Abstract
Electrochemical devices for efficient production of hydrogen as energy carrier rely still largely on rare platinum group metal catalysts. Chemically and structurally modified metal dichalcogenide MoS_{2} is a promising substitute for these critical raw materials at the cathode side where the hydrogen evolution reaction takes place. For precise understanding of structure and hydrogen adsorption characteristics in chemically modified MoS_{2} nanostructures, we perform comprehensive density functional theory calculations on transition metal (Fe, Co, Ni, Cu) doping at the experimentally relevant MoS_{2} surfaces at substitutional Mosites. Clear benefits of doping the basal plane are found, whereas at the Mo and Sedges complex modifications at the whole edge are observed. New insight into dopingenhanced activity is obtained and guidance is given for further experiments. We study a machine learning model to facilitate the screening of suitable structures and find a promising level of prediction accuracy with minimal structural input.
Introduction
The concept of hydrogen economy comprises the idea to produce, store, distribute and use hydrogen as renewable fuel^{1}. In this technology hydrogen can be cleanly produced by electrolytic splitting of water to hydrogen and oxygen if the process is powered by renewable energy sources^{1,2}. However, the watersplitting process relies currently on catalysts comprised of platinum group metals (PGMs), which are considered as critical raw materials in terms of supply^{3}. The metal dichalcogenide MoS_{2} has been suggested experimentally and theoretically as a promising candidate to replace the PGMs for the hydrogen evolution reaction (HER) at the cathode side^{2,4}. The recent steps in the development (see, for example^{5,6,7,8,9,10},) have been to modify it structurally, e.g., by synthesizing various types of nanostructures and chemically, e.g., by doping, which are both procedures to maximize the area of the active surface/edge configurations and sites to obtain optimal HER performance. For guiding and supporting the experimental search of replacement materials, detailed theoretical information on the chemically and structurally modified nanostructures is essential. The Gibbs free energy of adsorption ΔG _{H} for the reaction intermediate, i.e., hydrogen at the electrode surface, has been a widely used descriptor for predicting catalytic performance based on experimental correlations and mathematical models (Refs^{11,12} and references therein). It has been used for various transition metal dichalcogenides and doped MoS_{2} previously^{7,13,14}.
Synthesized MoS_{2} nanostructures have differently Scovered edges at various proportions, lengths and distributions depending on the preparation method^{6,15,16}. The structures can also contain less regular parts such as defects and terrasses. Importantly, each geometrically and chemically different part may correspond to specific HER efficiency. The undoped, pristine basal plane of 2HMoS_{2} is understood to be inactive^{4,13,17}. Several theoretical studies have been devoted to the pristine Mo and Sedges of MoS_{2} in terms of ΔG _{H}. Especially the Moedges are considered as active: the 100% Scovered Moedge of nanoclusters^{6} and the 50% Scovered Moedge in industrialstyle catalysts^{18}. Regarding modification with doping, Kibsgaard et al.^{6} studied Fe, Co, Ni and Cu and obtained truncated triangleshaped nanoclusters, finding Ni the best and Co the second best for promoting HER activity. In their clusters doping itself changes the morphology of the cluster (the relative linear lengths of the Mo and Sedges) and thereby the activity. Šarić et al.^{19} studied by density functional theory (DFT) calculations the corresponding Codoped nanoclusters. EscaleraLopez et al.^{20} reported NiMoS_{2} hybrid nanoclusters which showed a roughly 3fold increase in exchange current density compared with undoped nanoclusters. They associated the findings to Nidoped Moedge and Sedge sites. Deng et al.^{14} performed experiments on the doped basal plane of MoS_{2} and found the trend for HER activity as Pt (highest) > Co > Ni as dopants. They found a similar trend in their DFT calculations for various dopants. Li et al.^{21} studied single Pt atomic structure and dynamics in monolayer MoS_{2} experimentally and by DFT calculations. Dai et al.^{22} reported enhanced electrocatalytic properties for Codoped MoS_{2} nanosheets and attributed the finding to doping at the Mo and S edges. Wang et al.^{7} reported DFT calculations for ΔG _{H} of Mo and Sedges for pristine and TMdoped (Fe, Co, Ni, Cu) MoS_{2}. They also synthesized and characterized doped vertically aligned nanofilms which expose alternatingly infinite Mo and Sedges. Their results for the doped Sedge suggested enhanced catalytic activity as close to optimal (ΔG _{H} = 0 eV) values of hydrogen adsorption were found compared to the undoped edge. Finally, doped (Fe, Co, Ni) amorphous MoS_{2} was studied by Morales et al.^{5}.
In this work we provide a systematic study of the hydrogen adsorption structures and energetics for Fe, Co, Ni and Cudoped 2 H basal plane and Mo and Sedges at low H coverage conditions to clarify the precise effect of chemical modification of MoS_{2}. For comparison with earlier work, additional calculations are performed for Pd and Pt dopants and for higher H coverages. All the systems are calculated using the same level of description and without structural constraints, which provides a unique set of data. For Mo we study the 0%, 50% and 100% sulfidized edges and for S the 50%, 75% and 100% ones. The edge structures are illustrated in Fig. 1, denoted hereafter MoX or SX, where X indicates the degree of sulfur coverage in percents. We calculate relative substitutional energies (RSEs) to assess the affinities of doping at different edges and analyze the local structural changes. By using the calculated ΔG _{H} as a descriptor and comparing the results with experiments, we discuss the suitability of doping in the various cases for improving the HER activity. Since the detailed structureproperty relationship, directly or indirectly via ΔG _{H}, i.e., [atomic and electronic structure of the surface] → ΔG _{H} → [i _{0}, exchange current density], is far from trivial, our results offer new interpretations, suggestions and trends for experimental synthesis and for further theoretical work. For facilitating fast prediction of ΔG _{H} values (i.e., bypassing the DFT step), we illustrate a supervised machine learning (ML) model, which also informs about the importance of the structural features that determine the strength of H adsorption. Low H coverage is obtained in supercell calculations by adsorbing single H atoms on target areas. Studying this regime for the edge structures is consistent with the finding by Wang et al.^{7} for the Tafel slopes in their doped nanofilm experiments, which indicated that the ratelimiting HER step is the Volmer reaction, which corresponds to low H surface coverage. We will monitor ΔG _{H} not only in reference to the optimal condition (ΔG _{H} = 0 eV), but for description and classification consider also ΔG _{H}’s that are found within a range of values (such as −0.5 eV < ΔG _{H} < 0.5 eV). In this work we perform the calculations in electrically neutral supercells, but to assess the possible effects of nonneutral charge states, we also analyze explicitly two cases for an illustrative example: the doped basal plane and the undoped and Fedoped S100 edge in charge states +1, −1 and −2 of the supercell.
