Hydrogen evolution on non-metal oxide catalysts

Water splitting to produce hydrogen gas, using renewably produced electricity (electrocatalysis) or by direct conversion of solar energy (photocatalysis), is a strategy that addresses key environmental and energy challenges. The overall water splitting reaction proceeds as two half reactions, namely the oxygen evolution reaction (OER) and hydrogen evolution reaction (HER), each of which require catalysts specifically tailored to maximize efficiency. The benchmark catalysts for the HER are noble metals. However, their expense and rarity makes them economically unfeasible for large-scale H2 production from water. Consequently, there are considerable efforts to find cheap, abundant materials that can efficiently catalyze the HER. Over the last decade, metal chalcogenides and phosphides have emerged as promising candidates for HER. In this review article, we discuss a selection of the multitude of studies and materials in these two classes of catalyst to give a flavor of the relevant developments and properties of these materials. In addition to the selection of catalyst materials, preparation and structuring are playing a strong role in enhancing HER and overcoming fundamental challenges. The role of modeling in the performance of HER catalysts is also discussed and we end with a short perspective on the key attributes of a good HER catalyst.


Introduction
The development of clean, renewable energy systems is of the utmost importance to address the issues of climate change and rising global energy demands. With a rapidly rising world population, the global primary energy-consumption rate is expected to increase from 17 TW in 2010 to 27 TW by 2040 [1]. Renewable energy sources, such as solar, wind, and wave energy, are intermittent and often location specific. These constraints necessitate an efficient means for storage and transport of excess energy produced at peak times for reintroduction to the grid where and as required. This excess energy is best stored in a form that is transportable and is itself clean.
Water splitting, to produce hydrogen gas (H 2 ), is an attractive prospect for a variety of reasons. H 2 , produced from water using renewably produced electricity, via electrocatalysis, or by direct conversion of solar energy, via photocatalysis or photoelectrochemistry, offers a zero emissions fuel. H 2 has a lower heating value (120 MJ kg −1 ) almost three times that of gasoline (44 MJ kg −1 ) [2] and the only by-product of its combustion or recombination with oxygen in a fuel cell is water.
To make H 2 fuel competitive, it must be produced at a cost of less than $4 kg −1 of H 2 [3,4]. If we consider using solar to produce hydrogen, the US Department of Energy reported that their solar to hydrogen (STH) efficiency target for realistic application of hydrogen production from photocatalytic water splitting is 5%, which would allow a cost of $4.6 kg −1 for hydrogen generation, which is very close to the $4 kg −1 target. Improvements in the efficiency of the hydrogen evolution reaction (HER) will substantially drive down the cost. In addition, the European Strategic Energy Technologies Roadmap points out that new and enhanced catalysts are required [5].
The water splitting reaction, whether electro-or photocatalytically driven, proceeds as two half reactions; the oxygen evolution reaction (OER) and the HER are oxidation and reduction reactions, respectively. The HER proceeds at the (photo)cathode, for which the most efficient materials are platinum-group metals, PGMs. PGMs are critical materials with low abundance on earth, suffering from geopolitical issues around sourcing and are therefore extremely expensive. These issues limit the large-scale implementation and economic viability of water splitting technologies. This context has spurred significant scientific efforts toward the development of cheap, earth-abundant materials that can efficiently catalyse the HER. The last 15 years has seen a surge of interest in metal chalcogenides (sulfide, selenides, and tellurides) and phosphides as catalysts for HER, showing high activity and good stability in acidic media and over multiple cycles. An account of recent progress in this endeavor, to give the interested reader a perspective on the properties and HER activity of these non-metal oxide materials, is the subject of the present review.

Fundamentals of hydrogen production from water splitting
The overall water splitting reaction may be expressed as follows [6]: The expressions which describe the two half reactions, OER and HER, depend on the conditions under which the reaction takes place. In neutral or alkaline conditions, the half reactions are [6,7] Water splitting can be achieved electrochemically, where the impetus for the reaction is provided by the potential bias between the electrodes. The ideal thermodynamic voltage required to drive water splitting is 1.23 V at 298 K and 1 atm [6]. However, in practice, due to losses, kinetic barriers and non-idealities in the catalysts, larger voltages are required. The difference between the thermodynamic and the applied potential is known as the overpotential and it has contributions arising from activation barriers at the anode and cathode surfaces, among other considerations. This renders the HER and, particularly, the OER sluggish and necessitates catalysts to reduce the anodic and cathodic activation barriers and increase reaction rates. For the remainder of this review, we restrict our focus to the HER, and for the most part, in acidic conditions as this enhances the HER activity [8,9]; the reverse is true for OER [10]. Moreover, the mechanism for HER in alkaline media is not as well understood [7]. However, progress in the development of HER catalysts that operate in alkaline media has been the subject of a number of recent reviews [11,12].
