Defect engineering of 1T′ MX 2 (M = Mo, W and X = S, Se) transition metal dichalcogenide-based electrocatalyst for alkaline hydrogen evolution reaction

The alkaline electrolyzer (AEL) is a promising device for green hydrogen production. However, their energy conversion efficiency is currently limited by the low performance of the electrocatalysts for the hydrogen evolution reaction (HER). As such, the electrocatalyst design for the high-performance HER becomes essential for the advancement of AELs. In this work, we used both hydrogen (H) and hydroxyl (OH) adsorption Gibbs free energy changes as the descriptors to investigate the catalytic HER performance of 1T′ transition metal dichalcogenides (TMDs) in an alkaline solution. Our results reveal that the pristine sulfides showed better alkaline HER performance than their selenide counterparts. However, the activities of all pristine 1T′ TMDs are too low to dissociate water. To improve the performance of these materials, defect engineering techniques were used to design TMD-based electrocatalysts for effective HER activity. Our density functional theory results demonstrate that introducing single S/Se vacancy defects can improve the reactivities of TMD materials. Yet, the desorption of OH becomes the rate-determining step. Doping defective MoS2 with late 3d transition metal (TM) atoms, especially Cu, Ni, and Co, can regulate the reactivity of active sites for optimal OH desorption. As a result, the TM-doped defective 1T′ MoS2 can significantly enhance the alkaline HER performance. These findings highlight the potential of defect engineering technologies for the design of TMD-based alkaline HER electrocatalysts.


Introduction
Green hydrogen can be produced through water electrolysis using electricity from renewable sources like solar and wind, which is considered as a promising solution compared to 'gray' hydrogen generated from steam methane reforming, contributing to CO and CO 2 emissions [1].The cost of green hydrogen production is influenced by the expense of renewable electricity and the energy efficiency of water electrolyzers [1].The hydrogen evolution reaction (HER) via water splitting can occur either in acidic or alkaline environments [2].While acidic solutions are more efficient due to the high concentration of H+ ions and the availability of commercial proton membranes, HER electrocatalysts, such as Pt, are costly and rare [3].On the other hand, the industrial utilization of alkaline media for large-scale hydrogen production is more popular due to the use of earth-abundant catalysts [4,5].Despite technological advancements, the energy conversion efficiency of market-leading alkaline electrolyzers (AELs) remains relatively low, which calls for the design of new high-performance alkaline HER electrocatalysts.
Recent studies have shown promising results regarding TMDs as HER catalysts [6][7][8][9][10][11].The metallic 1T or 1T ′ TMDs show promise for HER due to their electronic structure, high conductivity, tunable properties, and active catalytic sites [12][13][14][15][16][17].Previous computational studies mainly focused on the H adsorption-free energy (∆G H * ) as a descriptor for 1T-TMDs in HER [6,18,19].This is because the HER in acidic media begins with the discharge of a proton (Volmer reaction, equation (1)) and can proceed through either the electrodesorption step (Heyrovsky reaction, equation ( 2)) or the proton recombination step (Tafel reaction, equation (3)) Heyrovsky reaction: ( Under alkaline conditions, the Volmer and Heyrovsky reactions differ due to the presence of hydroxide ions (OH -).The Volmer reaction (equation ( 4)) involves the electrochemical reduction of water (H 2 O) to form an adsorbed hydrogen species (H * ) and hydroxide ions.The Heyrovsky reaction (equation ( 5)) occurs when the adsorbed hydrogen species reacts with a proton, electron, and hydroxide ion to produce molecular hydrogen and hydroxide ions.The Tafel reaction (equation ( 6)) remains unchanged, representing the interaction between two adsorbed hydrogen species to form H 2 Volmer reaction: H Heyrovsky reaction: Tafel reaction: Consequently, breaking the covalent H-OH bond in the Volmer reaction becomes essential in an alkaline solution.This has led to a debate in the literature challenging the traditional approach of using the Gibbs free energy change of the hydrogen adsorption as the sole reaction descriptor for HER in favor of considering the complex phenomenological approach of the alkaline environment [20].In alkaline media, the adsorption of OH intermediate, which is proportional to the H-OH bond dissociation barrier according to the Brønsted-Evans-Polanyi relationship is equally important [21].To this end, the Gibbs free energy change of OH adsorption (∆G HO * ) can be considered another critical descriptor for alkaline HER.Previous studies on Pt-based electrocatalysts demonstrated that the desired values for ∆G H * and ∆G OH * are 0.0 eV and −0.3 eV, respectively [21].To our knowledge, no theoretical study has focused on TMDs for electrocatalytic HER in alkaline solutions by using both ∆G H * and ∆G OH * as descriptors.
In this study, we resort to the density functional theory (DFT) method to calculate both ∆G H * and ∆G OH * values of several TMD-based materials and assess the performance of these materials in alkaline HER.The DFT results demonstrate that defect engineering is a promising root for developing efficient TMD-based HER electrocatalysts in an alkaline solution.
The ∆G H * was computed from the following equation: where ∆E H* is the adsorption energy of H atoms, which can be calculated from the following equations where E H * and E * are the energies of the TMD monolayers with and without absorbed H atoms, respectively.T, ∆S, and ∆ZPE in equation ( 7) are the room temperature (T = 298.15K), entropy change, and zero-point energy change, respectively, which values are obtained from the literature [22,26,38].Accordingly, the ∆G OH * was computed as follows: The adsorption energy of OH was calculated as follows: E OH * is the energies of the monolayer with adsorbed OH, and E H2O is the energy of an isolated water molecule.