The rest of the paper is organized as follows. We first present the structural and hydrogen adsorption results for the doped 2 H basal plane and then for the doped Mo and Sedges. Next, we demonstrate the classification and regression models for predicting ΔG _{H} values and find the importances of the input variables. Before concluding, we discuss the more general implications, ideas and suggestions to experimental synthesis of MoS_{2} nanostructures.
Results
2H basal plane
Effect of doping on structure
The effect of substitutional doping on the local geometry of the basal plane is illustrated in Fig. 2. The doping level is 2.8% in the plane (that is, 1 of 36 Mo atoms in the topmost surface layer is replaced by the dopant in the supercell). For Fe the local geometry has a slightly reduced symmetry compared to the pristine structure, whereas a clearer symmetrybreaking effect occurs for Co, Ni and Cu, leading to a 5fold coordinated structure. A similar symmetry breaking is found for Pd and Pt. Numerical values for the nearestneighbor distances are reported in Supplementary Information. Our results for the local geometry are to some extent different from those reported previously by Deng et al.^{14}. Instead of our 5fold coordination for Co, Ni, Cu, Pd and Pt, they found a 4fold coordinated structure. These differences are discussed below further in the case of ΔG _{H} values. Finally, we note that when H adsorbs on the sulfur next to the Fe, Co, Ni and Cu dopant, no further essential symmetry breaking occurs, the only exception being that also Fe becomes 5fold coordinated. It is possible that there are nonsubstibutional and other available sites for the dopant atoms, but at least the calculations by Deng et al.^{14} suggest that they may have much higher formation energies than the substitutional one.
To study the charge state effects on the doped structures we carry out a standard formation energy analysis (see Methods). The analysis provides the relative stabilities of the doped systems at different charge states as a function of the electron chemical potential μ _{ e } (μ _{ e } measured from the valence band maximum). For Fe, Co and Ni the the results show that the neutral charge state is the most stable roughly in the range 0 eV \(\le {\mu }_{e}\mathop{ < }\limits_{ \tilde {}}0.6\) eV above which the negative charge states becomes the most likely. For Cu, the negative charge state becomes more likely above \({\mu }_{e}\sim 0.2\) eV. These findings do not hint at major changes in the oxidation number of the dopants that substitute Mo. Moreover, since \({\mu }_{e}\mathrm{ > 0.6}\) eV corresponds in principle already to a high cathodic overpotential, systems in that range of μ _{ e } are not any more in the optimal target area for good HER catalysts.
The modification of the electronic structure and the subsequent effects on geometry due to TM doping can be understood considering the d electrons in the local molecular symmetry. In pristine 2HMoS_{2} Mo is in the oxidation state IV, has two 4d electrons and is coordinated to six nearestneighbor sulfur atoms. According to Ref.^{23} the system has trigonal prismatic symmetry with point group \({D}_{3h}\). The two 4d electrons of Mo(IV) occupy a bonding d orbital with \({a}_{1}\) symmetry on top of the valence band, and the four unoccupied (nonbonding e and antibonding \(e^{\prime} \)) d states are higher in energy^{23}. By doping TM atoms substitutionally at the Mo site brings, as a first approximation, excess d electrons to the local structure. In addition, TM–S bond lengths contract compared with the Mo–S lengths due to a smaller atomic size of the TM atom. The excess d electrons start to occupy progressively the previously empty \(e\) and \(e^{\prime} \) states. As discussed above, for Co, Ni and Cu (5, 6 and 7 d electrons, respectively) the systems breaks to a lower 5fold symmetry (see Fig. 1), and this can be directly correlated with the antibonding \(e^{\prime} \) state becoming occupied. In short, progressive occupancy of the local antibonding d states triggers the symmetrylowering transition.
Effect of doping on H adsorption
A simple way to describe doping effects is that modifying the pristine MoS structure changes the binding of S at the surface. This consequently modifies the hydrogen adsorption free energy ΔG _{H} and provides a route to tune the HER activity. In the case of TM dopants (Fe, Co, Ni) at substitutional Mo sites, the specific occupancy of their local bonding and antibonding 3d states has been used as the explanation for the weaker binding between the dopant and sulfur^{24}.
Our results show that for the basal plane, doping with Fe, Co, Ni and Cu (as well as with Pd and Pt) is clearly beneficial for bringing ΔG _{H} values close to optimal adsorption condition (\({\rm{\Delta }}{G}_{{\rm{H}}}\approx 0\) eV) at the sulfur site that is the nearestneighbor to the dopant. For Ni, three local minima at the sulfur next to the dopant site were found during the search. This suggests that the local potential energy landscape in general is rich in detail but the adsorption energies are still rather close to each other. Farther away from the dopants larger ΔG _{H} values are found. ΔG _{H} values in the (−1) charge state are found to be similar within about ±0.1 eV to those of the neutral charge state (the largest difference 0.2 eV in the case of Cu).
