1T-MoS2 Coordinated Bimetal Atoms as Active Centers to Facilitate Hydrogen Generation

Anchoring single metal atoms has been demonstrated as an effective strategy to boost the catalytic performance of non-noble metal 1T-MoS2 towards hydrogen evolution reaction (HER). However, the dual active sites on 1T-MoS2 still remain a great challenge. Here, first-principles calculations were performed to systematically investigate the electrocatalytic HER activity of single and dual transition metal (TM) atoms bound to the 1T-MoS2 monolayer (TM@1T-MoS2). The resulted Ti@1T-MoS2 exhibits excellent structural stability, near-thermoneutral adsorption of H* and ultralow reaction barrier (0.15 eV). It is a promising single metal atom catalyst for HER, outperformed the reported Co, Ni and Pd anchoring species. Surprisingly, by further introducing Pd atoms coordinated with S atoms or S vacancies on the Ti@1T-MoS2 surface, the resulted catalyst not only maintains the high HER activity of Ti sites, but also achieves new dual active moiety due to the appropriate H* adsorption free energy on Pd sites. This work is of great significance for realizing dual active centers on 1T-MoS2 nanosheets and offers new thought for developing high-performance electrocatalysts for HER.


Introduction
The electrocatalytic hydrogen evolution reaction (HER: 2H + + 2e − → H 2 ) is the key to achieve clean hydrogen energy [1,2]. Highly active and stable electrocatalysts are required to drive the sluggish thermodynamic and kinetic processes of HER [3]. Until now, Pt/C is the benchmark catalyst for hydrogen production [4]. Nevertheless, the limited reserve and high price severely restrict its large-scale application. Considering that the HER kinetics under acidic conditions is much faster than that in alkaline solution, thus, it is highly desirable and particularly urgent to mining high activity, low cost, stable electrocatalysts for HER in acidic media [5]. Recently, transition metal embedded heteroatom-doped carbon nanosheets [6], two-dimensional (2D) transition metal sulfides [7,8], borides [9], oxides [10], phosphides [11] etc., have been reported as promising candidates to replace precious Pt for HER. However, so far, these catalysts are still far from being commercialized because of their poor conductivity or insufficient hydrophilicity.
In contrast, the advantages of two-dimensional (2D) 1T phase molybdenum disulfide (1T-MoS 2 ) nanosheet are its excellent electrical condutivity, sufficient hydrophilicity, acid resistance and low cost [12]. Compared to the semiconducting 2H phase MoS 2 , the great HER activity of metallic 1T-MoS 2 mainly originates from its affinity for binding H at the surface S sites, and the improved charge transfer kinetics [13]. Unlike 2H-MoS 2 where the catalytic activity arises from the edges, the much greater active surface area of 1T nanosheets with respect to the edge portion thus guarantees the higher HER activity [14,15]. Such catalyst has attracted enormous research interests and been regarded as one of the most promising electrocatalysts toward hydrogen evolution in acidic solutions [13,16,17]. Note that a large gap still exists for 1T-MoS 2 nanosheet to completely substitute Pt because of the high reaction barrier (1.15 eV) during the HER process [13]. In this regard, several efficient approaches have been proposed to boost the catalytic activity of catalysts, such designing novel ferrite-based materials [18], doping TiO 2 thin films [19] and fabricating Ni Nanowires [20]. In addition, anchoring single transition metal (TM) atoms on the 2D conductive substrates also emerges as an essential method for obtaining superior catalysts [21]. The experimental and theoretical works have reported that single Co, Ni or Pd atoms anchored on the 1T-MoS 2 basal plane exhibit the Pt-like electrocatalytic activity for HER in acid electrolyte and dramatically improve the durability because of the synergetic effect [16,17,22]. Notably, the strain induced by lattice mismatch and the formation of TM-S covalent bond in TM@1T-MoS 2 hybrids are favorable for achieving the phase transformation of MoS 2 from the semiconductive 2H to distorted metallic 1T phase [23]. The appropriate TM atoms integrated into 1T-MoS 2 efficiently contribute to maintaining the structural stability of 1T phase, also enhancing the corrosion resistance [24]. However, the HER activity of bimetal atoms bound to 1T-MoS 2 remains to be elucidated.
For mining superior catalysts, it is convenient and efficient to preliminarily evaluate their catalytic activity and stability via integrated computation [25]. In this work, firstprinciples calculations and automatic frameworks of material screening methods were employed to reveal the electrocatalytic HER activity of 3d, 4d, 5d TM single and dual atoms bound to the 1T-MoS 2 monolayer. Interestingly, we found that the Ti@1T-MoS 2 and PdTi@1T-MoS 2 catalysts exhibit excellent hydrogen evolution activity, comparable to the benchmark Pt catalyst. This work provides significant theoretical insights for the experimental synthesis of superior HER electrocatalysts.

Density Functional Theory Calculations
The structure and catalytic performance of mono/bimetal atoms mediated 1T-MoS 2 were investigated through first-principles calculations based on the spin-polarized density functional theory (DFT) [26] and automatic frameworks of material screening methods. This process was implemented in the Vienna ab initio simulation package (VASP) [27], combined with the high-throughput computational platform of Artificial Learning and Knowledge Enhanced Materials Informatics Engineering (ALKEMIE) [28]. VASP uses the projector-augmented wave method to describe the electron-core interaction, and allows performing structural optimizations, total-energy calculation, electronic structure calculation and ab initio molecular dynamics simulations [27]. It is currently one of the most popular commercial software in material simulation and computational material science. While, ALKEMIE is an open-source intelligent computational platform for accelerating materials discovery and design via high throughput calculations, data management with the private/shared database, and data mining through machine learning [28]. The exchangecorrelation interaction was treated by using the generalized gradient approximation (GGA) in the form of Perdew-Burke-Ernzerhof (PBE) [29]. The 1T-MoS 2 supercell consisting of 12 Mo and 24 S atoms was used as a model with vacuum layer as large as 20 Å along the z direction. The van der Waals interaction was considered using the empirical correction in the Grimme's scheme (DFT+D2). The cut-off energy for plane waves was set to 400 eV. While the convergence tolerance was set to 10 −4 eV in energy and 0.02 eV/Å in force during structural relaxation as well as static calculations.

