Synergism between metal single-atom sites and S-vacant two-dimensional nanosheets for efficient hydrogen evolution uncovered by density functional theory and machine learning

Abstract

Efficient electrocatalysts for the hydrogen evolution reaction (HER) are the key to hydrogen-electricity energy conversion. Leveraging density functional theory and machine learning, we herein reveal the synergism between metal single atoms (M-SAs) and S-vacant two-dimensional (2D) MnPS₃ nanosheets (S_v-MnPS₃). Specifically, M-SAs occupy S-vacancies and activate the neighboring S sites as new active sites for the HER. In turn, S_v-MnPS₃ improves the ability of metal-SAs for water dissociation by modulating their magnetic moments. During the HER, H* is generated on metal-SAs and then migrates to neighboring S sites on which H₂ is produced, representing catalytic synergism via hydrogen spillover. Among the M₁/S_v-MnPS₃ candidates, Pd₁/S_v-MnPS₃ possesses an optimal ΔG_H* of 0.01 eV and is both thermodynamically and electrochemically stable. Therefore, the synergism between Pd₁ and S_v-MnPS₃ enables Pd₁/S_v-MnPS₃ to be active and durable for the HER. This work provides insights into how to design and understand confined metal-SAs in 2D materials for efficient electrocatalysis.

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1. Introduction

Efficient electrocatalysts for the hydrogen evolution reaction (HER) are indispensable for hydrogen-electricity energy conversion.^1–9 Platinum is the most active metal for the HER but suffers from high costs and limited reserves. Thus, low- and non-Pt catalysts are imperative for the HER.^10,11 In this regard, single-atom catalysts (SACs) are promising due to their nearly 100% atom utilization and highly tunable active sites.^12–15 In particular, metal-SAs coupled with 2D materials could induce the production of new electronic states to benefit mutual activity.^16–18 Compared to traditional supports, 2D materials offer a larger specific surface area, unique geometric structures, and electronic properties. Moreover, 2D materials may modulate the catalytic performance of metal-SAs, and in turn, metal-SAs affect the intrinsic activity of 2D materials.¹⁹ However, the rational design of active metal-SAs/2D-material catalysts and robust stabilization of metal-SAs remain challenging, as the conventional trial-and-error method is time-consuming and inefficient. To this end, artificial intelligence and machine learning (ML) are booming not only for accelerating the exploration of new active electrocatalysts^20–26 but also for the fundamental understanding of enhancement mechanisms.^27–29

The hydrogen spillover effect has shown the capacity to enhance HER activity via catalytic synergism between two kinds of metal sites.³⁰ Specifically, one metal site acts for cleaving HO–H bonds and another metal site works for H₂ evolution.³¹ Nevertheless, whether such synergism remains effective between metal and nonmetal sites is unclear in metal-SAs/2D materials, although metal-SAs combined with diverse 2D materials, such as graphene, g-C₃N₄, and MoS₂, have been intensively developed.^32–35 In this regard, transition metal phosphorus trichalcogenides (MPX₃, in which M and X are metal and chalcogen atoms, respectively) represent a class of emerging 2D materials with significant potential in electrocatalysis due to their active adsorption sites, high surface area ratios, and excellent electronic properties.³⁶ However, S-vacancies (S_v) are often generated during synthesis even for MnPS₃ that already has a mature preparation method.³⁷ Thus, the exploration of S_v roles in electrocatalysis and possible synergism with metal-SAs is meaningful for developing efficient metal-SAs/MPX₃ catalysts.^38,39

We herein combine density functional theory (DFT) and machine learning (ML) to study a series of HER electrocatalysts composed of confined metal-SAs and S-vacant MnPS₃ (S_v-MnPS₃). The Pd₁/S_v-MnPS₃ catalyst possesses the best HER activity among M₁/S_v-MnPS₃ candidates, verified by its optimal ΔG_H* = 0.01 eV and low energy barriers for H₂O splitting and H₂ formation. The electrochemical NEB (eNEB) results indicate that the electrochemical barrier further decreases with applying potentials. The synergistic mechanisms and electronic interactions between Pd-SAs and S_v-MnPS₃ have been revealed, that is, Pd-SAs enable the neighboring S sites of S_v-MnPS₃ to be active for the HER, while S_v-MnPS₃ promotes the capacity of Pd₁ for water dissociation and H* generation. The hybridization of the d-orbitals of Pd with the d-orbitals of Mn and the p-orbitals of P induces strong electronic interactions that endow Pd₁/S_v-MnPS₃ with robust stability.

2. Computational methods and models

First-principles calculations were conducted utilizing the Vienna ab initio simulation package (VASP) with the embedded projector augmented wave (PAW) method.⁴⁰ The Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) was used to describe the exchange–correlation interactions.⁴¹ To accurately determine the long-range van der Waals (vdW) interactions between reaction intermediates and candidates, the empirical correction method (DFT-D3) was employed.^42,43 The cutoff energy of the plane-wave basis was set at 500 eV, and the convergence criteria for the residual force and the energy on every atom during the structure optimization were set to 0.03 eV Å⁻¹ and 10⁻⁵ eV, respectively.