The results (Table 1) demonstrate that the major improvement in ΔG _{H} values remains local close to the substitutional dopant atom. A similar finding was reported by Deng et al.^{14} for Pt. Naturally, the higher the substitutional dopant density at the outermost surface layer and without causing other structural modifications, the better the overall HER activity. Our ΔG _{H} values for the nearestneighbor adsorption are slightly different from those reported by Deng et al.^{14}. For Fe, Pd and Pt, their ΔG _{H} values are ~ 0.2–0.4 eV higher compared to ours and for the rest of the cases (undoped, Co, Ni and Cu) the values are similar. These differences must be attributed to different computational choices (most probably concerning the size and structure of the supercell), which leads to a different detailed relaxation geometry. Our result for the pristine basal plane \({\rm{\Delta }}{G}_{{\rm{H}}}=1.88\) eV is also close to the previously reported differential hydrogen free energy of adsorption \({\rm{\Delta }}{G}_{{\rm{H}}}^{diff}\) of 1.92 eV at low H coverage^{25}.
One can also search from our results structurebased hints that could predict optimal adsorption energies. From Table 1 for Fe…Ni it can be deduced that there is a negative correlation between the number of the valence shell electrons and ΔG _{H} values. We also found some dependence of ΔG _{H} on the Löwdin charge of the sulfur site before H adsorption. However, this latter dependency would be difficult to utilize for fast screening since it itself requires a DFT calculation. Predictive and powerful approaches can be probably best built using machine learning methods by encoding the geometries into multidimensional input attributes^{26}. For initial insight, in this work we employ a straightforward classification and regression analysis for ΔG _{H} prediction including as attributes the type of the surface, coordination number, dopant, and the dopanthydrogen distance.
Mo and Sedges
Effect of doping on structure
The studied doping level for the present edge structures is 16.7% (one Mo atom of the six along the edge row substituted). This is of the order of experimental values in the work of Wang et al.^{7}, who found by XPS that in Codoping the Co/Mo ratio is ~ 0.29 at the outermost row of the edge structures in their vertically aligned samples, which corresponds to the doping level of ~ 25% of the edge. They found that the ratio decreases continuously deeper from the edge. For small nanoclusters, Kibsgaard et al.^{6} concluded a 100% substitutional doping level at the Sedge. Our results are for supercells with stacked MoS_{2} layers which expose alternatingly the different edges (the system is periodic along the edges and in the direction of the plane normals, see example in Supplementary Information). The edges of these systems should thus correspond closely to the experimental samples discussed by Wang et al.^{7}. As a structural detail, we note that the ΔG _{H} values for H adsorption on the edges of isolated infinite MoS_{2} sheets (periodic in one dimension) differ from the ones presented here; a few test calculations revealed differences in ΔG _{H} of the order of ±0.3 eV. The effect of doping on the local symmetry and dopant energetics are discussed first before addressing hydrogen adsorption. The changes in the local symmetry due to substitutional doping are summarized in Table 2 (discussed in Supplementary Information in more detail). Examples of the relaxed edges are given in Fig. 3.
The charging effects on the edge structures are studied for the undoped and Fedoped S−100 structures as examples in the charges states +1, −1 and −2. The formation energy analysis shows that at the electron chemical potential in the range 0 eV \(\le {\mu }_{e}\mathop{ < }\limits_{ \tilde {}}0.6\) eV also the negative supercells (charge states −1, −2) are energetically relevant for both the cases. For the undoped edge also the +1 state is energetically relevant. This indicates that the edge systems themselves without and with dopants can trap charge, although no major changes can be observed in the atomic structures of the supercells. For the purposes of this work, the interesting question is to what extent charge states affect the ΔG _{H} values for H adsorption. This will be discussed in the corresponding section below.
Relative probability of doping at the edges
In the case of nanocluster model catalysts by Kibsgaard et al. (diameter ~65 Å at maximum)^{6}, there is strong evidence that the dopants have distinct tendencies to become incorporated into the different edges. Theoretical calculations by Schweiger et al. have elucidated the possible dopant energetics and morphologies in various sulfiding environments^{27}. Similar kind of energetics information for the probability of doping is now extracted from the present total energy calculations. If a given MoS_{2} nanostructure contains edges, the comparisons suggest onto which edge the dopant has the largest affinity. The results for relative substitutional energies (RSEs) are collected in Table 3 . The reference level corresponds to substituting the Mo atom by a dopant atom on the MoS_{2} basal plane. This reference is given by the energy difference \({E}_{{\rm{r}}{\rm{e}}{\rm{f}}}={E}_{{\rm{T}}{\rm{M}}{\rm{d}}{\rm{o}}{\rm{p}}{\rm{e}}{\rm{d}}{\rm{b}}{\rm{a}}{\rm{s}}{\rm{a}}{\rm{l}}{\rm{p}}{\rm{l}}{\rm{a}}{\rm{n}}{\rm{e}}}{E}_{{\rm{b}}{\rm{a}}{\rm{s}}{\rm{a}}{\rm{l}}{\rm{p}}{\rm{l}}{\rm{a}}{\rm{n}}{\rm{e}}}\). For each dopant, the lower the RSE for a particular edge, the more probably that edge is doped over the others. We note that in order to compare absolute stabilities of the dopants between each other for a given edge, one should extend the analysis to estimate appropriate bulk references. The current results are thus relevant only for comparing different edges for a given dopant.