Formation Energy
To evaluate the thermodynamic stability of mono/bimetal atoms immobilized on the basal plane of 1T-MoS 2 , the formation energy ∆E f was examined based on Equation (1) where E TM@1T-MoS 2 and E TMTi@1T-MoS 2 represent the total energies of single TM and bimetal TM/Ti atoms anchored on 1T-MoS 2 , respectively. The terms of E 1T-MoS 2 and E bulk TM (or E bulk Ti ) refer to the total energies of the pristine 1T-MoS 2 and a metal atom in the bulk phase, respectively. Accordingly, the more negative value of ∆E f indicates the higher thermodynamic stability of the hybrid system.

Reaction Free Energy
For HER, note that this work does not consider the Volmer-Heyrovsky mechanism, because of the large computational cost involved in aqueous solvent models. Instead, the Volmer-Tafel mechanism is used to explore the reaction kinetics of HER, which involves gas phase simulation of H* and H 2 *. Additionally, because the HER kinetics under acidic condition is much faster than that in alkaline solution, electrocatalysts usually show better performance in acidic solution [14]. Therefore, this work mainly aims at the HER performance of mono/bimetal atoms mediated 1T-MoS 2 in acidic solution. Such HER process consists of two elementary steps via Volmer-Tafel mechanism [24]: where * represents the active center. The Gibbs free energy ∆G of H* adsorption was defined as,  (5), where low overpotential contributes to accelerating the kinetics process of HER:

