substrate.

The increase in ΔG for low H coverage on the Cu and Ag substrates indicates the weakening of the bond strength between Mo2C and H. To understand the change in the bond strength, we performed Bader charge analysis, as shown in Table 1. In the Mo2C without a substrate, some of the six valence electrons in the Mo atom are transferred to the C atoms, resulting in positively charged Mo ions and negatively charged C ions. Bader charge analysis shows quantitative changes in the valence electrons: each Mo atom in Mo2C has 5.434 valence electrons, which implies that the Mo atom loses 0.566 electrons and thus the effective charge of the Mo ion becomes + 0.566. When an H atom is absorbed in the TH site of Mo2C, it forms bonds with the three nearest neighboring Mo atoms. Figure 4 shows the charge redistribution in the formation of the bonds, which is calculated by subtracting charge densities of the isolated Mo2C \({\rho }^{{Mo}_{2}C}\left(r\right)\) and H atom \({\rho }^{H}\left(r\right)\) from that of the H absorbed Mo2C \({\rho }^{{Mo}_{2}C+H}\left(r\right)\), i.e., \({\rho }^{{Mo}_{2}C+H}\left(r\right)-[{\rho }^{{Mo}_{2}C}\left(r\right) + {\rho }^{H}\left(r\right)]\). As shown in Fig. 4, the charge density increases near the H atom, but it decreases near the three Mo atoms. This indicates that the electrons in the three Mo atoms are transferred to the H atom and as a result the H atom becomes negatively charged. Using Bader charge analysis as shown in Table 1, we quantify the effective charges of the three Mo and H atoms to be + 0.658 and − 0.453, respectively. Beside the bonding between the H and Mo atoms, Coulomb attraction between the positively charged Mo and negatively charged H atoms induced by charge imbalance increases the bond strength.

Table 1 The effective charge of the Mo and H atoms in the isolated Mo2C and Mo2C on Ag (Mo2C/Ag), Cu (Mo2C/Cu), and Au (Mo2C/Au) substrates obtained from Bader charge analysis.
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Figure 4
figure 4

The charge redistribution in the formation of the H–Mo bonds. The redistribution is calculated by subtracting charge densities of the isolated Mo2C \({\rho }^{{Mo}_{2}C}\left(r\right)\) and H atom \({\rho }^{H}\left(r\right)\) from that of the H absorbed Mo2C \({\rho }^{{Mo}_{2}C+H}\left(r\right)\), i.e., \({\rho }^{{Mo}_{2}C+H}\left(r\right)-[{\rho }^{{Mo}_{2}C}\left(r\right) + {\rho }^{H}\left(r\right)]\). The red and green iso-surfaces denote increasing and decreasing of the charge density in the bond formation, respectively.

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The substrates modify the charge imbalance and thus the Coulomb attraction. For the Mo2C on the Ag and Cu substrates, the valence electrons in the Mo atoms increased to 5.502 and 5.492, respectively, compared to the isolate Mo2C (5.434). This indicated that the Ag and Cu substrates donate electrons to the Mo2C layer, and as a result the effective charge of the Mo atoms is reduced to + 0.498 and + 0.508 on the Ag and Cu substrates, respectively. This reduction also affects the effective charge of the Mo atoms after H absorption, and as shown in Table 1, the effective charges of the nearest neighboring Mo atoms became + 0.605 and + 0.604 on the Ag and Cu substrates, respectively, which is smaller than that of the isolated Mo2C (+ 0.658). On the other hand, the effective charge of the absorbed H atom (~ − 0.45) remains nearly the same for the different substrates (see Table 1). This is because the hydrogen bonding level is located far below Fermi level. Figure 5a,b show the density of states of the H absorbed Mo2C and Mo2C on the Ag substrate. For the both cases, the hydrogen bonding level is located around − 4.7 eV by level interaction between the Mo d-orbitals and H s-orbital (see Fig. 5c), while the Mo d-bands are distributed near the Fermi level. As such, the effective charges of the Mo atoms are easily changed by the substrates, but the effective charge of the H atom is not. Thus, the reduction of the effective charge of the Mo atom weakens the Coulomb attraction between the Mo and H atoms in the Mo2C on the Ag and Cu substrates, thereby increasing ΔG. On the other hand, for the Mo2C on the Au substrates, the electric charges of the Mo atoms are similar to those in the isolated Mo2C; thus, the variations of ΔG shown in Fig. 2 are also similar to those of the isolated Mo2C. Thus, the charge redistribution caused by the substrates can affect the HER activity of the 2D Mo2C.