The fact that the values in the table are negative confirms that from a thermodynamic perspective doping at the edges is systematically easier than doping at the basal plane. In general, our quantitative results are complex and there is a nontrivial dependence on the edge and on the dopant. In the experimental studies of nanoclusters by Kibsgaard et al.^{6}, the presence of dopants decreases the surface free energy of the Sedge. As a consequence, hexagonally shaped truncated triangles are obtained, instead of plain nanocluster triangles with Mo100 edges only. These hexagonally shaped structures contain both doped Sedges (S50 edge in the case of Co and Ni) and undoped Mo100 edges. According to Kibsgaard et al. there is a negative correlation between the relative length of the doped Sedge and the number of valence electrons of the dopant (Fe, Co, Ni and Cu). Although our results in Table 3 are for infinite layered systems and a lower doping level, they also show that doping takes place more likely at the S50 edge compared with the Mo100 edge (since RSEs for S50 are systematically lower than those for Mo100). Our values also support the assignment proposed in Ref.^{6} that the Fedoped Sedge is the S50 edge and not the S100 edge. If S100 edges were present, Fe doping would rather take place at the Mo100 edge (RSE for Mo100 is lower than that for S100).
The relevance of Table 3 is general and can be used as a guideline to analyze qualitatively and quantitatively other situations as well, especially the cases when the sulfiding atmosphere is changed^{16}. In the following we compare our values to the theoretical energetic calculations by Schweiger et al.^{27} for 100% Co and Nidoped nanoclusters (triangleshaped planar systems). The comparison is again semiquantitative, since our calculations are for extended layered systems and lower doping level. They predicted results for high (\({\mu }_{S}\ge \) −0.25 eV), intermediate (−1.1 eV \(\ge {\mu }_{S}\ge \) −0.25 eV) and low (\({\mu }_{S}\le \) −1.1 eV) chemical potential μ _{ s } of sulfur, corresponding to highly sulfiding, traditional sulfiding and highly reductive environments, respectively. However, the regime of low chemical potential of sulfur is less interesting, since they found a complete destabilization of the nanocluster, which led to the dopants’ segregation into separate phases and suggested this regime to be avoided.
First, for high chemical potential of sulfur Schweiger et al.^{27} predicted that both the Mo and Sedges can be doped. According to them in this case (i) Co is covered 100% by sulfur with 6fold coordination on both Mo and Sedges (in other words, the system contains Mo100 and S100 edges), and (ii) Ni has 5fold coordination on the Mo edge and 4fold coordination on the S edge. Their prediction (i) is consistent with the our RSEs of Table 3: the value for Mo100 (−2.88 eV) is close to S100 (−2.15 eV), but far from that of S50 or S75 (both close to about −4.3 eV). The closeness of the values suggests that both the Mo100 and S100 edges are likely to be simultaneously doped, but for example in the case of the Mo100 and S50 edges, the S50 edge would be preferably doped. Prediction (ii) corresponds to a situation slightly different from our case. In our case Ni has sixfold coordination both at the Mo50 and Mo100 edges and the doping is preferred at the S50 edge.
Second, for intermediate chemical potential of sulfur Schweiger et al. considered that pristine MoS_{2} particles have 50% sulfur coverage on both the edges (in other words, the system contains Mo50 and S50 edges). For Co doping, they found the nanoparticles to exhibit predominantly the Codoped S50 edge, which is consistent with our RSE for S50 being smaller than that for Mo50. For Ni doping, they reported the nanocluster to expose the Nidoped Mo0 edge and a small fraction of S50. This prediction is likewise in agreement with our values for Mo0 having a lower RSE (−5.33 eV) compared with that of S50 (−4.60 eV).
In general, the results bring new insight into the fundamental differences of how transition metals behave as dopants in MoS_{2}.
Effect of doping on H adsorption
The Gibbs free energy ΔG _{H} of adsorbed single hydrogen on the six edges is presented in Fig. 4, in which ΔG _{H} is given as a function of the distance from the dopant site (the numerical values are reported in Supplementary Information). Since H adsorbs in most of the cases on top of sulfur, the distance is indexed as the n th nearestneighbor sulfur position relative the dopant atom (the only exception is Mo0, for which index = 1 corresponds to adsorption on top of the bare metal atom). The values for the pristine edges are marked as horizontal lines (either one or two values are given depending on if more than one minimum is found). Examples of relaxed structures with adsorbed hydrogen are shown in Fig. 5. Some comparison values for ΔG _{H} are available from Wang et al.^{7} for Mo50 and S100, but too direct onetoone comparisons should be avoided, since they consider differential ΔG _{H} values, report results for 100% TM doping (compared to our 16.7%) and have a slightly different structural model and method to calculate the electronic structure.
At the Moedges, Mo0 can be driven toward optimal adsorption conditions with Fe, Co and Ni doping. This could be a relevant route especially in the case of Ni, which is predicted to be stabilized at the Mo0 edge of triangular nanoclusters at intermediate chemical potential of sulfur^{27}. Pristine Mo50 and Mo100 exhibit already as such \({\rm{\Delta }}{G}_{{\rm{H}}}\approx 0\) eV values for H adsorption. For Mo50 we find that doping with any of the four dopants (FeCu) worsens the adsorption energies, which is qualitatively the same conclusions as made by Wang et al. For Mo100 we find a neutral overall effect from Fe, Co and Cu, but from Ni worse ΔG _{H} values with strong site specificity.
The pristine S50 edge has the lower H adsorption energy close to neutral. Fe doping keeps the adsorption energies roughly unchanged, while the other dopants lead to worse values. The S75 edge can be enhanced by Fe and Ni, since the pristine edge adsorbs too strongly. The pristine S100 edge has adsorption free energy ~−0.5 eV and we predict no enhancement from doping. Finally, it is interesting that although substitutional Fe, Co and Ni at the Mo50, Mo100 and S100 edges all retain their sixfold coordination with respect to surrounding sulfurs, it is hard to find similarities between them in the ΔG _{H} values. Therefore, our results corroborate that it is challenging to predict the behavior of adsorption energies based only on the coordination structure of the dopant and the adsorbing sulfur. We observe, curiously, that the behavior of ΔG _{H} for Fe, Co and Ni is not smooth as a function of distance from the dopant atom (especially Mo50 and Mo100 in Fig. 4). This behavior can be related to the complex, possibly longrange relaxation with the interplay of the atomic and electronic degrees of freedom.