Structural Stability of Single Metal Atoms Mediated 1T-MoS 2
To rationally design single 3d, 4d and 5d transition metal (TM) atoms immobilized on the 2D 1T-MoS 2 basal plane (TM@1T-MoS 2 ) as HER catalysts, we used the screening procedure as illustrated in Figure 1a. Accordingly, we first constructed 24 TM@1T-MoS 2 models for structural optimization, then examined their stability by analyzing formation energy, structural evolution, as well as elastic constants, and finally assessed the HER catalytic performance of these stable catalysts by analyzing the free energy of H* intermediate and reaction mechanism. Structural stability is one of the most significant factors to determine the catalytic performance of TM@1T-MoS 2 materials. For single TM atoms on the basal plane of 1T-MoS 2 , there are three possible adsorption patterns, as shown in Figure 1b. Through structural optimization, the Cr, Mn, Fe, Mo, Ta, W and Re anchored species present obvious structural deformation, indicating these metal atoms adsorbed on 1T-MoS 2 would be unstable and not suitable for use as a HER catalyst. For other TM atoms adsorption, as reported in previous work of Lau et al. [24], the site c on top of the Mo atom is the most frequently observed adsorbate position with the lowest energy. As two typical representatives, the optimized structures of Ti@1T-MoS 2 and Pd@1T-MoS 2 are displayed in Figure 1b, where each TM atom is coordinated with three nonequivalent S atoms. It is worth noting that the adsorption of single TM atoms induces a slight distortion of the MoS 2 1T phase into a lower energy 1T structure, which, in turn, is stabilized by the adsorbed single atoms. Note that for brevity, we did not distinguish them here. As reported in the previous experimental and theoretical works, anchoring appropriate TM atoms are favorable for maintaining the stability of the 1T metastable phase of MoS 2 [23,24]. In the stability evaluation step, to specifically examine the thermodynamic stability of TM@1T-MoS 2 without obvious deformation, the formation energy ∆E f is calculated, as listed in Figure 1c. The immobilization of 3d Ti, V, Co, Ni, Cu, and 4d Zr, Nb, Rh, Pd, Ag, as well as 5d Hf atoms on 1T-MoS 2 exhibits very negative formation energy (∆E f < −0.85 eV). Particularly, Ti@1T-MoS 2 has the lowest formation energy, reaching −2.88 eV. Such strong interaction is beneficial to prevent the metal aggregation or being leached [30]. This demonstrates that these 11 TM@1T-MoS 2 hybrids are thermodynamically stable.
adsorption, as reported in previous work of Lau et al. [24], the site c on top of the Mo atom is the most frequently observed adsorbate position with the lowest energy. As two typical representatives, the optimized structures of Ti@1T-MoS2 and Pd@1T-MoS2 are displayed in Figure 1b, where each TM atom is coordinated with three nonequivalent S atoms. It is worth noting that the adsorption of single TM atoms induces a slight distortion of the MoS2 1T phase into a lower energy 1T′ structure, which, in turn, is stabilized by the adsorbed single atoms. Note that for brevity, we did not distinguish them here. As reported in the previous experimental and theoretical works, anchoring appropriate TM atoms are favorable for maintaining the stability of the 1T metastable phase of MoS2 [23,24]. In the stability evaluation step, to specifically examine the thermodynamic stability of TM@1T-MoS2 without obvious deformation, the formation energy f E Δ is calculated, as listed in Figure 1c. The immobilization of 3d Ti, V, Co, Ni, Cu, and 4d Zr, Nb, Rh, Pd, Ag, as well as 5d Hf atoms on 1T-MoS2 exhibits very negative formation energy ( Particularly, Ti@1T-MoS2 has the lowest formation energy, reaching −2.88 eV. Such strong interaction is beneficial to prevent the metal aggregation or being leached [30]. This demonstrates that these 11 TM@1T-MoS2 hybrids are thermodynamically stable. To explore the mechanical stability of thermodynamically stable TM@1T-MoS2, their elastic constants are calculated based on the Strain versus Energy method [31,32]. For 2D rectangular TM@1T-MoS2 crystals, there are four independent elastic constants, i.e., C11, C22, C12 and C66. Also, the cases of graphene (C11 = 357.0 N/m, C12 = 63.0 N/m) and 2H-MoS2 (C11 = 135.9 N/m, C12 = 33.3 N/m) are calculated and compared with the previous work [33,34] to verify the reliability of our results. According to the mechanical stability criteria [35], namely, C11 > 0, C66 > 0 and C11 × C22 > C12 × C12, we found that the elastic constants of To explore the mechanical stability of thermodynamically stable TM@1T-MoS 2 , their elastic constants are calculated based on the Strain versus Energy method [31,32]. For 2D rectangular TM@1T-MoS 2 crystals, there are four independent elastic constants, i.e., C 11 , C 22 , C 12 and C 66 . Also, the cases of graphene (C 11 = 357.0 N/m, C 12 = 63.0 N/m) and 2H-MoS 2 (C 11 = 135.9 N/m, C 12 = 33.3 N/m) are calculated and compared with the previous work [33,34] to verify the reliability of our results. According to the mechanical stability criteria [35], namely, C 11 > 0, C 66 > 0 and C 11 × C 22 > C 12 × C 12 , we found that the elastic constants of Zr@1T-MoS 2 and Nb@1T-MoS 2 do not meet the criteria. This indicates that the 2D structures of Zr@1T-MoS 2 and Nb@1T-MoS 2 are mechanically unstable. Remarkably, for single Ti, V, Co, Ni, Cu, Rh, Pd, Ag and Hf atoms anchored on 1T-MoS 2 , these 9 TM@1T-MoS 2 catalysts all meet the criteria well (Table S1), indicating their good mechanical stabilities. For example, the C 11 , C 22 , C 12 and C 66 of Ti@1T-MoS 2 are 86.7, 63.3, 46.8 and 9.1 N/m, respectively, which satisfies the mechanical stability criteria well.
Turning our attention to the temperature effect on their stability, ab initio molecular dynamics (AIMD) simulations are performed at and above room temperature (300 and 400 K). Taking Ti@1T-MoS 2 as an example, the AIMD result in Figure 2a shows that the atoms only slightly vibrate around their equilibrium sites on annealing at 300 K for 10 ps. Relative to the equilibrium state, the deviation of the Ti-S bond length is less than 0.2 Å. A similar case is also found at 400 K ( Figure 2b). These results indicate that the Ti@1T-MoS 2 catalysts are capable of remaining stable at room temperature or even higher. Considering the fact that the catalytic reactions generally occur in an aqueous environment, AIMD approach is also carried out to examine the stability of Ti@1T-MoS 2 in water solutions, which can be reflected by the fluctuations of the current density in experiment [36]. As shown in Figure 2c, after annealing at a temperature of 300 K for 10 ps, the structure of Ti@1T-MoS 2 remains intact in water without any noticeable deformation. This fact can be further verified by the uniform evolution of temperature and energy with the simulation time (Figure 2d), where their fluctuations are relatively small. Such findings imply the outstanding stability of Ti@1T-MoS 2 in aqueous solutions at ambient conditions. In their experiment, Lau et al. [24] provided direct experimental evidence that with proper treatment at environmental conditions, anchoring TM single-atoms on the 1T-MoS 2 basal plane is feasible and greatly helpful to prevent the reconstruction of MoS 2 nanosheets from the distorted 1T phase to 2H phase, thereby maintaining the stability of the 1T structure. Overall, the latest experimental progresses in Co@1T-MoS 2 [23], Ni@1T-MoS 2 [16], and Pd@1T-MoS 2 [24] make these TM@1T-MoS 2 nanomaterials with good thermodynamic, mechanical and thermal stability be promisingly synthesized for task-specific applications in the near future.
Relative to the equilibrium state, the deviation of the Ti-S bond length is less than 0.2 Å. A similar case is also found at 400 K ( Figure 2b). These results indicate that the Ti@1T-MoS2 catalysts are capable of remaining stable at room temperature or even higher. Considering the fact that the catalytic reactions generally occur in an aqueous environment, AIMD approach is also carried out to examine the stability of Ti@1T-MoS2 in water solutions, which can be reflected by the fluctuations of the current density in experiment [36]. As shown in Figure 2c, after annealing at a temperature of 300 K for 10 ps, the structure of Ti@1T-MoS2 remains intact in water without any noticeable deformation. This fact can be further verified by the uniform evolution of temperature and energy with the simulation time (Figure 2d), where their fluctuations are relatively small. Such findings imply the outstanding stability of Ti@1T-MoS2 in aqueous solutions at ambient conditions. In their experiment, Lau et al. [24] provided direct experimental evidence that with proper treatment at environmental conditions, anchoring TM single-atoms on the 1T-MoS2 basal plane is feasible and greatly helpful to prevent the reconstruction of MoS2 nanosheets from the distorted 1T phase to 2H phase, thereby maintaining the stability of the 1T structure. Overall, the latest experimental progresses in Co@1T-MoS2 [23], Ni@1T-MoS2 [16], and Pd@1T-MoS2 [24] make these TM@1T-MoS2 nanomaterials with good thermodynamic, mechanical and thermal stability be promisingly synthesized for task-specific applications in the near future.