A 2 × 2 supercell was built for the MnPS₃ nanosheet and the vacuum space was set to 20 Å in the z-direction to prevent the interaction between the adjacent periodical structures. An S atom at the center of MnPS₃ is moved away to form an S defect. For structural optimization and analysis of electronic properties, a 3 × 3 × 1 Monkhorst–Pack k-point mesh was employed to adequately sample the Brillouin zone. To evaluate the stability of candidates, the binding energy (E_bind) was determined using the equation E_bind = E_TM-substrate − E_TM − E_substrate, where E_TM-substrate, E_substrate, and E_TM refer to the total energies of candidates, the substrate monolayer, and the isolated metal atoms, respectively. Furthermore, we employed ab initio molecular dynamics simulations (AIMD) to probe the stability of the model at 300 K for 20 000 fs.^44,45 To estimate the HER electrocatalytic activities of candidates, we calculated the free energy profiles based on the computational hydrogen electrode (CHE) model, and more computational details are outlined in the ESI.† Solvation effects on the electrocatalytic behavior of models were investigated using the implicit solvation model within the VASPsol code.⁴⁶ The charge transfers between metal atoms and the substrate were calculated based on Bader charge analysis. The transition states involved in H₂O dissociation and H₂ formation were calculated utilizing the climbing image nudged elastic band (CI-NEB) method.⁴⁷ We adopted the electrochemical NEB (eNEB) method proposed by Duan et al. to investigate reaction kinetics under constant-potential conditions.⁴⁸ We performed the ML algorithms in the Python3 environment utilizing the Scikit-learn package.⁴⁹ In this work, we chose four different ML algorithms, namely k-neighbor regression (KNR), support vector regression (SVR), gradient-boosted regression (GBR), and random forest regression (RFR).⁵⁰ Further computational details for the ML methodologies are provided in the ESI.†

3. Results and discussion

3.1 Structure, stability, and electronic properties

Firstly, a comprehensive examination was conducted to assess the geometric characteristics and stabilities of confined metal-SAs in an S_v-MnPS₃ substrate. The optimized structures of the S_v-MnPS₃ and M₁/S_v-MnPS₃ models are presented in Fig. 1a. The results showed that an 8-membered ring was formed in the S_v-MnPS₃ substrate, which could favor the stabilization of the metal atoms. The bond lengths between the confined metal-SAs and the Mn atoms range from 2.18 to 2.67 Å and the confined metal-SAs can also form metal–nonmetal chemical bonds with P atoms and the bond lengths range from 2.04 to 2.78 Å, which are less than the sum of their respective radii (see Table S1†). Subsequently, we calculated the formation energy of S_v and found it to be about −4.15 eV, which indicates that S vacancies are easily formed during the synthesis process of MnPS₃, in line with the experimental observation.⁵¹ Furthermore, we calculated the cluster energies of metal for all candidates, using the equation E_cluster = E_bind − E_coh, in which E_bind and E_coh refer to the binding energies and cohesive energies of metals (Fig. 1b). The computed E_cluster values of confined metal-SAs are negative when Mn, Fe, Co, Ni, Cu, Ru, Rh, Pd, Pt, Au, V, Zn, Ag, Sc, Ti, and Zr atoms anchor the S_v-MnPS₃ monolayer, effectively hindering their segregation and undesired aggregation. However, the confined Cr, Ir, Mo, Os, Re, W, Hf, and Nb SAs possess positive E_cluster values, suggesting their high potential to form the corresponding metal clusters.

Fig. 1 (a) Optimized conformation diagram for S_v-MnPS₃ and M₁/S_v-MnPS₃ models; (b) the E_cluster values of confined metals for all candidates; and (c) the computed band structures of the Pd₁/S_v-MnPS₃ model. (The Fermi energy levels are indicated by red dashed lines.)

We next computed the electronic properties of M₁/S_v-MnPS₃ systems, which have a significant impact on their electrocatalytic activity. The strong interaction between metal-SAs and the substrates can induce significant charge redistribution. Based on Bader charge analysis, there are obvious charge transfers (0.04–1.43 e⁻) from metal-SAs to substrates (see Table S2†). Furthermore, taking Pd₁/S_v-MnPS₃ as an example, the hybridization strength between the metal and substrate was explored by calculating the partial density of states (PDOS), due to its good HER activity confirmed in subsequent studies. The results show strong hybridization between the d orbital of Pd atoms and the d orbital of Mn atoms, as well as the p orbital of P atoms, which explains the strong interaction between the metal-SAs and substrates (Fig. S1†). In addition, the hybridization degree between the d orbital of Mn and the p orbital of P is stronger for Mn₁/S_v-MnPS₃ with better stability than that between the d orbital of Au and the p orbital of P for Au₁/S_v-MnPS₃ with weak stability (see Fig. S2†). Good electrical conductivity can guarantee the rapid charge transfer of the electrocatalyst in chemical reactions. We analyzed the electrical conductivity of pristine S_v-MnPS₃ and Pd₁/S_v-MnPS₃ through band structure calculations. As shown in Fig. 1c and Fig. S4,† the pristine S_v-MnPS₃ possesses semiconducting properties due to its energy band structures, which fail to cross the Fermi energy level with a band gap of 0.13 eV, while the energy band of Pd₁/S_v-MnPS₃ passes through the Fermi level, inducing its metallic behavior. Thus, the introduction of Pd atoms can improve the electrical conductivity of catalysts.

