Defect engineering in the MA₂Z₄ monolayer family for enhancing the hydrogen evolution reaction: first-principles calculations

Abstract

Water electrolysis is a sustainable and clean method to produce hydrogen fuel via the hydrogen evolution reaction (HER). Using effective and low-cost electrocatalysts for the HER to substitute expensive noble metals is highly desired. In this study, by using first-principles calculations, we designed a defective MA₂Z₄ monolayer family as two-dimensional (2D) electrocatalysts for the HER, and their stability, electronic properties, and catalytic performance were investigated. As the most representative material of the MA₂Z₄ monolayer family, MoSi₂N₄ was first successfully synthesized in the experiment [Y. L. Hong et al., Science, 2020, 369, 670–674]. Our results reveal that vacancy regulation at the outer Z atom (V_Z) can obviously enhance the catalytic activity toward the HER, compared with the pristine MA₂Z₄. It is also shown that ΔG_H* can be close to 0 eV with V_P vacancies at active site 1, which should be the optimal performance for a HER catalyst. Moreover, we demonstrated that the HER performance prefers the Volmer–Heyrovsky mechanism. Our study provides a strategy for designing MA₂Z₄ monolayer family electrocatalysts, which are predicted to be employed in HER catalysts with low cost and high performance.

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1. Introduction

Hydrogen has become one of the most promising alternatives to substitute fossil fuels, owing to its zero pollution, high combustion value, high energy density, and renewable properties.^1–4 There are many approaches to produce hydrogen, such as the decomposition of coal, water, and hydrocarbon. Water electrolysis is a sustainable, clean, and low-cost method to produce H₂, and electrocatalysts can enhance the efficiency of water splitting observably.⁵ For the hydrogen evolution reaction (HER), platinum and its alloys are considered potential catalysts to activate the HER owing to the small Tafel slope, low overpotential, and high exchange current density.^6–8 However, the high price and scarcity hamper the exploration of nonnoble metal-based catalysts having HER catalytic activity comparable to it.

In recent years, lots of nonnoble metal-based catalysts, such as carbides,^9–12 borides,^13,14 phosphides,^15,16 sulfides,^17–19 nitrides^20–22 and so on, have been discovered and made significant progress as a potential catalyst for activating the HER. Among these materials, two-dimensional (2D) nano materials provide new opportunities for the HER because of the compelling structural and electronic properties. Graphene-based materials and transition metal dichalcogenides (TMDs) have gained much attention as 2D electrocatalysts for the HER due to their high electronic conductivity and uniformly distributed active sites.^23–25 Recently, a new type of 2D material MA₂Z₄ monolayer family,^26–28 in which M represents Mo, W or V, A represents Si or Ge, and Z represents an early transition stands for N, P, or As, have been proposed and exhibited high strength and remarkable stability. Among these materials, MoSi₂N₄ and WSi₂N₄ were first successfully synthesized by chemical vapor deposition with high strength (66 GPa), semiconductor properties (band gap 1.94 eV) and excellent stability.^29,30 The unique and adjustable structure of septuple Z–A–Z–M–Z–A–Z (7 atomic layer thicknesses) possesses great possibilities of integrating various properties. Because of the fascinating properties like other 2D materials, such as good ambient stability, high carrier mobility, and broad hole and electron mobilities,³¹ it is reasonably speculated that highly efficient HER catalysts may exist in the MA₂Z₄ monolayer family. Therefore, searching ideal electrocatalysts from the family by high-throughput screening must have great significance for the development of HER catalysts, but limited efforts have been made in this field.

In this study, using first-principles calculation, we designed and demonstrated defective MA₂Z₄, investigated their stability and electronic properties, and evaluated their performance as HER electrocatalysts. Our results reveal that vacancy regulation at the outer Z atom (V_Z) can obviously enhance the catalytic activity toward the HER, compared with pristine MA₂Z₄. It is also shown that ΔG_H* can be close to 0 eV with V_P vacancies at active site 1, which should be the optimal performance for a HER catalyst, so V_P vacancies MA₂P₄ should have optimal ΔG_H* and activation energy barrier for the rate-determining step among the family, and it exhibits more favorable performance. We also demonstrate that the Volmer–Heyrovsky mechanism is more preferred for the HER on defective MA₂Z₄. We compared our results with that of other researchers on MA₂Z₄, and it can be found that the V_Z defect is more effective for MA₂Z₄ in the catalysis of the HER. Thus, our effort on defective MA₂Z₄ makes it a highly promising electrocatalyst for th eHER, and our findings provide a deep understanding in designing efficient and durable electrocatalysts.