HER Activity and Kinetics of TM@1T-MoS2
Given the structures of 9 stable TM@1T-MoS2 crystals, in-depth study of their HER activity is essential to provide new research ideas for the further development of MoS2based hydrogen production catalysts. In this regard, the adsorption behaviors of H atom are examined at different sites, as marked in Figure S1. According to the calculated total energy listed in Table S2, the energetically most favorable configurations of H adsorption vary depending on the type of TM atoms fixed on the surface. For Pd@1T-MoS2 catalyst,

HER Activity and Kinetics of TM@1T-MoS 2
Given the structures of 9 stable TM@1T-MoS 2 crystals, in-depth study of their HER activity is essential to provide new research ideas for the further development of MoS 2based hydrogen production catalysts. In this regard, the adsorption behaviors of H atom are examined at different sites, as marked in Figure S1. According to the calculated total energy listed in Table S2, the energetically most favorable configurations of H adsorption vary depending on the type of TM atoms fixed on the surface. For Pd@1T-MoS 2 catalyst, our work demonstrates that S atoms near Pd become activated. Since the used 1T-MoS 2 supercell contains 12 nonmetal S atoms on the top atomic layer, the coverage (θ) of one H atom adsorption is calculated as 1/12. At this low θ, the adsorbed H atom preferentially binds to S atom on the Pd@1T-MoS 2 surface, which can be attributed to the fact that the electronegativity difference between H (2.10) and S atoms (2.58) is greater than that of H and Pd atoms (2.20). The corresponding free energy of H* adsorption (∆G H* ) reaches 0.36 eV, consistent with the reported results (0.35 eV) of Lau et al. [24] In their experiment, they have successfully synthesized Pd@1T-MoS 2 catalyst and confirmed their high activity for HER to dramatically accelerate the rate limiting recombination of H* to H 2 . In contrast, for Ti@1T-MoS 2 , and V@1T-MoS 2 systems, it is found that the adsorbed H atom prefers to be directly bonded with the single TM atoms fixed on the basal plane. Therefore, the anchored Ti and V single atoms are identified as the active sites for HER. Generally, the free energy of H* adsorption ∆G H* is used as an effective descriptor to evaluate the catalysts' activity for hydrogen evolution [37]. Too negative or too positive ∆G H* will result in slow HER kinetics. Therefore, when ∆G H* is as close to zero as possible, the catalyst has the optimal catalytic activity toward HER [38]. It is worth noting that, for Ti@1T-MoS 2 and V@1T-MoS 2 catalysts as summarized in Table S2, their ∆G H* is as low as 0.12 and 0.13 eV, respectively. Correspondingly, the absolute value |∆G H* | is significantly lower than the reported Pd@1T-MoS 2 catalyst (0.35) [24], and even comparable to Pt(111) [4] (theoretical ∆G H* = −0.09 eV at H coverage of 1/4). A volcano plot composed of ∆G H* and overpotential η HER is used to intuitively describe the HER activity of the screened 9 stable TM@1T-MoS 2 nanomaterials in Figure 3. The closer to the top of the volcano plot, the higher the hydrogen evolution activity of such catalysts [39]. Notably, for the Ti@1T-MoS 2 and V@1T-MoS 2 catalysts with acid corrosion resistance, they are closely located at the top of HER volcano plot, reaching 0.12, and 0.13 V, respectively. The ultralow overpotential of single Ti and V atoms anchored on 1T-MoS 2 , comparable to the benchmark Pt(111) (η HER = 0.09 V) [4] and pristine 1T-MoS 2 (0.14 V) catalysts [13], implies their potential catalytic activity for hydrogen evolution.
activity for hydrogen evolution [37]. Too negative or too positive ∆GH HER kinetics. Therefore, when ΔGH* is as close to zero as possible, t optimal catalytic activity toward HER [38]. It is worth noting that, f V@1T-MoS2 catalysts as summarized in Table S2, their ΔGH* is as low respectively. Correspondingly, the absolute value |ΔGH*| is significa reported Pd@1T-MoS2 catalyst (0.35) [24], and even comparable to Pt( ΔGH* = −0.09 eV at H coverage of 1/4). A volcano plot composed of ΔGH HER η is used to intuitively describe the HER activity of the screene MoS2 nanomaterials in Figure 3. The closer to the top of the volcano hydrogen evolution activity of such catalysts [39]. Notably, for the Ti@1 MoS2 catalysts with acid corrosion resistance, they are closely located volcano plot, reaching 0.12, and 0.13 V, respectively. The ultralow ove Ti and V atoms anchored on 1T-MoS2, comparable to the benchmark P V) [4] and pristine 1T-MoS2 (0.14 V) catalysts [13], implies their potent for hydrogen evolution. To gain insights into the HER kinetics, we took Ti@1T-MoS2 as search for the minimum energy pathway and calculated the reaction climbing-image nudged elastic band (NEB) method [40]. As reported [24], for Pd@1T-MoS2 catalyst, the H atom is first adsorbed on the ac then transferred to the proximal Pd atom to generate H2 (Figure 4a). S Ti@1T-MoS2 catalyst, the first H atom prefers to be directly bonded w chored on the basal plane, which can effectively boost the efficiency Then, H* reacts with another adsorbed H* to form H2, as displayed in tained results show that the single Ti atom on Ti@1T-MoS2 is the pri for catalyzing hydrogen evolution. The corresponding minimum e To gain insights into the HER kinetics, we took Ti@1T-MoS 2 as a representative to search for the minimum energy pathway and calculated the reaction barrier through the climbing-image nudged elastic band (NEB) method [40]. As reported in previous work [24], for Pd@1T-MoS 2 catalyst, the H atom is first adsorbed on the activated S atom and then transferred to the proximal Pd atom to generate H 2 (Figure 4a). Surprisingly, for the Ti@1T-MoS 2 catalyst, the first H atom prefers to be directly bonded with the Ti atom anchored on the basal plane, which can effectively boost the efficiency of proton transfer. Then, H* reacts with another adsorbed H* to form H 2 , as displayed in Figure 4b. The obtained results show that the single Ti atom on Ti@1T-MoS 2 is the principal active center for catalyzing hydrogen evolution. The corresponding minimum energy pathway of Volmer step and Tafel H-H recombination is visually presented in Figure 4c. It is clear that for Ti@1T-MoS 2 electrocatalyst, the reaction barrier of Tafel step reduces from 1.15 eV (undoped 1T-MoS 2 ) [13] to 0.15 eV, even showing much faster reaction kinetics than the reported Pd@1T-MoS 2 catalyst (0.33 eV) [24]. The anchored Ti atom dramatically accelerates the recombination of H* to H 2 . Therefore, the formed Ti@1T-MoS 2 hybrid is identified as a superior electrocatalyst toward HER at low H coverage of 1/12. Figure 4c. It is clear that for Ti@1T-MoS2 electrocatalyst, the reaction barrier of Tafel step reduces from 1.15 eV (undoped 1T-MoS2) [13] to 0.15 eV, even showing much faster reaction kinetics than the reported Pd@1T-MoS2 catalyst (0.33 eV) [24]. The anchored Ti atom dramatically accelerates the recombination of H* to H2. Therefore, the formed Ti@1T-MoS2 hybrid is identified as a superior electrocatalyst toward HER at low H coverage of 1/12. Furthermore, to demonstrate the catalytic capability of Ti@1T-MoS2 at different levels of H* coverage, we constructed the adsorption configuration with increased H* coverage (θ = 1/12, 2/12, 3/12 and 4/12) and calculated their ΔGH*. Herein, one H atom adsorption corresponds to a surface coverage of 1/12, while the adsorption of four H atoms corresponds to a coverage of 4/12. It is clear that in Figure S2, as the H coverage θ increases from 1/12 to 4/12, the ΔGH* of Ti@1T-MoS2 becomes more positive due to the lack of electrons in the surface S atoms and the insufficient active sites. Therefore, creating more active sites for the adsorption and activation of the reactant H* is highly significant, in order to achieve high HER activity of the catalyst in a wider H coverage.

