## 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 Mo-sites. Clear benefits of doping the basal plane are found, whereas at the Mo- and S-edges complex modifications at the whole edge are observed. New insight into doping-enhanced 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 water-splitting 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 Δ*G*_{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 S-covered 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 2H-MoS_{2} is understood to be inactive^{4,13,17}. Several theoretical studies have been devoted to the pristine Mo and S-edges of MoS_{2} in terms of Δ*G*_{H}. Especially the Mo-edges are considered as active: the 100% S-covered Mo-edge of nanoclusters^{6} and the 50% S-covered Mo-edge in industrial-style catalysts^{18}. Regarding modification with doping, Kibsgaard *et al*.^{6}studied Fe, Co, Ni and Cu and obtained truncated triangle-shaped 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 S-edges) and thereby the activity. Šarić *et al*.^{19} studied by density functional theory (DFT) calculations the corresponding Co-doped nanoclusters. Escalera-Lopez *et al*.^{20} reported Ni-MoS_{2} hybrid nanoclusters which showed a roughly 3-fold increase in exchange current density compared with undoped nanoclusters. They associated the findings to Ni-doped Mo-edge and S-edge 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 Co-doped MoS_{2} nanosheets and attributed the finding to doping at the Mo and S edges. Wang *et al*.^{7} reported DFT calculations for Δ*G*_{H} of Mo- and S-edges for pristine and TM-doped (Fe, Co, Ni, Cu) MoS_{2}. They also synthesized and characterized doped vertically aligned nanofilms which expose alternatingly infinite Mo- and S-edges. Their results for the doped S-edge suggested enhanced catalytic activity as close to optimal (Δ*G*_{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 Cu-doped 2 H basal plane and Mo- and S-edges 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 Mo-*X* or S-*X*, 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 Δ*G*_{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 structure-property relationship, directly or indirectly via Δ*G*_{H}, i.e., [atomic and electronic structure of the surface] → Δ*G*_{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 Δ*G*_{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 rate-limiting HER step is the Volmer reaction, which corresponds to low H surface coverage. We will monitor Δ*G*_{H} not only in reference to the optimal condition (Δ*G*_{H} = 0 eV), but for description and classification consider also Δ*G*_{H}’s that are found within a range of values (such as −0.5 eV < Δ*G*_{H} < 0.5 eV). In this work we perform the calculations in electrically neutral supercells, but to assess the possible effects of non-neutral charge states, we also analyze explicitly two cases for an illustrative example: the doped basal plane and the undoped and Fe-doped S-100 edge in charge states +1, −1 and −2 of the supercell.