3.2 Electrocatalytic HER activity

After determining the geometry and stability of the catalysts, we evaluated the electrocatalytic performance of these stable candidates for the HER. The overall HER pathway in an acid medium can be summarized using a three-state diagram including an initial H⁺ + e⁻ state, the adsorbed H* intermediate, and the final product H₂ (see Fig. 2a). We first explored the electrocatalytic HER performance of the pristine S_v-MnPS₃ catalyst. The results showed that the Gibbs free energies of H adsorption on S, Mn, and P sites were −2.20, −2.86, and −2.91 eV respectively, which were all much lower than the −0.09 eV of the best Pt catalyst (Fig. S5†). Moreover, for H* adsorption on M₁/S_v-MnSP₃, two possible sites were considered, including the metal site and its adjacent S sites (see Fig. S6†). The Gibbs free energy of the H* intermediate (ΔG_H*) is regarded as a descriptor of the HER catalytic performance and an optimal HER catalyst should hold thermal neutrality. Thus, ΔG_H* values on 48 structures were calculated as displayed in Fig. 2a and b, in which ^asM/S_v-MnPS₃ refers to the metal atom as the active site and M/^asS_v-MnPS₃ represents the S atom as the active site. The results showed that the calculated ΔG_H* values range from −1.38 to 2.78 eV for all considered cases. As expected, the electrocatalytic properties of the system are closely related to the type of confined metal. Interestingly, the confined M atoms can activate the S atoms in the substrate to act as active sites for the HER.

Fig. 2 (a) and (b) The free energy profiles of the HER for stable candidates. ^asM/S_v-MnPS₃ refers to the metal as the active site and M/^asS_v-MnPS₃ represents S as the active site. (c) The computed ΔG_H* values for stable candidates. (d) The obtained volcano curve of the exchange current i₀versus ΔG_H* values for stable candidates.

The S_v-MnPS₃-confined metal-SA catalysts with enhanced HER activity can be classified into two types according to HER active sites. In the first type, metal SAs act as active sites (as) for the ^asCo/S_v-MnPS₃, ^asRh/S_v-MnPS₃, ^asFe/S_v-MnPS₃, ^asW/S_v-MnPS₃, and ^asRe/S_v-MnPS₃ catalysts, and their Gibbs free energies are −0.09, 0.09, −0.13, 0.14 and −0.14 eV, respectively. In the second type, the S adjacent to the metal acts as active site for the Ni/^asS_v-MnPS₃, Cu/^asS_v-MnPS₃, Pd/^asS_v-MnPS₃, and Fe/^asS_v-MnPS₃ catalysts and their Gibbs free energies are 0.07, 0.02, 0.01, and 0.15 eV, respectively. Based on these calculated Gibbs free energies, the Pd/^asS_v-MnPS₃ catalyst shows good catalytic activity with a Gibbs free energy close to 0 eV, which is smaller than that of the commercial benchmark catalyst Pt/C (ΔG_H* = −0.09 eV),⁵² implying that it can serve as a good HER catalyst (Fig. 2c). Furthermore, we calculated the theoretical exchange current density i₀ as a function of ΔG_H* using the following equation: for ΔG_H* ≤ 0, i₀ at pH = 0 will be determined as: , for ΔG_H* > 0, i₀ at pH = 0 will be determined as: , where k₀ refers to the rate constant which is set to 1, and k is the Boltzmann constant under ambient conditions. An obvious volcano curve can be obtained (see Fig. 2d). It can be found that M/S_v-MnPS₃ with a rather weak/strong H* adsorption energy is located at the bottom of the “right/left” leg, corresponding to an extremely low exchange current value. However, some models exhibit moderate adsorption strength for H*, including ^asCo/S_v-MnPS₃, ^asRh/S_v-MnPS₃, Ni/^asS_v-MnPS₃, Cu/^asS_v-MnPS₃, and especially Pd/^asS_v-MnPS₃, located near the peak of the volcano, revealing their quite high exchange current densities. Therefore, the five catalysts are predicted to possess electrocatalytic activity for the HER.

3.3 The kinetic mechanism and effect of the pH value on HER activity

The CHE model used in our calculations provides a good description of the reaction mechanism for the HER; however, the CHE model presents limitations because it does not account for the effects of applied electrode potential (U vs. RHE) and pH under working conditions.^52,53 Herein, we utilize the constant potential method to investigate the effect of U_RHE and pH values on the HER activity, which offers insight into the effect of electrochemical interfaces on the thermodynamics of the HER.