The charged undoped and Fedoped S100 edges show some variation in the H adsorption characteristics compared to the neutral charge state (see Table 4). For the undoped case, since \({\rm{\Delta }}{G}_{{\rm{H}}}\approx 0\) eV at the (−1) state, it is in principle possible that at small cathodic overpotentials there are beneficial charge state dependent effects for HER. In contrast, for the Fedoped edge, none of the adsorption energies at sites 1.−3. is significantly affected in the studied charge states.
At the actual HER operating conditions the steadystate hydrogen coverage depends on the exact reaction mechanisms and rates. In a detailed analysis ΔG _{H} should thus be evaluated at a systemspecific coverage of the surface^{11,13,25}. Differential adsorption free energies \({\rm{\Delta }}{G}_{{\rm{H}}}^{{\rm{d}}{\rm{i}}{\rm{f}}{\rm{f}}}\) have been considered in the literature to take this aspect into account^{4}. DFT calculations were used to estimate the relevant H coverages for the pristine^{25} and TMdoped edges^{7} in MoS_{2}. These calculations suggested both low and high coverages depending on the system, but specifically for Fe, Co, Ni and Cudoped Mo50 and for Fe and Codoped S100, a low H coverage was reported. Importantly, in the electrochemical characterization of the TM doped edgeterminated nanofilms in Ref.^{7} the Tafel slopes were found in the range (103–118) mV/decade, which is an experimental suggestion that the ratelimiting step in HER is the Volmer step. If this step determined completely the reaction rate, the relevant hydrogen coverage would be close to zero^{28}, and our low Hcoverage values would thus be the most representative for theoretical interpretation.
To gauge the effect of a larger H coverage we perform some additional tests for absolute and differential adsorption energies (ΔG _{H}, \({\rm{\Delta }}{G}_{{\rm{H}}}^{{\rm{d}}{\rm{i}}{\rm{f}}{\rm{f}}}\)) for pristine Mo50 at 0.5 monolayer H coverage and for pristine S100 at 1 monolayer coverage. These edges and coverages correspond to the systems studied by Wang et al. Our values for \({\rm{\Delta }}{G}_{{\rm{H}}}^{{\rm{d}}{\rm{i}}{\rm{f}}{\rm{f}}}\) are found in the range (0.0–0.2) eV and (0.3–0.5) eV for Mo50 and S100, respectively. In other words, pristine Mo50 remains close to optimal adsorption conditions even at higher H coverages, and for S100 the differential adsorption energy is found slightly positive due to stronger hydrogenhydrogen repulsion effects. Wang et al. report the corresponding \({\rm{\Delta }}{G}_{{\rm{H}}}^{{\rm{d}}{\rm{i}}{\rm{f}}{\rm{f}}}\) values 0.06 eV and −0.45 eV, with some discrepancy in the latter value to our results. The discrepancy may be due to the different choice of the supercell, which in our case is a periodically repeating system of vertically oriented layers. Šarić et al.^{19} reported recently \({\rm{\Delta }}{G}_{{\rm{H}}}^{{\rm{d}}{\rm{i}}{\rm{f}}{\rm{f}}}\) values for Mo50 in the case of nanocluster edges and find close to optimal condition at 0.5 monolayer coverage, in agreement with our finding.
In this framework the main question to answer is which kind of doping would improve hydrogen adsorption optimally toward efficient HER on edgecontaining MoS_{2} nanostructures. This question is answered in section Discussion.
Classification and regression analysis
For additional insight machine learning ensemble models (Random Forest, RF) were constructed for the classification and regression tasks for the full dataset containing both basal plane and edge results (see details in Methods) with ΔG _{H} as the target quantity. For the classification task, we tested both a tighter and a looser range, ±0.3 eV and ±0.5 eV, respectively. The aim is to obtain a model which predicts whether a given surface structure would lead to a ΔG _{H} value for H adsorption in the optimal window, while in regression the model predicts the numerical value of ΔG _{H}. The objective is to extract more information from the present systematically screened data and assess if a simple approach can be used for future predictions. In addition, the RF models give insight into the importance of the chosen features in explaining factors that affect ΔG _{H}. Table 5 reports the final RF models’ results. As explanatory features, we include (i) the type of the system (Type: basal plane, Mo0,…), (ii) number of electrons in the outermost valence shell (Nval), (iii) coordination number of the dopant (Coord, how many sulfurs surround the dopant atom before structural relaxation), and (iv) nearestneighbor position of the adsorbing sulfur with respect to the dopant atom (Nn). The training/test set split is 112/14 cases (see Supplementary Information).
The validation accuracy in classification is found to be about 78% for both the broader ±0.5 eV and the narrower ±0.3 eV window. The result for the test set is likely strongly dependent on the samples in the set and the crossvalidation score is a better metric for the model’s expected accuracy. For comparison, the crossvalidation accuracy for the logistic regression model for the ±0.5 eV window is only about 60%. The level reached by RF in terms of accuracy is very promising since no detailed geometrical features are encoded as input. The importance of features is robust irrespective of the chosen window and the data confirm that the type of the system (basal plane, Mo0,…) is a significant explaining factor for assessing if the ΔG _{H} value is in the chosen window. The number of outermost electrons (Nval) and the location of the adsorption site with respect to the dopant (Nn) are expectedly important factors. All these three factors are roughly equally important, while the coordination number of the dopant (Coord) has little relevance.
The performance of the regression model for the training and the test data is shown in Fig. 6. For predicting exact numerical values the model behaves moderately with 0.34 eV mean average error on test data. In the future, the models can be developed further by acquiring more data, encoding the true geometrical structure into features, and studying other algorithms for the learning task. The data set can be also extended to larger H concentrations to predict H coverage effects on ΔG _{H}.