The HER proceeds at the cathode in a two-step process and there are two possible pathways: the Volmer-Tafel reaction and the Volmer-Heyrovsky reaction [13]. The Volmer step is common to both pathways and may be described as: Volmer : H + + e − → H ads This is called the 'discharge step' as an electron is transferred to a proton at the cathode surface, resulting in a surface bound H species, i.e. H ads . The second step involves desorption, and is described by the Tafel or Heyrovsky reactions: Tafel : H ads + H ads → H 2 Heyrovsky: H ads + H + + e − → H 2 The adsorption (discharge) step competes with the desorption steps and the optimal catalyst will strike a balance between these processes. This balance may be characterized by the Gibbs free energy of adsorption of a H atom (∆G H ) at the catalyst surface [14]. This quantity is widely accepted as a descriptor for the HER activity of a catalyst and may be computed from first principles via density functional theory (DFT) using: Figure 1. Free energy diagram for hydrogen evolution at various metal surfaces, with no applied potential, (U = 0). The modeled conditions correspond to standard temperature and pressure (STP: 300 K, 1 bar) and pH = 0. By definition, the free energy of H + + e − is the same as that of 1 /2 H2 at standard conditions. The free energies of adsorption are computed with DFT and corrected for entropy and zero point energies. Coverages of 1/4 are used. Reproduced with permission from [15], © 2005 ECS. where ∆E DFT , is the thermodynamic energy difference between the initial and final (H ads ) state, computed with DFT; ∆ZPE accounts for zero-point energy corrections; and the T∆S term contains entropic contributions. Large, positive ∆G H implies that adsorption is the difficult step whereas large, negative values of ∆G H indicate strong adsorption of hydrogen and therefore render the desorption step difficult. Thus, consistent with the Sabatier principle, the optimal value for ∆G H is close to 0 eV, and indeed, this is the case for the benchmark catalyst, Pt, as shown in figure 1 and compared to other metals.
There are measured quantities that can quantify the intrinsic HER activity of a material. One such parameter is the turnover frequency (TOF) of an active site, which, as the name suggests, is the number of reactions per unit time. The surface of a given catalyst material will present sites of different types, with variations that depend on factors including ion species, coordination, edge sites, and defects. In principle, each site will have an intrinsic activity or TOF, but this is not measurable by experimental means. Instead, practical approaches estimate the average per site TOF, based on measurements of total electrode activity and the number of active sites, or site density, SD [16,17]. Thus, the challenge in evaluating and comparing the intrinsic activities of materials for HER depends on reliable, standardized measurements of the SD.
Strategies for determining the number of catalytic sites include measurements of the specific catalyst surface area via electrochemical techniques, such as capacitance measurements, or gaseous adsorption methods, such as BET, among others [18]. These approaches are based on the reasonable assumption that the number of active sites will scale with the surface area. However, they are not applicable to all materials and their accuracy can be hindered by differences in the availability and accessibility of active sites between measurement and HER conditions. This, in turn, makes TOF a challenging parameter to evaluate conclusively, in a way that admits comparison between materials.
Thus, many researchers omit intrinsic activity measurements and opt instead for total electrode activities as the metric to assess the catalyst performance. The quantities used for the measurement of total electrode activity, described below, depend on multiple factors, including intrinsic activity, specific surface area, catalyst loading, substrate, and other effects [16]. This means that, for a given material, they can be optimized through electrode preparation and design. Hence, a material with high intrinsic activity may not perform as well as an intrinsically less active material when using total electrode metrics, due to sub-optimal electrode design.
Two quantities commonly used when comparing the total electrode activity of HER catalysts are the Tafel slope and the overpotential [7,9]. A Tafel plot relates the overpotential (η) to log 10 of the measured current density (j), via: The rate-limiting step of the HER is elucidated from the slope of the Tafel plot, represented by m in the above formula. Typically, values for the Tafel slope of 120, 30, and 40 mV dec −1 indicate that the Volmer, Tafel, and Heyrovsky steps, respectively, determine the rate of reaction [19]. A small Tafel slope is a desirable quality in a catalyst because this indicates a large change in the current density, in response to small increments in the overpotential.
Another important quantity which emerges from the Tafel plot is the exchange current density, j 0 , which is the current density at equilibrium conditions (η → 0). This quantifies the ability of a material to catalyze the HER and the best catalysts will exhibit high j 0 .