2. Computational methods

Our first-principles calculations were performed using the Vienna Ab initio Simulation Package (VASP).³² The projected augmented wave (PAW) potentials were used to analyze the interactions between core electrons and valence electrons.³³ The electron exchange–correlation interactions were described using the Perdew–Burke–Ernzerhof (PBE) functional within generalized gradient approximation (GGA).³⁴ The DFT-D3 exchange–correlation functional was introduced in structural optimization to take the van der Waals interaction into account. The vacuum space along the z-direction was set to 20 Å in order to eliminate the interactions between MA₂Z₄ and its periodic images.

The plane-wave energy cutoff was set to be 500 eV. The convergence criterion was set as 10⁻⁵ eV for total energy. All the atomic positions and lattice structures were fully relaxed with the threshold of a maximum force of 0.02 eV Å⁻¹. In order to ensure the accuracy and efficiency of the calculation, a Gamma-centered k-point mesh with a Monkhorst–Pack method 5 × 5 × 1 was employed for all considered structures after the convergence test.³⁵ The amount of charge transfer between the C atoms and H atoms was calculated using Bader code.³⁶ We also calculated H* adsorption energy barriers using the climbing image-nudged elastic band (CI-NEB) method.³⁷ The CI-NEB is an efficient method to determine the minimum energy path and saddle points between a given initial and final position,^38,39 and in our CI-NEB calculations, the initial and the final structures were fully optimized.

The adsorption energy (ΔE_H) is defined as

where E(*H) and E(*) are the total energy of structures with and without hydrogen adsorption, respectively, and E(H₂) is the total energy of a H₂ molecule.

The Gibbs free energy (ΔG_H*) is defined as:

ΔG_H* = ΔE_H + ΔE_ZPE − TΔS_H (2)

where ΔE_H is the adsorption energy, ΔE_ZPE is the difference in zero-point energy, T is the temperature (298.15 K) and ΔS_H is the entropy difference of adsorbed H and H in the gas phase. We approximated the entropy of hydrogen adsorption as , where is the entropy of gas phase H₂ under standard conditions, and TΔS_H was set to be −0.202 eV (ref. 40 and 41) after calculation in this study.

3. Results and discussion

3.1 Geometries and stability of MA₂Z₄

The optimized structures of MA₂Z₄ (M = Mo, W, V; A = Si, Ge; Z = N, P, As) are shown in Fig. 1(a). The MA₂Z₄ monolayer is a seven-layer honeycomb structure, in which the order of the M, A, and Z atom covalent bond is Z–A–Z–M–Z–A–Z, and the layers are connected by van der Waals (vdW) forces.⁴² In the pristine structure, the adsorption sites can be divided into four types. The site 1 is the top site of Z atoms, the site 2 is the top site of inside Z atoms, site 3 is the top site of A atoms, and the site 4 is the top site of M atoms.

Fig. 1 Top and side views of (a) optimized pristine MA₂Z₄, (b) V_M-MA₂Z₄, (c) V_A-MA₂Z₄, and (d) V_Z-MA₂Z₄. Note that the dotted red circle represents the defect site and numbers represent possible H adsorption sites. Purple, blue, and pink balls represent M, A, and Z atoms, respectively. The red diamond represents the primitive structure, and t is the thickness of MA₂Z₄ (for interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

For pristine MA₂Z₄, the calculated lattice constants, and the thickness of the monolayer layer are listed in Table 1 (while A–Z (d₁, d₂) and M–Z (d₃) bond lengths; A–Z–A (θ₁), Z–A–Z (θ₂) and Z–M–Z (θ₃, θ₄) angles are listed in Table S1†). Clearly, the lattice constants exhibit an increasing trend with the increasing atomic radius of either M, A, or Z. For instance, for W-based MA₂Z₄, the lattice constant (a = b) has the order of WSi₂N₄ (2.54 Å) < WGe₂N₄ (3.04 Å) < WSi₂P₄ (3.46 Å) < WGe₂P₄ (3.55 Å) < WSi₂As₄ (3.60 Å) < WGe₂As₄ (3.70 Å). The thicknesses (t) of MoSi₂N₄ (7.00 Å), MoSi₂P₄ (9.34 Å), MoSi₂As₄ (9.90 Å), and WSi₂N₄ (7.01 Å), and the lattice constants (a = b) of MoSi₂N₄ (2.90 Å), MoSi₂P₄ (3.45 Å), MoSi₂As₄ (3.58 Å), and WSi₂N₄ (2.54 Å) agree well with previous reports.^43–47 According to the symmetry of MA₂Z₄ structures, we consider three kinds of vacancies, which are outside the Z atom vacancy, A atom vacancy, and M atom vacancy to verify the performance of defective structures in Fig. 1(b)–(d). The dotted red circle represents the M atomic vacancy, A atomic vacancy, and outside Z atomic vacancies, respectively. We select four atoms next to the vacancy as the H atom adsorption sites; the specific positions are marked with numbers in Fig. 1(b)–(d).