Discussion
The results of this work including the output from the machine learning model confirm that the edge type is the most important factor that predicts if the doped system exhibits values in a range around \({\rm{\Delta }}{G}_{{\rm{H}}}=0\) eV at low H coverages. An equally important factor is the type of the dopant. Looking from a general perspective, our findings thus corroborate the importance of two of the proposed avenues of developing better MoS_{2} catalysts^{8}: nanostructuring (tailoring the material at the atomic scale toward the most suitable edge structures) and enhancing the internal activity (engineering the structure chemically by doping).
For the 2 H basal plane doping by Fe, Co, Ni and Cu, as well as by Pd and Pt, is predicted to improve without exception HER activity since all of them create favorable local sites for H adsorption in the range −0.35 eV \( < \,{\rm{\Delta }}{G}_{{\rm{H}}} < \,0.25\) eV (see Table 1 and summary in Table 6). The formation energy analysis of the charged systems showed that nonneutral charge states are not very likely for the Fe−, Co− and Nidoped basal plane at electron chemical potentials of interest. Moreover, the supercells in charge state (−1) have ΔG _{H} values similar to the neutral ones. The experimental findings by Deng et al.^{14} compare interestingly to our predictions. In their experiments the content of Pt, Co and Ni was constant, 1.7 wt% in the MoS_{2} samples, and for Pt they found that single atoms were uniformly dispersed in the plane. They found the Ptdoped basal plane experimentally the most active (our value ΔG _{H} = −0.24 eV, see Table 1), Codoped the second (−0.09 eV) and Nidoped the last (−0.33 eV). Our ΔG _{H} results are clearly in the correct window around 0 eV, but on a detailed level our prediction for Co being the best does not coincide with their finding. This is an interesting discrepancy since any DFT inaccuracies in the ΔG _{H} values are not expected to be so large to explain the behavior. In fact, the above finding is possible evidence that the prefactor in the expression for exchange current i _{0} may play a crucial role in determining the position of the maximum i _{0} with respect to ΔG _{H}. The prefactor depends on the ratios of the rate constants and can lead to a shift to more negative or positive values from \({\rm{\Delta }}{G}_{{\rm{H}}}=0\) eV^{12}. In the current case the results suggest maximum i _{0} to be found for \({\rm{\Delta }}{G}_{{\rm{H}}} < 0\) eV, which corresponds to low H coverages and the Volmer reaction being the ratedetermining step^{12}. This conclusion naturally assumes that there are no other explaining factors, such as additional structural defects, surface damage or nonuniform distribution of the dopants, that determine the order of the experimental HER efficiencies for Pt−, Co− and Nidoping.
For the basal plane systematic experimental attempts of doping should thus be continued to understand precisely both the structureproperty and the theoryexperiment relationship with respect to improving HER efficiency: (i) Exact order of HER efficiencies with respect to theoretical ΔG _{H} and the possible shifts of the maximum from the exact \({\rm{\Delta }}{G}_{{\rm{H}}}=0\) eV criterion and (ii) How many active sites each dopant creates. An interesting scenario would be to continue the experimental work by Deng et al.^{14} by comparing at least Co, Cu and Fe as dopants and carrying out doping at more than one concentration. The results of such an experiment would considerably help to elaborate the theoretical picture. It can be noted that in experiments some adverse additional effects may come into play: in a recent study it was interpreted that the basal plane becomes covered by Ni atoms or aggregates, and this was likely masking signals of dopantenhanced electrochemical activity^{20}.
For the Mo and Sedges two sets of results are summarized in Table 6 based on calculations in the neutral charge state of the supercell: (i) Dopants that bring the ΔG _{H} values of the pristine edge closer to 0 eV; (ii) Dopants that create adsorption sites with energies in the range −0.5 eV \( < \,{\rm{\Delta }}{G}_{{\rm{H}}}\, < \,0.5\) eV. Also the two relevant experimental systems are given: System A (with Mo100 and S50 edges) corresponds to nanoclusters by Kibsgaard et al.^{6} prepared by physical vapor deposition, and System B (with Mo50 and S100 edges) to vertically aligned nanofilms as discussed by Wang et al.^{7}. For system A’s activity, Kibsgaard et al. found Nidoping to be the best followed by Codoping, wheres Fedoped, Cudoped and pristine nanoclusters exhibited the lowest activity. According to them, doping takes place only at the S50 edge. For System B’s activity, Wang et al. concluded by DFT calculations that the S100 edge can be activated by doping.
We consider first System A with pristine Mo100 and doped S50 edges of the nanoparticles. As discussed earlier, our predictions agree with the preferential doping of S50 instead of Mo100. Using the exact criterion ΔG _{H} = 0 eV for analysing the increase in HER efficiency upon doping, our data is not in good accordance with the experimental findings. In our calculations both pristine Mo100 and S50 already have close to optimal ΔG _{H} values, which the doping can possibly only worsen. In fact, recent DFT simulations for the 100% Codoped Mo50 edge at the correct finite CoMoS nanoparticle geometry point to optimal differential adsorption energies^{19}. Therefore, our computational structures are probably too different from the nanoparticle geometry obtained by Kibsgaard et al. for reliable predictions. In a more general perspective on low dopant concentration effects at extended edges, Fig. 4 and Table 6 show that especially Fe, Co and Cu doping (if achievable) at Mo100, and Fe, Co and Ni doping at S50 create adsorption sites with energies in the range −0.5 eV \( < \,{\rm{\Delta }}{G}_{{\rm{H}}} < \) 0.5 eV.