Fig. 3a displays the calculated energies of Pd₁/S_v-MnPS₃ and H* as a function of U (vs. SHE) following the quadratic function: energy (*) = −1.88 (U_SHE)² + 0.97 U_SHE − 471.32 eV and energy (H*) = −1.41 (U_SHE)² + 0.32 U_SHE − 473.85 eV. Since the adsorption strength of the H* intermediate can directly affect HER activity, the variations of ΔG_H* with U (vs. RHE) and pH are given in Fig. 3b. The ΔG_H* values gradually approach zero as the pH increases, allowing the H* adsorption strength of Pd₁/S_v-MnPS₃ to satisfy Sabatier's principle⁵⁴ more readily under alkaline conditions. In addition, we utilized the constant potential method to investigate the effect of applied electrode potential under working conditions on the HER performance. The results show that the as-designed catalyst has a Gibbs free energy (ΔG_H*) close to 0 when a potential of −0.90 V_RHE is applied in an alkaline medium (see Fig. 3c and d). However, a higher potential is needed in an acidic environment (−1.71 V_RHE) to reach the thermal equilibrium.

Fig. 3 (a) The energies of Pd/^asS_v-MnPS₃ and the corresponding reaction intermediates as a function of U_SHE. (b) pH-dependent and potential-dependent contour plot of the adsorption energies of H* on the Pd/^asS_v-MnPS₃ catalyst. The computed ΔG_H* values with different applied potentials at (c) pH = 0 and (d) pH = 14.

Based on the above calculation results, we have reasonable confidence that the Pd₁/S_v-MnPS₃ catalyst will also possess good HER activity in an alkaline medium. The most critical step in the alkaline HER is the water dissociation process, which contains three steps: initial state (IS). i.e., H₂O adsorption, transition state (TS), and final state (FS). H₂O molecules are firstly adsorbed on Pd sites and the OH–H bond is cleaved (see Fig. 4a). Subsequently, H* intermediates spontaneously transfer to the S atoms of the Pd₁/S_v-MnPS₃ substrate and further are caught by S atoms. Finally, H₂ molecules are released on the S sites of Pd₁/S_v-MnPS₃. The kinetic barrier of Pd₁/S_v-MnPS₃ (ΔG_a = 0.99 eV) during this process is comparable to those of some experimental reports with a barrier of 1.08 eV,⁵⁵ indicating that it can effectively dissociate H₂O on the as-designed Pd₁/S_v-MnPS₃ catalyst. As water dissociation occurred on the Pd site, we computed the adsorption Gibbs free energy of *OH on the Pd site. The computed ΔG_*OH value is −0.19 eV, indicating that the *OH adsorption on the Pd site is quite weak and easy to desorb. Furthermore, the corresponding energy barriers to form H₂ on Pd₁/S_v-MnPS₃ are computed using Heyrovsky mechanisms (H* + H⁺ + e⁻ → H₂ + *) because the S sites of adsorbed H atoms are at long distances from each other which prevent Tafel reaction mechanisms. CI-NEB results uncover that the Pd₁/S_v-MnPS₃ catalyst possesses a small kinetic barrier (ΔG_b) of 0.67 eV for H₂ release (Fig. 4b) via the Heyrovsky path.

Fig. 4 (a) The minimum-energy pathways and the corresponding barriers for the H₂O dissociation process on the Pd₁/S_v-MnPS₃ catalyst. (b) The minimum-energy pathways and the corresponding barriers for H₂ production on the Pd₁/S_v-MnPS₃ catalyst through Heyrovsky mechanisms. The pink, yellow, red, white, purple, and green balls represent P, S, O, H, Mo, and Pd atoms, respectively. Calculation of H₂ formation (c) and H₂O dissociation (d) of Pd₁/S_v-MnPS₃ transition states at different applied potentials.

In addition, we computed the kinetic barrier of H₂ formation and water dissociation on Pd₁/S_v-MnPS₃ at different applied potentials by using the eNEB method developed by Duan et al.⁴⁸ We changed the applied potential from 0 to −0.2 V_RHE and found that the more negative the applied potential, the lower the energy barrier between TS and IS, and the easier it is for the reaction to occur (see Fig. 4c and d). The results reveal that the barriers for H₂ formation and H₂O dissociation on Pd₁/S_v-MnPS₃ are significantly decreased to 0.32 eV and 0.38 eV at −0.20 V_RHE, respectively. This conclusion is consistent with realistically electrochemical reactions.

3.4. Machine learning and catalytic origin for the HER

ML algorithms are utilized to describe the relationships between the HER activity and the structure and chemical properties of catalysts (see Fig. 5a). Given the critical role of ΔG_H* in the electrocatalytic HER, the ΔG_H* values are used as target data for ML models. Feature engineering is critical for ML calculations. Herein, we select eight features of metal atoms including structural and electronic properties as input data (see Table S2†). Specifically, we consider the distance between the active site and H species (d), the radius (r_d), the d-band center (ε_d), the electronegativity (X), the charge transfer (Q), the first ionization energy (I_m), the d electron number (N_m) and the magnetic moment (μ_B) of metal-SAs. Subsequently, we randomly divide the 48 data sets into 38 training sets and 10 test sets by selecting different ML algorithms, such as SVR, GBR, RFR, and KNR. The coefficient of determination values (R²) and the root-mean-square error (RMSE) are calculated to assess the accuracy of the HER models. The RFR, KNR, and SVR algorithms possess lower R² and higher RMSE values in both the test set and training set, thus suggesting these ML models are unsatisfactory (Fig. 5b). Conversely, the GBR algorithm possesses a good fitting effect, with a training score and test score (R² value) of 0.99 and 0.90 and an RMSE of 0.09 V in the training set and 0.16 V in the test set, respectively. Moreover, we compare the DFT-calculated and ML-predicted ΔG_H* values (Fig. 5c), and a strong linear relationship between them is observed.