Bimetal Active Sites on TMTi@1T-MoS2
At present, most studies on the atomic-level active sites of 1T-MoS2 only consider one type of single metal active center. Yet, the bimetal active centers on 1T-MoS2 remain a great challenge to be solved urgently. When two or more types of single metal atoms are introduced, one metal atom, not only serves as an active site, but also acts as a catalytic accelerator by modifying the electronic structure and coordination environment of another metal atom [41]. Ideally, such hybrids are beneficial to balance the interaction between the active center and reaction intermediate H*, thus, further enhancing the overall HER activity [42]. In view of this, we rationally designed the bimetal active centers on the 1T-MoS2 basal plane, and explored the regulation of their HER activity by controlling the synergistic effect between different single metal atoms and 1T-MoS2 conductive substrate. Furthermore, to demonstrate the catalytic capability of Ti@1T-MoS 2 at different levels of H* coverage, we constructed the adsorption configuration with increased H* coverage (θ = 1/12, 2/12, 3/12 and 4/12) and calculated their ∆G H* . Herein, one H atom adsorption corresponds to a surface coverage of 1/12, while the adsorption of four H atoms corresponds to a coverage of 4/12. It is clear that in Figure S2, as the H coverage θ increases from 1/12 to 4/12, the ∆G H* of Ti@1T-MoS 2 becomes more positive due to the lack of electrons in the surface S atoms and the insufficient active sites. Therefore, creating more active sites for the adsorption and activation of the reactant H* is highly significant, in order to achieve high HER activity of the catalyst in a wider H coverage.