By turning next to Wang et al.’s synthesized MoS_{2} (System B, Mo50 and S100 edges), our computational structures resemble closely the actual experimental ones (correct stacking of the layers and similar doping level). For these edges as discussed earlier (Table 3), doping can be expected at both the Mo50 and S100 edges. The exact criterion ΔG _{H} = 0 eV at our low H coverage case suggests that the activity at Mo50 cannot be improved, since the pristine edge already satisfies the optimal condition. The exact criterion ΔG _{H} = 0 eV cannot thus explain the experimental result that Fe, Co and Ni doping increases HER activity. To reconcile the discrepancy with the experiment, we recall from Fig. 4 that at the Mo50 edge Fe, Co, Ni and Cu create adsorption sites with −0.7 eV \( < \,{\rm{\Delta }}{G}_{{\rm{H}}} < \,0\) eV compared to the 0 eV value at the pristine edge. A similar argument as in the case of the basal plane can now be invoked by considering that the rate constants of the partial reactions of HER may have strongly differing prefactors^{12}. In the framework of our results, since experiments clearly indicate doping enhanced HER activity over the pristine system, we must conclude that at the Mo50 edge there is a possible shift of the maximum position of \({i}_{0}\) toward negative ΔG _{H} values. Such a shift corresponds to low H coverages and to Volmer reaction being the ratedetermining step, which is indeed suggested by the experimental Tafel slopes on these systems^{7}. According to Zeradjanin et al.^{12} a negative shift would reduce the achievable \({i}_{0}\) values.
Despite a large body of research on MoS_{2}, there is still a vast structural space to screen for optimal configurations for HER and their detailed reaction parameters. In particular, the search space expands when one includes different dopants and doping levels, various hydrogen coverages and any new type of nanostructure (e.g. finite clusters and terraced surfaces, lowdimensional systems). A comprehensive ab initio modeling would shed light on the reaction mechanisms of HER. However, these are major tasks especially considering the perspective of materials screening and one may need to resort to more approximative analyses. In addition to ΔG _{H}, many factors that affect the activity need to be considered in the detailed analysis, such as other atomistic descriptors, effects of watercatalyst interface, substrate, charging and oxidation states of the dopant atoms. Charge state analysis of the undoped S100 edge showed that cathodic overpotential may induce changes in the system by favoring at some values of electron chemical potential charge states for which H adsorption energy is closer to 0 eV than in the neutral state (see Table 4). However, for the Fedoped S100 edge a similar behavior was not found, which suggests that the charge effects are subtle and strongly case specific. It should be thus noted that the detailed charge state and spin multiplicity effects related to doped structures on H adsorption may not be appropriately represented by neutral charge state calculations. The question merits further studies especially in the case of MoS_{2} edges to further refine the oxidation states and the relevant ΔG _{H} values. Interesting questions remain also regarding the possible competing H adsorbing sites^{29} (e.g. one deep and one shallow) that can have detailed influence on the HER behavior. Such a more complete analysis of multiple local adsorption sites is beyond the scope of the present work, but have been discussed in our work by Kronberg et al.^{17} on siteselective adsorption.
Conclusions
We have performed a comprehensive analysis of transition metal doping at MoS_{2} surfaces in terms of structures, energetics and hydrogen adsorption characteristics in view of understanding the factors that affect the hydrogen evolution reaction. We study the basal plane and the differently sulfurterminated molybdenum (Mo0, Mo50, Mo100) and sulfur (S50, S75, S100) edges of the 2HMoS_{2} polytype. Fe, Co, Ni and Cu are considered as dopants at substitutional Mo sites. We use the Gibbs free energy ΔG _{H} of hydrogen adsorption to screen possible HER efficiency improvements upon doping and discuss the results with respect to experimental findings in the literature. For the edge structures, we study doping level of 16.7% and H coverage of 16.7% monolayers (single H adsorption on the edge segment of the supercell). We clarify the relative substitutional energies (RSEs) of the dopant atoms at different edges and find a large variation in the doping affinities. The edges are much easier to dope than the basal plane and the large variation suggests important implications about which edges will become effectively doped in synthesized MoS_{2} nanostructures. Structurewise, Fe, Co and Ni cause only minor or small local restructuring both at the basal plane and at the edges, whereas in some cases Cu leads to stronger deformations, which is likely connected to the occupancy of the localized d states.
At the basal plane, hydrogen adsorption energy on sulfur next to the Fe, Co, Ni and Cu dopant atoms is clearly lowered toward optimal adsorption condition (ΔG _{H} = 0 eV). Charging of the doped basal plane is found to be neither likely nor influence essentially the ΔG _{H} values. At the Mo and Sedges, doping affects the adsorption energies at the whole edge in a nontrivial way, leading either to beneficial or adverse overall effects. We discuss our findings in detail with respect to experimental cases and identify the potential and challenges in using precise ΔG _{H} values to interpret experimental improvements in efficiency. Charging of the edges is an additional degree of freedom that merits further studies. Charging may potentially modify the here reported neutral state H adsorption energies and thereby the HER activity as a function of cathodic overpotential. The present results illustrate that the HER efficiency depends critically and in a subtle way on the edge and dopant distribution in the synthesized nanostructures. We also investigate a machine learning model for predicting ΔG _{H} values from a minimal input of the system to bypass the computationally demanding DFT calculation. Already at the minimal level of modeling with a small dataset, the results show a promising accuracy for finding ΔG _{H} within a ±0.5 eV window.
The approaches of the present work to predict efficiency improvements in HER would be interesting to apply in the future to other types of materials such as MoC, MoSe_{2} and phosphides. In general, we anticipate that having a large collection of DFT data on hydrogen adsorption characteristics available and emerging automatized predictive algorithms at hand, the design and synthesis of platinum group free electrocatalytic materials will substantially speed up.