Figure 5
figure 5

Electronic structure of the H absorbed Mo2C. Density of states of (a) the H absorbed Mo2C and (b) the H absorbed Mo2C on the Ag substrate. Shaded gray is the total density of state and blue line is the projected density of state onto the absorbed H atom, which is rescaled by multiplying by factors of 50 in (a) and 250 in (b). Fermi level is set to zero. In (b), shaded sky blue is the projected density of state onto the Ag substrate. (c) Schematics of the formation of the H bonding level. The filled gray represents the Mo d-bands and Fermi level is denoted by the red dotted line. The level interaction between the Mo d-orbital and H s-orbital form the bonding level around -5 eV in (a), which is dispersive also by interaction with other levels.

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Here we have focused on the Mo2C as a typical example of MXene. There are other MXenes such as Ti, Nb, Cr-based MXene, and these are also atomically thin two-dimensional systems. As such, a substrate can alter the electronic properties of a whole MXene in contrast to conventional bulk materials, of which the properties are changed only in the interface region. For example, as shown in Table 1, substrates change the effective charge of all the Mo atoms in the Mo2C monolayer, which affects the HER activity. In this regard, we believe that the substrates can also alter the HER activity of the other two-dimensional MXenes, and this could provide a way to tune the catalytic activity of two-dimensional MXenes.

Summary

In summary, we investigated the substrate effect on the HER activity of 2D Mo2C and compared its activity with that of metal catalysts such as Ag, Cu, Au, and graphene. The HER activity of the isolated Mo2C exhibits relatively large variation depending on the hydrogen coverage, showing low activity at low hydrogen coverage and high activity at high hydrogen coverage. While the substrate effect is not significant, we have shown that Ag and Cu substrates can tune the HER activity of Mo2C, especially at low hydrogen coverage, such that HER activity becomes high for all H coverages. Our results suggest a method for tuning the HER activity of two-dimensional electrocatalysis.

Methods

The optimized geometries and relevant total energies were calculated using DFT calculations55,56 with the Perdew-Burke-Ernzerhof (PBE) exchange–correlation functional57, as implemented in the Vienna ab initio simulation package58. Previous work has shown that the revised PBE (RPBE) functional provides more accurate adsorption energy than the PBE functional.59 We have also tested the accuracy of the PBE functional in our systems and found that the PBE functional results are in good agreement with the RPBE functional ones within 0.03 eV (see Fig. 2b). The projected augmented wave potentials were used to represent the ion cores60,61. The wave functions were expanded in a plane wave basis set up to a cut-off energy of 400 eV. To model the Mo2C monolayer (see Fig. 1a), we used a periodic supercell containing 48 atoms (4 × 2\(\sqrt{3}\) unit cells). For the Ag, Au, Cu, and Pt substrates, we employed periodic slab models containing six atomic layers along the (001) direction. In all the calculations, the slabs were separated by a vacuum gap of at least 20 Å. The 2 × 2 × 1 Monkhorst–Pack k-point mesh was used for Brillouin-zone integration. We used optimized lattice parameters for the Mo2C and substrates and the lattice parameters of the Mo2C monolayer for the Mo2C on a substrate (Fig. 1b). In all the cases, the lattice mismatches were below 10%, and the effect of the lattice mismatches was small because hydrogen atoms are directly bonded to Mo2C, not the substrates. Note that the metallicity of the Mo2C monolayer is maintained under tensile and compressive strain. We fixed the positions of the atoms in the two bottom layers of the substrates, and the atomic positions of the other atoms were fully relaxed until the residual forces were less than 0.01 eV/Å.

The HER activity was measured using the variation of the reaction free energy in hydrogen adsorption ΔG, represented by

$$ \Delta G = \Delta E_{{\text{H}}} + \Delta ZPE - T\Delta S, $$

where ΔEH, ΔZPE, and ΔS are the changes in the DFT total energies, zero-point energy, and entropy of a hydrogen atom when absorbing an electrocatalyst from an H2 molecule, respectively, and T is the system temperature. Here, we consider standard conditions (T = 298.15 K, p = 1 bar, pH = 0), i.e., acidic HER process, and (ΔZPE − TΔS) is set to 0.24 eV28,44,54,62,63. ΔEH can be calculated using either

$$ \Delta E_{{\text{H}}} = E\left( {X + nH} \right){-} \, E\left( {X + \left( {n - 1} \right)H} \right){-} \, E\left( {H_{{2}} } \right)/{2} $$

for the individual process or

$$ \Delta E_{{\text{H}}} = \left[ {E\left( {X + nH} \right){-}E\left( X \right){-}nE\left( {H_{{2}} } \right)/{2}} \right]/n $$

for the average process63. Here, E(H2), E(X), and E(X + nH) are the total energies of the H2 molecule, electrocatalyst X, and electrocatalyst X with n hydrogen atoms, respectively. The difference between the two is qualitatively insignificant; therefore, we used the latter only.