Pristine 1T ′ MX 2 (M = Mo, W and X = S, Se) TMD
The ∆G H * and ∆G OH * were first used as the descriptors to evaluate the alkaline HER performance of pristine 1T ′ MX 2 (M = Mo, W and X = S, Se) TMD, which atomic structure was illustrated in figure 1(a).Due to the low symmetry of 1T ′ phase of TMDs, some X atoms are higher (termed as High X) than the rest (termed as Low X) in the top layer.Both figures 1(b) and (c) show the adsorption of hydrogen atom intermediates on High X atoms and Low X, respectively.The OH intermediate was adsorbed at the top of the metal of the MX 2 monolayer, which is associated with the High and Low X sites.The ∆G H * and ∆G OH * values are shown in figure 1(d) and listed in table S1.It can be found that ∆G H * values of sulfides are lower than that of the selenides, indicating higher reactivity of S for H adsorption compared to Se.This can be understood in terms of the lower S electronegativity, which also agrees with the conclusions of previous studies dealing with MoSe 2 and WSe 2 that showed lower HER activity and poor H * adsorption compared to MoS 2 and WS 2 [39,40].In general, the stronger adsorption of H on Low X is reflected by the slightly short X-H bond lengths listed in table S1.The stronger adsorption of H on Low X can be ascribed to the weaker interaction between M and Low X, which can be evidenced by the longer bond length between Low X and M [41,42].Interestingly, the ∆G H * values on Low S are close to the desired one of 0.0 eV.It suggests that these 1T ′ MoS 2 and WS 2 can be suitable acidic HER electrocatalysts.However, all pristine TMDs considered here have high ∆G OH * larger than 1.5 eV, far from the ideal value of −0.3 eV [21].The high ∆G OH * values indicate that water dissociation becomes the rate-determination step (RDS) for alkaline HER due to the low activity of these TMDs.Thus, their reactivity for water dissociation needs to be further improved to enable a better energy conversion efficiency of 1T ′ TMD for alkaline HER electrocatalysis.

Single X vacancy defective TMD
The occurrence of vacancies in metallic TMDs has been experimentally demonstrated to possess a much higher reactivity [15].As such, the defective TMDs hold the potential for higher energy conversion efficiency during alkaline HER.Recent studies have revealed that the intrinsic properties of TMDs, such as electronics, optical, mechanical, and thermal properties, can be altered by defects in the TMDs [43][44][45][46].Previous studies considered six kinds of point defects: monochalcogenide vacancy (X vacancy), dichalcogenide vacancy (2X vacancy), aligned dichalcogenide vacancy, and aligned monochalcogenide vacancy (2Xs vacancy), metal vacancy (M vacancy), vacancy complex of M and three adjacent chalcogens (MX3 vacancy), and vacancy complex of M and three adjacent chalcogen pairs (MX6 vacancy) [43,47,48].It has been demonstrated that X vacancy is the easiest to form, with the highest abundance in the defective TMDs [43].In this regard, only X vacancy was considered in this study.The X vacancy can be generated by removing either Low or High X from the pristine TMDs, as shown in figures 2(a) and (b) respectively.For all four kinds of 1T ′ TMDs considered in this study, the formation of Low X vacancy is more energetically preferred (see table S2).Consequently, only the Low X vacancy was considered in the remaining part of this work.
The hydrogen can be adsorbed on the top of the Low or High X next to the Low X vacancy, as shown in figure 2(c), respectively.Similarly, the trend observed on the pristine TMD monolayer, the adsorption of H atoms on the Low X is energetically preferred.The single X vacancy defects have considerable impacts on H adsorption.The ∆G H * values of MoS 2 and WS 2 decrease by 31% and 16%, respectively (see tables S1 and S2).Accordingly, the ∆G H * values of MoSe 2 and WSe 2 reduced by 22% and 17%, respectively (see tables S1 and S2).This observation implies that X vacancies in TMDs can alter their electronic structure and boost their catalytic activity for the HER.
Figure 2(d) shows the adsorption configuration of the intermediate OH on the X vacancy site of 1T ′ TMDs.Unlike the H adsorption on the X atoms, where the electronic properties of the X atoms were indirectly affected by the neighboring X vacancy, the OH species directly adsorb at the X vacancy site.Consequently, the impact of X vacancy on the ∆G OH * is much more significant than that of their corresponding pristine TMDs.The ∆G OH * values are shown in figure 2(e) and listed in table S2.All the ∆G HO * values on the X vacancy site are significantly reduced by 165%, 163%, 183%, and 178% for MoS 2 , MoSe 2 , WS 2 , and WSe 2 , respectively (see tables S1 and S2), which indicates a tremendous improvement in the reactivity of 1T ′ TMDs for OH adsorption.It is worth noting that the relative reduction amplitude of ∆G OH * values is more affected by the metal since the OH is directly associated with the metals.The ∆G OH * values exhibit a particularly significant decrease more significantly on WX 2 .Figure 2(e) displays a volcano plot, illustrating that the ∆G OH * values are lower than the optimal value of −0.3 eV.The low ∆G OH * values indicate that the X vacancy sites within all TMD monolayers are too reactive to OH desorption.Consequently, the OH desorption becomes the RDS for alkaline HER.To further improve the TMD-based alkaline HER performance, manipulating the activity of the X vacancy site becomes the critical factor.Since the S vacancy site in the 1T ′ MoS 2 monolayer has the highest performance, as evidenced by figure 2(e), the defective 1T ′ MoS 2 monolayer was then used as the model system for the further electrocatalyst design.