Table 1 The optimized geometric and electronic structure parameters of the MA₂Z₄ monolayer including the lattice constant (a, b); the thickness of monolayer layer (t) and the corresponding data in previous reports

Structure	a = b (Å)	Reported a = b (Å)	t (Å)	Reported t (Å)	Structure	a = b (Å)	Reported a = b (Å)	t (Å)	Reported t (Å)
MoSi2N4	2.90	2.89 (ref. 44)	7.00	7.01 (ref. 45)	WGe2N4	3.04	3.09 (ref. 44)	7.48	—
MoSi2P4	3.45	3.46 (ref. 48)	9.34	9.37 (ref. 46)	WGe2P4	3.55	3.54 (ref. 48)	23.10	—
MoSi2As4	3.58	3.61 (ref. 48)	9.90	9.94 (ref. 46)	WGe2As4	3.70	3.69 (ref. 48)	10.20	—
MoGe2N4	3.03	3.02 (ref. 48)	7.48	7.39 (ref. 46)	VSi2N4	2.86	2.88 (ref. 28)	6.87	—
MoGe2P4	3.53	3.53 (ref. 48)	9.63	—	VSi2P4	3.48	3.48 (ref. 48)	9.15	9.25 (ref. 49)
MoGe2As4	3.67	3.69 (ref. 48)	10.20	—	VSi2As4	3.58	3.65 (ref. 44)	9.78	—
WSi2N4	2.90	2.91 (ref. 47)	7.01	7.01 (ref. 47)	VGe2N4	3.00	3.01 (ref. 28)	7.36	—
WSi2P4	3.46	3.46 (ref. 48)	9.32	—	VGe2P4	3.55	3.56 (ref. 48)	9.48	—
WSi2As4	3.60	3.61 (ref. 48)	9.91	—	VGe2As4	3.66	3.72 (ref. 48)	10.40	—

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Then, we calculate the formation energy to verify the stability of the structure. The results are shown in Fig. 2. The formation energy of vacancy is calculated using the following formula:

E_f = E_vacancy − E_primitive + E_v-atom (3)

where E_vacancy is the energy of MA₂Z₄ with a vacancy, and E_primitive is the energy of primitive MA₂Z₄. E_v-atom is the chemical potential of the vacancy atom, which can be obtained from the corresponding elementary unit cell or gas molecule.⁴⁵ As we know, a lower formation energy indicates an energetically favourable and feasible defective structure, so we try to find the more stable structure among three types of vacancies of all defective structures. Our calculation results show that the formation energy of V_Si-MoSi₂N₄ is 0.33 eV per atom, which agrees well with previous reports (0.32 eV per atom),⁴⁵ and the defect formation energies of MoGe₂P₄, WGe₂P₄ and VGe₂P₄ are the three smallest energies among all 18 structures, which are also smaller than the previous reported transition metal doped MoSi₂N₄ (0.29 eV per atom)⁴⁵ and non-transitional metal MoSi₂N₄ (0.34 eV per atom),⁴⁵ showing that it is more favourable in experimental preparation. We will therefore focus on MA₂P₄ in the following investigation.

Fig. 2 The formation energies of MA₂Z₄ (M = Mo, W, V; A = Si, Ge; Z = N, P, As). Note that the orange histograms represent the formation energy of V_M, cyan histograms represent the formation energy of V_A, and the yellow histograms represent the formation energy of V_Z-MA₂Z₄, respectively.