Fig. 5 (a) Schematic diagram of the machine learning process. (b) The RMSE and R² results in the training and test sets in the HER for different algorithms. (c) The comparison between DFT-calculated and ML-predicted ΔG_H* values. (d) The feature importance analysis using the GBR algorithm.

Next, the importance of feature values is evaluated using the GBR algorithm. We found that the most significant feature is the first ionization energy (I_m), with a feature importance of 0.2520, followed by the magnetic moment (μ_B) of M atoms (0.2551) (see Fig. 5d). The r_m, ε_d, d, N_m, Q, and X values of metal atoms have much smaller contributions to ΔG_H*, but are of great significance.

As an intrinsic property of metals, I_m could often guide us in choosing the appropriate anchored metal-SA for a given substrate, regardless of the coordination environment. However, it is also critical to achieve efficient interfacial catalysis by changing the coordination environment of active sites. Establishing the relationship between the HER activity and the electronic structures of catalysts is critical for uncovering the active origin. In this regard, the μ_B values of confined metals are plotted as a function of ΔG_H* due to their non-negligible importance validated by feature engineering in affecting HER performance, and subsequently, an obvious volcano curve can be obtained (see Fig. 6a). The Pd/^asS_v-MnPS₃ catalyst is located on the top of the volcano curve, explaining that the Pd atom possesses optimal magnetic moments that could activate S atoms in the substrate to act as hydrogen precipitation active sites to achieve synergistic catalysis (see Fig. 6b).

Fig. 6 (a) The obtained volcano curve of the μ_Bversus the |ΔG_H*| values on catalysts. (b) Schematic illustration of the hydrogen overflow phenomenon based on synergistic dual active sites to enhance activity for the HER.

Given that Pd₁/S_v-MnPS₃ is the best-performing HER catalyst in the whole system, we conducted a more in-depth discussion on its stability. The calculated dissolution potential (U_diss) value for the Pd atom of the Pd₁/S_v-MnPS₃ catalyst is 0.5 V, suggesting that the ability of the anchored Pd atom to endure within the Pd₁/S_v-MnPS₃ catalyst is strong. Additionally, we generate the surface Pourbaix diagram of Pd₁/S_v-MnPS₃ to elucidate the most stable surface configurations at different equilibrium potentials and pH values, providing insights into its electrochemical stability in aqueous solutions (see Fig. S7†). The calculation results reveal that the limiting potential of the HER on the Pd₁/S_v-MnPS₃ catalyst is significantly lower than the oxidation potentials of various oxidation species of Pd, demonstrating its good electrochemical stability. Simultaneously, ab initio molecular dynamics (AIMD) simulations were conducted to further explore the thermodynamic stability of Pd₁/S_v-MnPS₃. The results show that the geometric structure of Pd₁/S_v-MnPS₃ remains intact even after exposure to 300 K for 20 000 fs in AIMD simulations, indicating its good thermodynamic stability (see Fig. S8†).

4. Conclusions

In summary, we explored the synergism between metal-SAs and S_v-MnPS₃ as well as M₁/S_v-MnPS₃ materials as potential HER electrocatalysts via combining DFT and ML. The results show that Pd₁/S_v-MnPS₃ possesses an optimal ΔG_H* of 0.01 eV on the S active sites. H₂O dissociation to generate H* is accelerated on Pd-SAs due to their moderate magnetic moment tuned by S_v-MnPS₃. Such synergism between metal-SAs and 2D substrates may work for other energy catalysis reactions. Furthermore, there is catalytic synergism between Pd₁ and nonmetal S single-atom sites via hydrogen spillover, that is, H* adsorbates are generated on Pd₁ and then migrate to neighboring S on which H₂ is produced. This work offers an example of combining DFT and ML to accelerate the exploration and understanding of new energy-conversion catalysts.

Author contributions

X. Z. conceived and supervised the research. X. Y. L. conducted the calculations. J. X. Z. and D. X. J. revised the manuscript. X. Z. revised and finished the manuscript.

Data availability

Data are available on request from the authors.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (no. 22479059), the Jilin Province Science and Technology Development Program (YDZJ202401329ZYTS), and “the Fundamental Research Funds for the Central Universities”.