3d TM doped defective MoS 2
Various research studies have aimed to enhance the efficiency of HER catalysts doping with TM dopants [32].To this end, we purposely incorporate widely used 3d TM such as Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn dopants to defective 1T ′ MoS 2 with S vacancy to optimize the adsorption strength of OH and H species on TMDs for alkaline HER.The calculated plot of ∆G OH * against ∆G H * is shown in figure 3. Our DFT results demonstrate that ∆G H * increases after introducing early 3d TM dopants (see table S3) and that it decreases with the introduction of late 3d TM dopants except in the case of Zn-doped MoS 2 (see table S4).Noteworthy, the ∆G H * values of Fe-, Co-, Ni-and Cu-doped defective 1T ′ MoS 2 are close to the optimal ∆G H * value of 0.0 eV.The ∆G H * value is often used as the only descriptor to screen the performance of the acidic HER electrocatalyst [32].Consequently, the S atoms next to the metal dopant and S vacancy are highly favorable for acidic HER.
The  for alkaline HER.Indeed, the recent experiments have demonstrated that the Ni-and Co-doped 1T ′ MoS 2 possess low overpotentials of −145 mV and −160 mV at a current density of 10 mA cm −2 , respectively, for alkaline HER [49], which validates our theoretical results.Our results further demonstrate that the combination of the Co and Ni dopants with the S vacancy may be the origin of the high performance toward alkaline HER [49][50][51][52].Furthermore, our DFT results predict that the Cu-doped 1T ′ defective MoS 2 may have the best alkaline HER performance, where ∆G OH * and ∆G H * are −0.22 and −0.06 eV, respectively.
Compared with the undoped defective MoS 2 , the ∆G OH * values of these promising electrocatalysts significantly increase, indicating a reduction in their activity after doping.To better understand the impact of the TM dopants to deliver promising HER catalysts, the charge density difference of Cu-doped defective MoS 2 with the adsorbed OH species was calculated (see figure 4).For the sake of comparison, the charge density difference of the undoped defective MoS 2 with adsorbed OH species is also shown in figure 4. On the undoped defective 1T ′ MoS 2 , a large amount of charge densities are accumulated on the adsorbed OH.Accordingly, the charge densities of neighboring Mo atoms are depleted.The substantial charge transfer agrees with the low ∆G HO * value of the defective 1T ′ MoS 2 shown in figure 2(e).As a result, the desorption of OH becomes the RDS during the alkaline HER.In contrast, the Cu-doped MoS 2 exhibits almost no charge density depletion on the Cu dopant.A small charge density accumulation between OH and Cu dopant is also observed.This supports that a weaker interaction between Cu and OH  species leads to the observed higher ∆G OH * value, which is beneficial to the desorption of adsorbed OH species and further enhances the alkaline HER performance.
The Fe-, Co-, Ni-, and Cu-doped 1T ′ defective MoS 2 monolayers have different ∆G OH * values from −0.88 eV to −0.22 eV.This is expected due to the direct interaction between OH and the metal dopants.To understand the trend of the ∆G OH * values of Fe-, Co-, Ni-, Cu-doped 1T ′ defective MoS 2 monolayers, the d-band center of the spin-down states of these dopants was calculated and listed in table S5. Figure 5 shows a direct correlation of d-band center energy with the free energy of OH adsorption to the surface of the doped catalyst.Our results indicate that the trend of this d-band center of the metals is positively correlated with the variance in the adsorption energies of OH intermediates on their doped 1T ′ defective MoS 2 .A reduced d-band center value from Fe to Cu suggests fewer vacant states, resulting in a higher Gibbs free energy change of OH adsorption.Hence, the shift of the d-band center can be used to explain the reactivity trend of these catalysts to OH adsorption.Furthermore, the stability of the most promising Cu-doped defective MoS 2 was tested by ab initio molecular dynamics (AIMD) simulation within the Born-Oppenheimer schemes.Figure S1 shows the energy profile of Cu-doped defective MoS 2 over 3 ps at 300 K with the time step of 1 fs.The AIMD results demonstrate that the energies are well conserved over the time, which demonstrates that the system is thermodynamically stable after the introduction of Cu dopants and S vacancies.