3.2 Activity of defect MA₂Z₄ toward the HER

To evaluate the catalytic activity of the vacancy defects of MA₂Z₄, we calculated the ΔG_H* of vacancies at M, A, inside Z atoms, and outer Z atoms, respectively. ΔG_H* is an important descriptor to evaluate the performance of the catalyst; an excellent catalyst should keep ΔG_H* near zero, marked in dark purple in Fig. 3. We can see that the adsorption performance of MA₂Z₄ materials is improved after vacancy regulation. We also find that the vacancy at the M atom (V_M) makes some structure distortion, such as V_Mo-MoSi₂As₄ and V_V-VGe₂X₄,;the vacancy at the A atom (V_A) makes the ΔG_H* value more negative, which indicates that it is more difficult for hydrogen atoms to be desorbed. So, we demonstrate that MA₂Z₄ materials are not suitable for vacancy regulation at the M or A atom. The results show that vacancy regulation at the outer Z atom (V_Z) can enhance the adsorption of the H atom, and all structures are stable after adsorption, which are consistent with the previously calculated formation energy. The results also show that the catalytic performance of the original MA₂P₄ and V_P-MA₂P₄ are better than that of other materials, which means that the vacancy defects at the outer P atom are the most suitable regulation method for MA₂Z₄ materials.

Fig. 3 Calculations of the adsorption performance of MA₂Z₄ under origin MA₂Z₄ (a) and under the N vacancy (b); P vacancy (c); As vacancy (d) regulation and the Gibbs free energy of the H atom at sites 1, 2, 3 and 4. Catalytic performance can be expressed by different colors, in which darker purple indicates stronger catalytic activity and white indicates weak catalytic activity.

We then studied the differences of catalytic performance between different active sites after the best vacancy regulation methods are selected. As mentioned before, using the MA₂P₄ structure as an example, we find that the catalytic activity of all sites is improved after V_P was introduced, and the site 1 (V_P1) showed the best catalytic activity, as shown Fig. 3.

According to the calculation results, we selected MoGe₂P₄, WGe₂P₄ and VGe₂P₄ structures to calculate their corresponding volcanic curves to observe the reaction rate, as shown in Fig. 4.⁴¹ We can see that both WGe₂P₄ and VGe₂P₄ are closer to Pt at the volcano summit, especially in the case of V_P, reflecting their strong hydrogen evolution ability. It can be seen from Fig. 4(d) that ΔG_H* can be closer to 0 than primitive structures. We can see that the ΔG_H* of WGe₂P₄ at 1 site is 0.95 eV, and the ΔG_H* of WGe₂P₄ becomes 0.05 eV after V_P was introduced; the ΔG_H* of MoGe₂P₄ is 0.91 eV, and the ΔG_H* of MoGe₂P₄ becomes −0.02 eV after V_P was introduced while ΔG_H* of VGe₂P₄ decreased by 0.1 eV (from 0.13 eV to 0.03 eV).

Fig. 4 The volcanic curve of (a) MoGe₂P₄, (b) WGe₂P₄, and (c) VGe₂P₄ for each vacancy. (d) Gibbs free energy versus the reaction coordinate of the HER for MoGe₂P₄, WGe₂P₄, and VGe₂P₄ when V_P was introduced on site 1.

The favorable and unfavorable factors for HER performance are listed as follows in Table 2. We investigated the properties of the pristine structure firstly, which is found to be inert for the HER, and then we investigated the properties of the defective material through the introduction of vacancies, and the results show that MoGe₂P₄ with a P vacancy and outside P as the H adsorption site is the best structure among them. The calculation results reveal that ΔG_H* decreases significantly, demonstrating that V_P-MA₂Z₄ is very effective in reducing ΔG_H*; this is consistent with our previous discussion. Thus, our results clearly suggest that the ΔG_H* of V_P-MA₂Z₄ can be manipulated to achieve the optimal HER activity. In addition, the ΔG_H* of other materials in the catalytic active region after vacancy introduction are presented in Fig. S1 of the ESI.†

Table 2 The vacancy type, ΔG_H*, and H adsorption site of MoGe₂P₄, WGe₂P₄ and VGe₂P₄ are shown in the following table

Structure	Vacancy type	ΔGH*	Adsorption site
MoGe2P4	Pristine	0.74	2
	M	0.09	3
	A	−1.31	2
	Z	−0.02	1
WGe2P4	Pristine	0.43	2
	M	−0.08	3
	A	0.32	1
	Z	0.05	1
VGe2P4	Pristine	0.01	4
	M	—	—
	A	−0.95	2
	Z	0.03	1