Bimetal Active Sites on TMTi@1T-MoS 2
At present, most studies on the atomic-level active sites of 1T-MoS 2 only consider one type of single metal active center. Yet, the bimetal active centers on 1T-MoS 2 remain a great challenge to be solved urgently. When two or more types of single metal atoms are introduced, one metal atom, not only serves as an active site, but also acts as a catalytic accelerator by modifying the electronic structure and coordination environment of another metal atom [41]. Ideally, such hybrids are beneficial to balance the interaction between the active center and reaction intermediate H*, thus, further enhancing the overall HER activity [42]. In view of this, we rationally designed the bimetal active centers on the 1T-MoS 2 basal plane, and explored the regulation of their HER activity by controlling the synergistic effect between different single metal atoms and 1T-MoS 2 conductive substrate. As illustrated in the inset of Figure 5a, by further introducing single Ti, V, Mo, Ni, Cu, Pd and Pt atoms into the Ti@1T-MoS 2 nanomaterial, a new bimetal site was created. After structural optimization, the anchored bimetal atoms also induce a slight structural distortion of 1T-MoS 2 . To confirm their stability, we calculated the formation energy as shown in Figure 5a. Importantly, the TiTi@1T-MoS 2 , VTi@1T-MoS 2 , NiTi@1T-MoS 2 , CuTi@1T-MoS 2 , PdTi@1T-MoS 2 hybrids show very negative formation energy of lower than −1 eV, implying their good thermodynamic stability. Turning our attention to their hydrogen evolution activity, Figure 5b shows the considered H* adsorption models in which one H atom binds to a metal or nonmetal atom. Here, the PdTi@1T-MoS 2 catalyst with bimetal sites is taken as a typical representative of these stable TMTi@1T-MoS 2 hybrids. Interestingly, the H* adsorption properties on the aforementioned five bimetal catalysts are very similar, i.e., the first H atom is inclined to be directly bonded to the electron-rich Ti atom, as summarized in Table S3. The proximal metal atom plays an efficient role in further activating the Ti atom. Importantly, for VTi@1T-MoS 2 and CuTi@1T-MoS 2 , their ∆G H* of one H atom adsorbed on Ti site is only about −0.01 and +0.01 eV (Figure 5c), respectively, even closer to zero than that on Pt(111) with −0.09 eV. However, the H* adsorption on the V or Cu site shows high ∆G H* , reaching 0.53, and 0.64 eV (Table S3), respectively. That is to say, in such catalysts, only one metal site exhibits catalytic activity for HER. Unexpectedly, for PdTi@1T-MoS 2 catalyst, the free energy ∆G H* of one H adsorption on the Pd or Ti sites has very close values, being 0.20, and 0.12 eV, respectively. When H coverage increases from 1/12 to 2/12 (i.e., H* is adsorbed on the Ti and Pd sites simultaneously), the Pd site still maintains the HER activity (∆G H* = 0.20 eV in Figure S3). The bonding strength of the adsorbed H* to the dual Pd and Ti sites is neither too strong nor too weak. Both of them are able to serve as the active sites for H adsorption. For electrocatalyzing hydrogen evolution, the unique dual active centers make PdTi@1T-MoS 2 applicable for wider H coverage.
As illustrated in the inset of Figure 5a, by further introducing single Ti, V, Mo, Ni, Cu, Pd and Pt atoms into the Ti@1T-MoS2 nanomaterial, a new bimetal site was created. After structural optimization, the anchored bimetal atoms also induce a slight structural distortion of 1T-MoS2. To confirm their stability, we calculated the formation energy as shown in Figure 5a. Importantly, the TiTi@1T-MoS2, VTi@1T-MoS2, NiTi@1T-MoS2, CuTi@1T-MoS2, PdTi@1T-MoS2 hybrids show very negative formation energy of lower than −1 eV, implying their good thermodynamic stability. Turning our attention to their hydrogen evolution activity, Figure 5b shows the considered H* adsorption models in which one H atom binds to a metal or nonmetal atom. Here, the PdTi@1T-MoS2 catalyst with bimetal sites is taken as a typical representative of these stable TMTi@1T-MoS2 hybrids. Interestingly, the H* adsorption properties on the aforementioned five bimetal catalysts are very similar, i.e., the first H atom is inclined to be directly bonded to the electron-rich Ti atom, as summarized in Table S3. The proximal metal atom plays an efficient role in further activating the Ti atom. Importantly, for VTi@1T-MoS2 and CuTi@1T-MoS2, their ΔGH* of one H atom adsorbed on Ti site is only about −0.01 and +0.01 eV (Figure 5c), respectively, even closer to zero than that on Pt(111) with −0.09 eV. However, the H* adsorption on the V or Cu site shows high ΔGH*, reaching 0.53, and 0.64 eV (Table S3), respectively. That is to say, in such catalysts, only one metal site exhibits catalytic activity for HER. Unexpectedly, for PdTi@1T-MoS2 catalyst, the free energy ΔGH* of one H adsorption on the Pd or Ti sites has very close values, being 0.20, and 0.12 eV, respectively. When H coverage increases from 1/12 to 2/12 (i.e., H* is adsorbed on the Ti and Pd sites simultaneously), the Pd site still maintains the HER activity (ΔGH* = 0.20 eV in Figure S3). The bonding strength of the adsorbed H* to the dual Pd and Ti sites is neither too strong nor too weak. Both of them are able to serve as the active sites for H adsorption. For electrocatalyzing hydrogen evolution, the unique dual active centers make PdTi@1T-MoS2 applicable for wider H coverage.

Sulfur Vacancy-Mediated Hydrogen Adsorption on TMTi@1T-MoS2
Based on the experimental findings of Pető et al., the formation of S vacancy is unavoidable on the basal plane of 2D 1T-MoS2 crystals at room temperature [43]. To this end, we investigated the effects of S vacancy on the catalytic activity of bimetal catalysts (denoted as TMSvTi@1T-MoS2, TM = Ti, V, Ni, Cu, Pd and Pt), where Ti atom was coordinated with three S atoms (site-S) and the other TM was deposited into the S vacancy (site-Sv). The reason why the early transition metal Ti was chosen to coordinate with S is that it has