Conclusion
In this study, we performed DFT calculations to explore MoS 2 , WS 2 , MoSe 2 , and WSe 2 -based electrocatalysts for alkaline HER applications.Different from the conventional methods for acidic HER electrocatalyst design, both ∆G OH * and ∆G H * were used as descriptors to evaluate the electrocatalytic performance.This is due to the importance of OH adsorption during water splitting in alkaline solution.Our findings indicated that MoS 2 performed best among the four pristine TMDs.However, the pristine TMDs show low reactivity in the adsorption of OH species.As a result, the water dissociation becomes the RDS.Defect engineering strategies, such as introducing single X vacancies, were further investigated to enhance their HER reactivity.However, the defective TMDs with single X vacancies show high reactivity to the adsorption of OH species.Consequently, the adsorbed OH species can efficiently desorb from the vacancy site.To improve the performance of the catalysts, the 3d metal dopants were theoretically screened in the 1T ′ defective MoS 2 .Among all the systems investigated, Cu-doped MoS 2 with one S vacancy emerged as the most promising electrocatalyst for HER in alkaline media.The electronic property analysis revealed that the superior performance of Cu-doped defective MoS 2 can be attributed to the suitable d-band center of Cu cations, which greatly reduces the activity of active sites to achieve the desired OH and H adsorption strengths.This reduced reactivity was further confirmed through the charge density difference analysis.These findings provide insights into the potential of defective TMDs as catalysts for alkaline HER and highlight the importance of defect engineering strategies for further improvement.

Figure 1 .
Figure 1.Atomic structure of a typical (a) pristine 1T ′ MX 2 TMD; (b) pristine 1T ′ MX 2 TMD with hydrogen atom to the High X; (c) pristine 1T ′ MX 2 TMD with hydrogen atom to the Low X; and (d) plot of ∆G OH * against ∆G H * of MX 2 TMDs.Color code: yellow: X (S or Se), and purple: TM (Mo or W).
HO * value is another important indicator for the alkaline HER catalysts' design.The introduction of early 3d TM doping led to a significant change in ∆G OH * values.Generally, ∆G OH * values increase with the increase of the atomic number of the 3d TM dopant.The only exceptions are the Fe-and Zn-doped 1T ′ MoS 2 , which shows relatively low ∆G OH * value compared to Mn-and Cu-doped ones, respectively.Our calculations demonstrate that Co-, Ni-, and Cudoped materials have the highest ∆G HO * values, which are also close to the desired value of −0.3 eV.As a result, Co-, Ni-and Cu-doped 1T ′ MoS 2 are promising electrocatalysts

Figure 2 .
Figure 2. (a) Defective 1T ′ TMD with one Low X vacancy; (b) defective 1T ′ TMD with one High X vacancy; (c) defective 1T ′ TMD with one Low X vacancy with H bonded on Low X site; (d) defective 1T ′ TMD with OH adsorbed at Low X vacancy site; and (e) Volcano plot of ∆G HO * against ∆G H * of four TMDs with single X vacancy.Color code: yellow: X (S, Se), and purple: TM (Mo, W).

Figure 3 .
Figure 3. Volcano plot of ∆G OH * against ∆G H * using the 3d TMs doped single MoS 2 with single S vacancy.

Figure 4 .
Figure 4. Charge density difference of pristine MoS 2 and Cu-doped MoS 2 with the adsorbed OH species: top: side view; bottom: top view.The iso-surface value is 0.01.Blue iso-surface: charge density depletion; yellow iso-surface: charge density accumulation.

Figure 5 .
Figure 5.The relationship between the d-band center of 3d transition metals and their G OH * on 1T ′ single S vacancy defective MoS 2 .