References

1. H. Jiang, J. Gu, X. Zheng, M. Liu, X. Qiu, L. Wang, W. Li, Z. Chen, X. Ji and J. Li, Defect-rich and ultrathin N doped carbon nanosheets as advanced trifunctional metal-free electrocatalysts for the ORR, OER and HER, Energy Environ. Sci., 2019, 12, 322–333.
2. N. Yao, P. Li, Z. Zhou, Y. Zhao, G. Cheng, S. Chen and W. Luo, Synergistically Tuning Water and Hydrogen Binding Abilities Over Co4N by Cr Doping for Exceptional Alkaline Hydrogen Evolution Electrocatalysis, Adv. Energy Mater., 2019, 9, 1902449.
3. J. Huang, B. Chai, J. Xiao, X. Zhang, G. Fan and G. Song, Construction of 1D/3D Co9S8/Mn0.3Cd0.7S Schottky heterojunction for dramatically boosted photocatalytic H2 evolution performance, Chem. Eng. J., 2024, 481, 148501.
4. C. Yang, X. Li and Y. Liang, Recent advances in molybdenum diselenide-based electrocatalysts: preparation and application in the hydrogen evolution reaction, Inorg. Chem. Front., 2023, 10, 5517–5554.
5. S. Khamgaonkar, M. Okasha and V. Maheshwari, Recent advances towards increasing the Pt utilization efficiency for hydrogen evolution reaction: a review, Inorg. Chem. Front., 2023, 10, 6812–6848.
6. J. Hu, C. Zhang, P. Yang, J. Xiao, T. Deng, Z. Liu, B. Huang, M. K. H. Leung and S. Yang, Kinetic-Oriented Construction of MoS2 Synergistic Interface to Boost pH-Universal Hydrogen Evolution, Adv. Funct. Mater., 2020, 30, 1908520.
7. D. Zhang, H. Zhao, B. Huang, B. Li, H. Li, Y. Han, Z. Wang, X. Wu, Y. Pan, Y. Sun, X. Sun, J. Lai and L. Wang, Advanced Ultrathin RuPdM (M = Ni, Co, Fe) Nanosheets Electrocatalyst Boosts Hydrogen Evolution, ACS Cent. Sci., 2019, 5, 1991–1997.
8. J. Zhao, R. Urrego-Ortiz, N. Liao, F. Calle-Vallejo and J. Luo, Rationally designed Ru catalysts supported on TiN for highly efficient and stable hydrogen evolution in alkaline conditions, Nat. Commun., 2024, 15, 6391.
9. T. Zhang, Q. Ye, Z. Han, Q. Liu, Y. Liu, D. Wu and H. J. Fan, Biaxial strain induced OH engineer for accelerating alkaline hydrogen evolution, Nat. Commun., 2024, 15, 6508.
10. X. Chen, X.-T. Wang, J.-B. Le, S.-M. Li, X. Wang, Y.-J. Zhang, P. Radjenovic, Y. Zhao, Y.-H. Wang, X.-M. Lin, J.-C. Dong and J.-F. Li, Revealing the role of interfacial water and key intermediates at ruthenium surfaces in the alkaline hydrogen evolution reaction, Nat. Commun., 2023, 14, 5289.
11. L. Fu, Y. Li, N. Yao, F. Yang, G. Cheng and W. Luo, IrMo Nanocatalysts for Efficient Alkaline Hydrogen Electrocatalysis, ACS Catal., 2020, 10, 7322–7327.
12. X. Li, X. Yang, Y. Huang, T. Zhang and B. Liu, Supported Noble-Metal Single Atoms for Heterogeneous Catalysis, Adv. Mater., 2019, 31, 1902031.
13. W. Xie, H. Li, G. Cui, J. Li, Y. Song, S. Li, X. Zhang, J. Y. Lee, M. Shao and M. A.-O. X. Wei, NiSn Atomic Pair on an Integrated Electrode for Synergistic Electrocatalytic CO(2) Reduction, Angew. Chem., Int. Ed., 2021, 60, 7382.
14. Y. Shang, X. Duan, S. Wang, Q. Yue, B. Gao and X. Xu, Carbon-based single atom catalyst: Synthesis, characterization, DFT calculations, Chin. Chem. Lett., 2022, 33, 663–673.
15. J. Sui, H. Liu, S. Hu, K. Sun, G. Wan, H. Zhou, X. Zheng and H.-L. Jiang, A General Strategy to Immobilize Single-Atom Catalysts in Metal–Organic Frameworks for Enhanced Photocatalysis, Adv. Mater., 2022, 34, 2109203.
16. R. Gusmão, M. Veselý and Z. Sofer, Recent Developments on the Single Atom Supported at 2D Materials Beyond Graphene as Catalysts, ACS Catal., 2020, 10, 9634–9648.
17. Y. Li, Z.-S. Wu, P. Lu, X. Wang, W. Liu, Z. Liu, J. Ma, W. Ren, Z. Jiang and X. Bao, High-Valence Nickel Single-Atom Catalysts Coordinated to Oxygen Sites for Extraordinarily Activating Oxygen Evolution Reaction, Adv. Sci., 2020, 7, 1903089.
18. X. Zhou, L. Zhang, H. Liu, Q. Yang, S. Zhu, H. Wu, T. Ohno, Y. Zhang, T. Wang, D. Su and C. Wang, The powerful combination of 2D/2D Ni-MOF/carbon nitride for deep desulfurization of thiophene in fuel: Conversion route, DFT calculation, mechanism, J. Colloid Interface Sci., 2024, 658, 627–638.