Methods
DFT calculations
The PBE functional^{30} was used in the density functional theory calculations including the spin polarization. All calculations were performed with the CP2K/Quickstep software^{31,32}. Van der Waals interactions were taken into account with the D3 method of Grimme et al. with BeckeJohnson damping (DFTD3(BJ))^{33,34}. Doublezeta plus polarization quality molecularly optimized basis sets (MOLOPTSRDZVP)^{35} and normconserving GoedeckerTeterHutter (GTH) pseudopotentials^{36,37,38} were used. The kinetic energy cutoff was 550 Ry and the cutoff of the reference grid 60 Ry. The Poisson equation for the electrostatic potential was solved assuming periodic boundary conditions. For modeling the basal plane the slab consisted of two horizontal layers with 6 × 6 MoS_{2} units in both the layers. The rectangular cell parameters were (l _{ x } = 15.70, l _{ y } = 21.75, l _{ z } = 26.64) Å. For the Mo and Sedges the slab model consisted of four vertically oriented layers with 6 × 3 MoS_{2} units in each layer and the cell parameters were (l _{ x } = 18.84, l _{ y } = 24.24, l _{ z } = 27.15) (see Supplementary Information for an example). These lattice parameters correspond to pristine systems and were optimized as described in Ref.^{17} In both the cases the structure repeated periodically in the x and y directions. A layer of about 9 Å vacuum was used in the nonrepeating z direction at both sides of the slab. In the calculations of doped systems with or without hydrogens the lattice parameters were fixed to the above values and the atomic positions were optimized using the BroydenFletcherGoldfarbShanno algorithm until the force on any atom was less than 0.023 eV/Å.
We calculated the Gibbs free energy of adsorbed hydrogen ΔG _{H} as
in which for \({\rm{\Delta }}{E}_{{\rm{ZPE}}}T{\rm{\Delta }}{S}_{{\rm{H}}}\), the zeropoint energy minus the entropic terms, we used the numerical value of 0.29 eV as estimated in ref.^{4} ΔE _{H} corresponds to the energy difference
where n is the number of hydrogen atoms, \({E}_{{{\rm{MoS}}}_{2}+n{\rm{H}}}\) the total energy of the system in which n hydrogens have adsorbed, \({E}_{{{\rm{MoS}}}_{2}}\) the total energy of the system before H adsorption, and \({E}_{{{\rm{H}}}_{2}}\) the total energy of molecular hydrogen in the gas phase.
We used the standard formation energy analysis to assess the relative stabilities of doped structures as a function of the charge state^{39,40}. Formation energy of a doped system in charge state q is given by
where E ^{q} is the total energy of the system in charge state q, E _{ v } the energy of the valence band maximum, μ _{ e } the electron chemical potential relative to E _{ v }, n _{ i } the number of atoms of type i and μ _{ i } the the corresponding chemical potential. For E _{ v } we used values calculated with neutral supercells.
Classification and regression model
We trained a machine learning (ML) ensemble model Random Forests^{41} (RF) to solve two tasks related to predicting the HER activity of a given system: (i) Classification task, which aims to predict if for a given structural input the resulting value of Gibbs free energy of hydrogen adsorption, ΔG _{H}, is within a chosen window. (ii) Regression task, which aims to predict the actual value of the target variable ΔG _{H}. The problem of predicting ΔG _{H} can be expected to be nonlinear (i.e., not necessarily any straightforward connection between structure and ΔG _{H} due to many factors, such as longrange rearrangement of the electronic structure induced by the dopant and the hydrogen). For this ML problem, RF model provides a robust method that is considered to avoid overfitting and has been successfully used in cheminformatics (see Ref.^{42} and references therein).
The setup for training the RF model and the selection of features is minimal for the purposes of this work. We work only with very basic features of the studied systems, which do not require DFT or MD simulations. Five features were initially considered: (i) The seven different possible types of the system (Type, i.e., basal, Mo0, Mo50,… as a categorical variable), (ii) atomic number (Z) of the dopant, (iii) number of electrons in the outermost valence shell (Nval) of the dopant, (iv) ideal coordination number of the dopant (Coord, i.e., how many sulfurs surround the dopant atom before relaxation) and (v) nearestneighbor position of the adsorbing sulfur site with respect to the position of the dopant (Nn). These features can be all considered to affect ΔG _{H} to various degree. However, since the features Z and Nval are strongly correlated, we found that a better accuracy could be obtained, as expected, by dropping Z altogether in the model.
The full dataset contains 126 cases in which hydrogen adsorbs on the basal plane or the edge of a doped or the pristine MoS_{2} (see Supplementary Information). The cases were randomly divided into a training set (112 cases) and a test set (14 cases). The RF classification model was trained and the parameters tested with the former set using internal crossvalidation with five folds (repeated with different partitions). In testing the parameters the \(\mathrm{0.5\ }{\rm{eV}}\le \,{\rm{\Delta }}{G}_{{\rm{H}}}\le \,\mathrm{0.5\ }{\rm{eV}}\) window was used. We employ Python’s RF estimators (classifier and regressor) as implemented in scikitlearn^{43}. In the final RF model two hundred trees were grown and for the other parameters the default values were used. The regression model and the classifier for the narrower window was trained with the same parameters. For the regression model we report the R ^{2} value on the training and the test set. The importance of features reported from the RF model is based on the Gini score for the classifier and on the drop in the sum squared error for the regressor.
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Acknowledgements
The work was supported by the European Union’s Horizon 2020 research and innovation programme (CritCat Project, grant agreement No. 686053) and the Academy of Finland through its Centres of Excellence Program (project no. 251748). We acknowledge the generous computing resources from CSC  IT Center for Scientific Computing including the Grand Challenge project CritCat. We thank Nico Holmberg for discussions.
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M.H. and K.L. conceived the project. R.K. provided the initial pristine structures and input files. M.H. performed the main DFT simulations, analysed the results and wrote the manuscript. K.L. and R.K. contributed to the interpretation of the results. All authors reviewed the manuscript.
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Hakala, M., Kronberg, R. & Laasonen, K. Hydrogen adsorption on doped MoS_{2} nanostructures. Sci Rep 7, 15243 (2017). https://doi.org/10.1038/s4159801715622z
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