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3.3 Origin of the HER catalytic activity

3.3.1 DOS and band structures. In order to understand the reasons for improving HER performance, we study the electronic properties of V_P vacancy structures, including their band structure, projection state density, differential charge density and Bader charge analysis. For the VA₂Z₄ series, they all show metallic properties; it can be found that when a vacancy is introduced, impurity states near the Fermi level increase, thus improving H* adsorption strength.^20–22 For the MoA₂Z₄ and WA₂Z₄ series, they present semiconductor properties. Among them, MoSi₂N₄, MoGe₂N₄, MoGe₂P₄, MoGe₂As₄, WSi₂N₄ and WGe₂N₄ are indirect band gap semiconductors, while MoSi₂P₄, MoSi₂As₄, WSi₂P₄, WSi₂As₄, WGe₂P₄ and WGe₂As₄ are direct band gap semiconductors. For the MA₂N₄ series, the band gaps are relatively larger (>1.20 eV), and the band gaps are smaller for MGe₂P₄ and MGe₂As₄ (<0.50 eV). When the vacancy occurs, the impurity states of several catalysts begin to aggregate near the Fermi level, and unmatched electrons may appear on the plane, and these unstable electrons will increase the conductivity of the catalyst, similarly reducing the band gap of the catalyst, and improving the conductivity of the catalysts and the activity of hydrogen evolution. This is consistent with the result that the value of ΔG_H* begins to approach zero.

We study the partial density of state (PDOS) MGe₂P₄ (M = Mo, W, V) with V_P vacancies and corresponding pristine structures, as shown in Fig. 5. The curves we describe in the PDOS diagram are all from atoms near vacancies. It can be seen from the figures that compared with the pristine structure, the V_P vacancy structures show larger occupied states near the Fermi level, which are mainly derived from M-d orbitals, and the occupied states near the Fermi level gradually increase from MoGe₂P₄ to WGe₂P₄ and then to VGe₂P₄. When M = W and V, the P-p orbitals have a significant elevation near the Fermi level, which is related to the absence of the P atom in the outer layer. Meanwhile, we can see that when M = W, the Ge-p orbital also gets some lift; this indicates that the introduction of vacancies can effectively improve the dominance of d electrons and p electrons near the Fermi level, thus improving the catalytic activity.

Fig. 5 The band and PDOS diagram of (a, c and e) pristine MGe₂P₄ (M = Mo, W, V) and the (b, d and f) MGe₂P₄ (M = Mo, W, V) with the V_P vacancy.

3.3.2 Electron density difference and charge transfer. The Bader charge of H* and differential charge density are calculated for exploring the charge transfer mechanism between H* and defective structures and the relationship with hydrogen evolution activity. We calculated the Bader charge of adsorbed H* on defective MA₂Z₄ with V_Z vacancies, as shown in Fig. 6, the M atoms of Mo, W, and V are represented in green, blue, and red, respectively. We find that electrons are transferred from H* to the N atom, while the electrons are transferred from the P or As atom to H*, because of the difference of the electronegativity of the Z atoms. The electronegativity of the N atom is greater than that of P and As, which affects the charge transfer when H* is adsorbed, resulting in the value of ΔG_H*. We further show that there is a larger charge transfer between H* and Z atoms when V_Z vacancies are introduced, which means that the stabilization of the H* species in HER performance may originate from the enhanced charge density. As mentioned above, the ΔG_H* calculations also suggested that V_Z could much more efficiently enhance the HER activity, especially V_P structures.

Fig. 6 The correlation of ΔG_H* and Bader charge analysis of adsorbed H in defective structures.

To further explore the charge transfer mechanism between defective structures and H*, the differential charge transfer density (Δρ(r)) is calculated. Δρ(r) is calculated as

Δρ(r) = ρ_cat+H(r) − ρ_cat(r) − ρ_H(r) (4)

where ρ_cat+H(r), ρ_cat(r), and ρ_H(r) denote charge density of the catalyst with adsorbed H, without H and H atoms, respectively. As mentioned above, we calculated the chosen V_P structure, and the calculated Δρ(r) results of MoGe₂P₄, WGe₂P₄, and VSi₂P₄ are shown in Fig. 7. It is shown that the electrons accumulate around H atoms and reduce around the P atoms which are bonded to H atoms, indicating a charge transfer from MA₂P₄ to H*, which is consistent with the Bader charge analysis.