19. Y. Wang, J. Mao, X. Meng, L. Yu, D. Deng and X. Bao, Catalysis with Two-Dimensional Materials Confining Single Atoms: Concept, Design, and Applications, Chem. Rev., 2019, 119, 1806–1854.
20. M. Sun, A. W. Dougherty, B. Huang, Y. Li and C.-H. Yan, Accelerating Atomic Catalyst Discovery by Theoretical Calculations-Machine Learning Strategy, Adv. Energy Mater., 2020, 10, 1903949.
21. D. Jiao, D. Zhang, D. Wang, J. Fan, X. Ma, J. Zhao, W. Zheng and X. Cui, Applying machine-learning screening of single transition metal atoms anchored on N-doped γ-graphyne for carbon monoxide electroreduction toward C1 products, Nano Res., 2023, 16, 11511–11520.
22. X. Zhang, K. Li, B. Wen, J. Ma and D. Diao, Machine learning accelerated DFT research on platinum-modified amorphous alloy surface catalysts, Chin. Chem. Lett., 2023, 34, 107833.
23. X. Zhang, J. Liu, R. Li, X. Jian, X. Gao, Z. Lu and X. Yue, Machine learning screening of high-performance single-atom electrocatalysts for two-electron oxygen reduction reaction, J. Colloid Interface Sci., 2023, 645, 956–963.
24. X. Bai, S. Lu, P. Song, Z. Jia, Z. Gao, T. Peng, Z. Wang, Q. Jiang, H. Cui, W. Tian, R. Feng, Z. Liang, Q. Kang and H. Yuan, Heterojunction of MXenes and MN4−graphene: Machine learning to accelerate the design of bifunctional oxygen electrocatalysts, J. Colloid Interface Sci., 2024, 664, 716–725.
25. S. Huang, H. Xiang, J. Lv, D. Zhu, L. Yu, Y. Guo and L. Xu, Au nanozyme-based colorimetric sensor array integrates machine learning to identify and discriminate monosaccharides, J. Colloid Interface Sci., 2024, 672, 200–208.
26. M. Sun and B. Huang, Direct Machine Learning Predictions of C3 Pathways, Adv. Energy Mater., 2024, 14, 2400152.
27. X. Xu, X. Li, W. Lu, X. Sun, H. Huang, X. Cui, L. Li, X. Zou, W. Zheng and X. Zhao, Collective Effect in a Multicomponent Ensemble Combining Single Atoms and Nanoparticles for Efficient and Durable Oxygen Reduction, Angew. Chem., Int. Ed., 2024, 63, e202400765.
28. L. Yang, J. Fan, B. Xiao and W. Zhu, Unveiling “Sabatier principle” for electrocatalytic nitric oxide reduction on single cluster catalysts: A DFT and machine learning guideline, Chem. Eng. J., 2023, 468, 143823.
29. M. Sun and B. Huang, Machine Learning Across Metal and Carbon Support for the Screening of Efficient Atomic Catalysts Toward CO2 Reduction, Adv. Energy Mater., 2023, 13, 2301948.
30. L. Zhao, B. Wang and R. Wang, A Critical Review on New and Efficient 2D Materials for Catalysis, Adv. Mater. Interfaces, 2022, 9, 2200771.
31. Z. Wu, Q. Li, G. Xu, W. Jin, W. Xiao, Z. Li, T. Ma, S. Feng and L. Wang, Microwave Phosphine-Plasma-Assisted Ultrafast Synthesis of Halogen-Doped Ru/RuP2 with Surface Intermediate Adsorption Modulation for Efficient Alkaline Hydrogen Evolution Reaction, Adv. Mater., 2024, 36, 2311018.
32. Z. Fan, H. Wan, H. Yu and J. Ge, Rational design of Fe-M-N-C based dual-atom catalysts for oxygen reduction electrocatalysis, Chin. J. Catal., 2023, 54, 56–87.
33. H. Li, C. Tsai, A. L. Koh, L. Cai, A. W. Contryman, A. H. Fragapane, J. Zhao, H. S. Han, H. C. Manoharan, F. Abild-Pedersen, J. K. Nørskov and X. Zheng, Activating and optimizing MoS2 basal planes for hydrogen evolution through the formation of strained sulphur vacancies, Nat. Mater., 2016, 15, 48–53.
34. R. Pang, H. Xia, J. Li, S. Guo and E. Wang, Recent Developments of Atomically Dispersed Metal Electrocatalysts for Oxygen Reduction Reaction†, Chin. J. Chem., 2023, 41, 581–598.
35. Z. Wei, Y. Liu, J. Ding, Q. He, Q. Zhang and Y. Zhai, Promoting Electrocatalytic CO2 Reduction to CO via Sulfur-Doped Co-N-C Single-Atom Catalyst†, Chin. J. Chem., 2023, 41, 3553–3559.
36. R. Wang, J. Huang, X. Zhang, J. Han, Z. Zhang, T. Gao, L. Xu, S. Liu, P. Xu and B. Song, Two-Dimensional High-Entropy Metal Phosphorus Trichalcogenides for Enhanced Hydrogen Evolution Reaction, ACS Nano, 2022, 16, 3593–3603.
37. R. Jana, C. Chowdhury and A. Datta, Transition-Metal Phosphorus Trisulfides and its Vacancy Defects: Emergence of a New Class of Anode Material for Li-Ion Batteries, ChemSusChem, 2020, 13, 3855–3864.