Sulfur Vacancy-Mediated Hydrogen Adsorption on TMTi@1T-MoS 2
Based on the experimental findings of Pető et al., the formation of S vacancy is unavoidable on the basal plane of 2D 1T-MoS 2 crystals at room temperature [43]. To this end, we investigated the effects of S vacancy on the catalytic activity of bimetal catalysts (denoted as TM Sv Ti@1T-MoS 2 , TM = Ti, V, Ni, Cu, Pd and Pt), where Ti atom was coordinated with three S atoms (site-S) and the other TM was deposited into the S vacancy (site-Sv). The reason why the early transition metal Ti was chosen to coordinate with S is that it has a relatively large electronegativity difference with S, favoring the stability of Ti atom immobilized on the 1T-MoS 2 basal plane. A widely used parameter for predicting the HER activity of specific catalyst is the H adsorption Gibbs free energy (∆G H* ). We calculated ∆G H for H adsorption on diverse sites and compared it to that of pristine TMTi@1T-MoS 2 without S vacancy. The main findings were presented in Figure 6 and Table S4. Our theoretical result reveal that for V Sv Ti@1T-MoS 2 , Ni Sv Ti@1T-MoS 2 , Cu Sv Ti@1T-MoS 2 , Pd Sv Ti@1T-MoS 2 , Pt Sv Ti@1T-MoS 2 bimetal catalysts, the H atoms with coverage θ = 1/12 prefers to bind to the TM Sv atoms deposited in the S vacancies. Among them, ∆G H* of V Sv Ti@1T-MoS 2 displays similar values of 0.18 eV and 0.15 eV at the site-S and site-Sv, respectively (Figure 6b). This means that both V and Ti bimetals of V Sv Ti@1T-MoS 2 are able to act as active sites to boost the hydrogen adsorption and desorption at low H coverage, further enhancing the HER activity. However, at higher H coverage θ = 2/12, ∆G H* of V Sv Ti@1T-MoS 2 becomes more positive reaching 0.34 eV, indicating a not very favorable H adsorption. Therefore, the V Sv Ti@1T-MoS 2 catalyst is only suitable for low H coverage.
VSvTi@1T-MoS2 displays similar values of 0.18 eV and 0.15 eV at the site-S and site-Sv, respectively (Figure 6b). This means that both V and Ti bimetals of VSvTi@1T-MoS2 are able to act as active sites to boost the hydrogen adsorption and desorption at low H coverage, further enhancing the HER activity. However, at higher H coverage θ = 2/12, ΔGH* of VSvTi@1T-MoS2 becomes more positive reaching 0.34 eV, indicating a not very favorable H adsorption. Therefore, the VSvTi@1T-MoS2 catalyst is only suitable for low H coverage.
Differently, ΔGH* of PdSvTi@1T-MoS2 is lowered to 0.09 eV and −0.05 eV at low (θ = 1/12) and higher (θ = 2/12) H coverage, respectively (see Figure 6d,f). These findings clearly show that at low H coverage, the Pd atoms deposited on the S vacancies (PdSv) serve as the main active sites for H adsorption. While at high H coverage, both PdSv and Ti acts as the dual active sites to facilitate the hydrogen evolution. The enhanced catalytic activity is clearly related to the presence of substitutional PdSv sites, which saturate the S vacancies and induce charge redistribution. The experimental results of Lau et al. [24] also confirmed the enhanced HER activity of 1T-MoS2 monolayer doped with Pd atom at the S vacancy site.

Discussion
To deeply gain insight into the underlying modulation mechanism for PdTi@1T-MoS2 catalyst, we investigated its electronic structure as illustrated in Figure 7. Introducing single Pd atom into Ti@1T-MoS2 can alter the coordination environment of the initially anchored Ti site, leading to the rearrangement of d orbitals. From the projected density of states shown in Figure 7a, it is clear that the electron-rich Ti-d orbital mainly occupies the conduction band above the Fermi level, ranging from 0.5 to 1.5 eV. Differently, the Pd-d orbital mainly dominates the valence band ranging from −4 to −1 eV. As a result, the PdTi@1T-MoS2 hybrid shows excellent electronic conductivity, which, in turn, boosts the Differently, ∆G H* of Pd Sv Ti@1T-MoS 2 is lowered to 0.09 eV and −0.05 eV at low (θ = 1/12) and higher (θ = 2/12) H coverage, respectively (see Figure 6d,f). These findings clearly show that at low H coverage, the Pd atoms deposited on the S vacancies (Pd Sv ) serve as the main active sites for H adsorption. While at high H coverage, both Pd Sv and Ti acts as the dual active sites to facilitate the hydrogen evolution. The enhanced catalytic activity is clearly related to the presence of substitutional Pd Sv sites, which saturate the S vacancies and induce charge redistribution. The experimental results of Lau et al. [24] also confirmed the enhanced HER activity of 1T-MoS 2 monolayer doped with Pd atom at the S vacancy site.

Discussion
To deeply gain insight into the underlying modulation mechanism for PdTi@1T-MoS 2 catalyst, we investigated its electronic structure as illustrated in Figure 7. Introducing single Pd atom into Ti@1T-MoS 2 can alter the coordination environment of the initially anchored Ti site, leading to the rearrangement of d orbitals. From the projected density of states shown in Figure 7a, it is clear that the electron-rich Ti-d orbital mainly occupies the conduction band above the Fermi level, ranging from 0.5 to 1.5 eV. Differently, the Pd-d orbital mainly dominates the valence band ranging from −4 to −1 eV. As a result, the PdTi@1T-MoS 2 hybrid shows excellent electronic conductivity, which, in turn, boosts the catalytic activity for hydrogen production. In addition, the electron localization function (ELF) [44] is calculated to characterize the localized distribution characteristics of electrons, involving atomic binding and lone electron pairs in the PdTi@1T-MoS 2 system. It is displayed in Figure 7b, where the upper limit 1 of ELF corresponds to the perfect localization of electrons, while the lower limit 0 for complete delocalization (or no electrons), and the middle value 0.5 corresponds to electron gas-like pair probability. It is clearly seen that for single Ti and Pd atoms co-fixed on the 1T-MoS 2 crystal, the red area is mainly distributed outside the S atom, where ELF value reaches 0.77~0.82. The highly localized electrons of S atom are not favorable for the adsorption of the reactant H*. Notably, the area near the Pd and Ti atoms is shown in light blue, and the corresponding ELF value is 0.13 or even lower. This indicates that the electrons around Ti and Pd are highly delocalized, thus contributing to the adsorption of proton hydrogen, further achieving more catalytic active sites. These results confirm the superior HER performance of PdTi@1T-MoS 2 electrocatalyst due to its improved active center and good conductivity.
catalytic activity for hydrogen production. In addition, the electron localization function (ELF) [44] is calculated to characterize the localized distribution characteristics of elec trons, involving atomic binding and lone electron pairs in the PdTi@1T-MoS2 system. It i displayed in Figure 7b, where the upper limit 1 of ELF corresponds to the perfect locali zation of electrons, while the lower limit 0 for complete delocalization (or no electrons) and the middle value 0.5 corresponds to electron gas-like pair probability. It is clearly seen that for single Ti and Pd atoms co-fixed on the 1T-MoS2 crystal, the red area is mainly distributed outside the S atom, where ELF value reaches 0.77~0.82. The highly localized electrons of S atom are not favorable for the adsorption of the reactant H*. Notably, th area near the Pd and Ti atoms is shown in light blue, and the corresponding ELF value i 0.13 or even lower. This indicates that the electrons around Ti and Pd are highly delocal ized, thus contributing to the adsorption of proton hydrogen, further achieving more cat alytic active sites. These results confirm the superior HER performance of PdTi@1T-MoS electrocatalyst due to its improved active center and good conductivity. Our theoretical findings provide an important guidance for the experimental synthe sis of target HER catalyst. By introducing monodisperse Pd and Ti atoms on the basa plane, the precise engineering atomic structures contributes to the formation of more ac tive sites on 1T-MoS2. Several powerful synthetic methods have been proposed to pre cisely fabricate the atomic dispersed catalysts, including mass-selected soft landing atomic layer deposition (ALD), co-precipitation and impregnation wet-chemical route [45,46]. Therefore, we hope that the PdTi@1T-MoS2 catalyst can be fabricated in the nea future for electrocatalyzing HER in acid electrolytes.