Fig. 7 Differential charge density of (a) MoGe₂P₄, (b) WGe₂P₄, and (c) VGe₂P₄. Note that the yellow and blue colors represent charge accumulation and depletion respectively. The isosurface level is 0.002 e Bohr⁻³.

3.4 The reaction pathways of defective MA₂Z₄

The hydrogen evolution reaction is a multi-step electrochemical reaction, which is divided into two cases: Volmer–Tafel or Volmer–Heyrovsky reactions. First, the surface-adsorbed hydrogen is rapidly formed by the combination of protons and electrons on the electrode (Volmer reaction, H⁺ + e⁻ → H*).⁵⁰ Subsequently, two optional subsequent steps: where one proton in water binds with another adsorbed H atom on the surface to form a H₂ molecule (Heyrovsky reaction, H⁺ + e⁻ + H* → H₂),⁵¹ or Tafel reaction, which refers to two adsorbed hydrogen binding to each other to form a H₂ molecule (2H* → H₂).⁵²

The potential barrier and temperature determine the reaction rate, so we calculated the transition state of V_P-MA₂Z₄ using the CI-NEB method, as shown in Fig. 8. For V_P-MoGe₂P₄, the potential barriers to the Tafel reaction and the Heyrovsky reaction are 3.31 eV and 1.05 eV, and the final state energy of the Heyrovsky reaction is −3.82 eV relative to the initial state. This means that the hydrogen evolution reaction of V_P-MoGe₂P₄ is more suitable for the Heyrovsky reaction with a low potential barrier and the reaction is exothermic. Similarly, V_P-WGe₂P₄ tends to have a Tafel reaction with a potential barrier of 2.95 eV, and V_P-VGe₂P₄ tends to have a Heyrovsky reaction with a potential barrier of 2.27 eV. In summary, the V_P-MoGe₂P₄ structure has the best catalytic performance and the lowest reaction barrier and is likely to carry out the Volmer–Heyrovsky reactions in solution.

Fig. 8 The reaction pathways for the HER. (a) Tafel reaction of V_P-MoGe₂P₄, (b) Heyrovsky reaction of V_P-MoGe₂P₄, (c) Tafel reaction of V_P-WGe₂P₄, (d) Heyrovsky reaction of V_P-WGe₂P₄, (e) Tafel reaction of V_P-VGe₂P₄ and (f) Heyrovsky reaction of V_P-VGe₂P₄. The initial state (IS), the transition state (TS) and the final state (FS) are linked by dotted lines in the figure; the red line indicates the corresponding barrier.

4. Conclusion

We theoretically designed a defective MA₂Z₄ monolayer family, and investigated their stability and unique role as electrocatalysts toward the HER systematically. We find that V_P-MA₂Z₄ possesses a superior HER performance over pristine MA₂Z₄. Importantly, the optimal HER activity can be achieved with V_P vacancies active site 1, which indicates that the catalytic properties of the defect MA₂Z₄ can be tuned easily and effectively. Our calculations reveal that ΔG_H* decreases significantly with the outer Z atom (V_Z), so the vacancy defect at the outer Z atom is the most suitable regulation method for MA₂Z₄ materials. The electronic structure analysis shows that when vacancies are introduced, several new defect states move closer to the Fermi level, leading to semiconductor properties and an improvement of the hydrogen adsorption strength. We also find the charge transfer from the Z atoms to H* atom by calculating the electron charge density differences and Bader charges analysis, which indicates the effective performance of a HER catalyst. We further demonstrate that the HER on defect MA₂Z₄ prefers the Volmer–Heyrovsky mechanism. Our study shows that the designed defect MA₂Z₄ monolayer family is highly activated toward the HER electrocatalyst, the optimal HER activity can be achieved, and abundant catalytic activity sites are provided; MoGe₂P₄ with a P vacancy and outside P as the H adsorption site is found to be the best. It is expected that the strategies developed in this study may be applied for designing 2D electrocatalysts for low-cost and high-performance HER applications.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Key Research and Development Program of China (No. 2021YFB3601201), the Open-Foundation of Key Laboratory of Laser Device Technology, China North Industries Group Corporation Limited (No. KLLDT202103) and the Open Project Program of Shandong Semiconductor Materials and Optoelectronic Information Technology Innovation Center, Ludong University. We are grateful for the helpful discussion with Prof. Pengfei Guan and the computational support from the Beijing Computational Science Research Center (CSRC).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2se01389d

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