38. J. Zhu, J. Li, R. Lu, R. Yu, S. Zhao, C. Li, L. Lv, L. Xia, X. Chen, W. Cai, J. Meng, W. Zhang, X. Pan, X. Hong, Y. Dai, Y. Mao, J. Li, L. Zhou, G. He, Q. Pang, Y. Zhao, C. Xia, Z. Wang, L. Dai and L. Mai, Surface passivation for highly active, selective, stable, and scalable CO2 electroreduction, Nat. Commun., 2023, 14, 4670.
39. L. Lv, R. Lu, J. Zhu, R. Yu, W. Zhang, E. Cui, X. Chen, Y. Dai, L. Cui, J. Li, L. Zhou, W. Chen, Z. Wang and L. Mai, Coordinating the Edge Defects of Bismuth with Sulfur for Enhanced CO2 Electroreduction to Formate, Angew. Chem., Int. Ed., 2023, 62, e202303117.
40. J. Hafner, Ab initio simulations of materials using VASP: Density-functional theory and beyond, J. Comput. Chem., 2008, 29, 2044–2078.
41. Y. Fang, B. Xiao, J. Tao, J. Sun and J. Perdew, Ice phases under ambient and high pressure: Insights from density functional theory, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 87, 214101.
42. J. Moellmann and S. Grimme, DFT-D3 Study of Some Molecular Crystals, J. Phys. Chem. C, 2014, 118, 7615–7621.
43. R. Costa-Amaral, A. Forhat, N. A. M. S. Caturello and J. L. F. D. Silva, Unveiling the adsorption properties of 3d, 4d, and 5d metal adatoms on the MoS2 monolayer: A DFT-D3 investigation, Surf. Sci., 2020, 701, 121700.
44. S. Banerjee, G. Periyasamy and S. K. Pati, Possible application of 2D-boron sheets as anode material in lithium ion battery: A DFT and AIMD study, J. Mater. Chem. A, 2014, 2, 3856–3864.
45. W. Zhang, K. Mao and X. C. Zeng, B-Doped MnN4-G Nanosheets as Bifunctional Electrocatalysts for Both Oxygen Reduction and Oxygen Evolution Reactions, ACS Sustainable Chem. Eng., 2019, 7, 18711–18717.
46. Q. Zhang and A. Asthagiri, Solvation effects on DFT predictions of ORR activity on metal surfaces, Catal. Today, 2019, 323, 35–43.
47. M. Yang, Z. Wang, D. Jiao, Y. Tian, Y. Shang, L. Yin, Q. Cai and J. Zhao, Tuning precise numbers of supported nickel clusters on graphdiyne for efficient CO2 electroreduction toward various multi-carbon products, J. Energy Chem., 2022, 69, 456–465.
48. Z. Duan and P. Xiao, Simulation of Potential-Dependent Activation Energies in Electrocatalysis: Mechanism of O–O Bond Formation on RuO2, J. Phys. Chem. C, 2021, 125, 15243–15250.
49. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot and É. Duchesnay, Scikit-learn: Machine Learning in Python, Scikit-learn: Machine Learning in Python, 2011, 12, 2825–2830.
50. P. Shan, X. Bai, Q. Jiang, Y. Chen, S. Lu, P. Song, Z. Jia, T. Xiao, Y. Han, Y. Wang, T. Liu, H. Cui, R. Feng, Q. Kang, Z. Liang and H. Yuan, Bilayer MN4-O-MN4 by bridge-bonded oxygen ligands: Machine learning to accelerate the design of bifunctional electrocatalysts, Renewable Energy, 2023, 203, 445–454.
51. K. M. Roccapriore, N. Huang, M. P. Oxley, V. Sharma, T. Taylor, S. Acharya, D. Pashov, M. I. Katsnelson, D. Mandrus, J. L. Musfeldt and S. V. Kalinin, Electron-Beam Induced Emergence of Mesoscopic Ordering in Layered MnPS3, ACS Nano, 2022, 16, 16713–16723.
52. X. Wu, S. Zhou, Z. Wang, J. Liu, W. Pei, P. Yang, J. Zhao and J. Qiu, Engineering Multifunctional Collaborative Catalytic Interface Enabling Efficient Hydrogen Evolution in All pH Range and Seawater, Adv. Energy Mater., 2019, 9, 1901333.
53. D. Zhang, O. V. Prezhdo and L. Xu, Design of a Four-Atom Cluster Embedded in Carbon Nitride for Electrocatalytic Generation of Multi-Carbon Products, J. Am. Chem. Soc., 2023, 145, 7030–7039.
54. H. Ooka, J. Huang and K. Exner, The Sabatier Principle in Electrocatalysis: Basics, Limitations, and Extensions, Front. Energy Res., 2021, 9, 654460.
55. C. Kong, Y. Han, L. Hou and L. Gao, The effect of metal matrix M (M = Co, Ni, Cu) on the water dissociation performance of oxophilic Cr from density functional theory, New J. Chem., 2023, 47, 15894–15900.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4qi01723d

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