Conclusions
In summary, we reported the mono/bimetal atoms mediated 1T-MoS2 as highly sta ble and efficient electrocatalysts for HER via systematically controlling the composition and electronic structure. Using the density functional theory and automatic framework of material screening methods, it is found that the single Ti atoms anchored on the 1T MoS2 (Ti@1T-MoS2) basal plane are able to serve as the active center for H* adsorption instead of the proximal S. The obtained Ti@1T-MoS2 catalyst exhibits excellent structura stability, near-thermoneutral adsorption of H* and ultralow reaction barrier (0.15 eV), out performed the reported Co, Ni, Pd anchoring species. More importantly, for bimetal Pd and Ti atoms immobilized together on 1T-MoS2, the major advantage of such PdTi@1T MoS2 catalyst is that, it maintains the high activity of single Ti atom, and achieves new dual active sites, where the bonding strength of adsorbed H* to the dual Pd and Ti sites i Our theoretical findings provide an important guidance for the experimental synthesis of target HER catalyst. By introducing monodisperse Pd and Ti atoms on the basal plane, the precise engineering atomic structures contributes to the formation of more active sites on 1T-MoS 2 . Several powerful synthetic methods have been proposed to precisely fabricate the atomic dispersed catalysts, including mass-selected soft landing, atomic layer deposition (ALD), co-precipitation and impregnation wet-chemical routes [45,46]. Therefore, we hope that the PdTi@1T-MoS 2 catalyst can be fabricated in the near future for electrocatalyzing HER in acid electrolytes.

Conclusions
In summary, we reported the mono/bimetal atoms mediated 1T-MoS 2 as highly stable and efficient electrocatalysts for HER via systematically controlling the composition and electronic structure. Using the density functional theory and automatic frameworks of material screening methods, it is found that the single Ti atoms anchored on the 1T-MoS 2 (Ti@1T-MoS 2 ) basal plane are able to serve as the active center for H* adsorption instead of the proximal S. The obtained Ti@1T-MoS 2 catalyst exhibits excellent structural stability, near-thermoneutral adsorption of H* and ultralow reaction barrier (0.15 eV), outperformed the reported Co, Ni, Pd anchoring species. More importantly, for bimetal Pd and Ti atoms immobilized together on 1T-MoS 2 , the major advantage of such PdTi@1T-MoS 2 catalyst is that, it maintains the high activity of single Ti atom, and achieves new dual active sites, where the bonding strength of adsorbed H* to the dual Pd and Ti sites is neither too strong nor too weak. The unique dual active centers make PdTi@1T-MoS 2 applicable for wider H coverage, comparable to the benchmark Pt catalyst. This work provides an attractive design strategy to improve the electrocatalytic activity of 1T-MoS 2 for HER.

Supplementary Materials:
The following are available online at https://www.mdpi.com/article/ 10.3390/ma14154073/s1, Figure S1: Two different adsorption sites of H atom on the surface of TM@1T-MoS 2 catalysts, Figure S2: Side views of the lowest energy structure and corresponding Gibbs free energy of H* adsorption (∆G H* ) at different H coverage on the Ti@1T-MoS 2 surface, Figure S3: H atom adsorption configuration on PdTi@1T-MoS 2 , Table S1: The elastic constants C 11 , C 22 , C 12 , C 66 (N/m) used to evaluate whether the TM@1T-MoS 2 systems meet the mechanical stability criteria, Table S2: The total energy E tot and free energy ∆G H* of H* adsorption on TM@1T-MoS 2 , as well as the overpotential η HER (V), Table S3: Total energy E tot and free energy ∆G H* of H* adsorption on TMTi@1T-MoS 2 . Table S4: ∆G H* of TM Sv Ti@1T−MoS 2 (TM = Ti, V, Ni, Cu, Pd and Pt) at θ = 1/12 and 2/12, where Ti atom was coordinated with three S atoms and the other TM was deposited into the S vacancy.

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.