The overpotential, denoted η j , and measured relative to the standard/reversible/normal hydrogen electrode (SHE/RHE/NHE), is that potential required to produce a current density, j [16]. This value for the current density corresponds to the current per unit area of the electrode and is typically chosen as 10 mA cm −2 , by convention. This convention is used because this current density in a PEC cell corresponds to an STH efficiency of approximately 10% [9,20]. To avoid the complications of sign, only the magnitudes of η j will be quoted in this review. The area is simply the geometric area of the electrode and neglects intricacies of the electrode surface. Consequently, considerations such as surface nanostructuring and catalyst loadings are not taken into account.
For comparison purposes, we will refer to the Tafel slope, the overpotential, η j , and in some cases the exchange current density, j 0 , should these values be provided in the cited study. A detailed account of these quantities can be found in a review by Anantharaj and colleagues [21].
For stability tests, some common approaches are to compare the performance of the catalyst after ∼1000-20 000 voltammetry (CV) cycles or to measure variations in the overpotential (current density) required to maintain continuous performance at a fixed current density (overpotential) for N hours [22]. Measurements are referred to as potentiostatic/galvanostatic where the overpotential/current density are maintained constant. Details of these tests will also be included.
The quantities ∆G H and j 0 establish a crucial link between computational and experimental results, which can be illustrated using a 'volcano plot' [15]. The volcano plot in figure 2 shows experimentally measured j 0 for a variety of metals plotted against their computed values for ∆G H . The Pt-group metals are clustered at the top of the volcano, exhibiting high values for j 0 , and computed ∆G H close to 0 eV. Reactive metals, at which H adsorbs too strongly, appear on the left of the volcano, while the unreactive metals appear on the right hand side.
Equipped with these descriptors, we have criteria against which we can assess the candidacy of a material to catalyse the HER. In particular, computational methods allow for high throughput screening of HER catalysts. However, while ∆G H is a useful yardstick, other details of the HER should not be neglected. Such details include the catalyst surface area, availability of active sites, coverage effects and the nature of the real catalyst surface. For instance, H coverage can have a strong impact on the computed ∆G H and must be accounted for when performing simulations of potential HER catalysts [23,24]. As an example of the latter consideration, computing ∆G H for a pristine metal surface loses relevance should that surface form an oxide layer under operating conditions. Indeed, the issue of aligning computational models of catalyst surfaces with the physical systems, as they present under operating conditions, is profound. One consideration is the impact of the solvent, and computational approaches to describing the catalyst-electrolyte interface will be discussed in section 6 of this review. Moreover, the nature of the catalyst surface is dependent on its environment [25,26] and ex situ characterization can fall short in the description of crucial surface features which emerge during operation.
For example, an x-ray absorption fine structure spectroscopic study of a PtO/TiO 2 catalyst during water splitting revealed differences in the catalyst structure between the ex situ and operating conditions [27].
Having identified PtO as the active site, the authors reported an increased Pt-O bond length, from 2.07 to 2.13 Å, and a decrease in the coordination number, from 4 to 2.5, for the catalyst in operando, relative to the catalyst ex situ, both before and after use.
The changes induced during operation can be significant, leading to the assertion from some authors that the term 'pre-catalyst' is more appropriate when referring to the ex situ materials [28,29]. Despite this, it is often assumed that catalysts are stable under HER operating conditions and that in situ and operando analysis is more pertinent under harsh OER conditions [26]. While this assumption can be true, it should of course be the subject of rigorous testing. Deng and co-workers used operando Raman spectroscopy to confirm the consensus that S atoms are the active sites in the HER catalysis at amorphous MoS x [30]. In addition, spatially resolved, operando measurements performed with scanning electrochemical cell microscopy (SECCM) indicate increased HER activity at edge sites of MoS 2 [31][32][33].
Zhang et al used post-catalysis analysis of Co 2 P and reported that the composition of the electrode surface was largely unchanged in acidic conditions but degraded to hydroxides in alkaline conditions [34]. However, in situ x-ray absorption spectroscopy (XAS) measurements suggest that metallic cobalt is the active component for HER [35]. Starting from amorphous metallic Co nanoparticles in pH 7 potassium phosphate solution, the authors found that the metal/phosphate ratio varied with changes in the cathodic potential. Saadi et al used operando spectroscopic techniques to show that the active component in HER at CoP films in acidic conditions consisted of an amorphous material with Co in a near-zerovalent state and P in a reduced state [36]. Moreover, the authors reported considerable differences in the composition of the catalyst between ex situ and operando characterization.
Zhu et al used a combination of operando measurements, such as in situ XAS, Raman spectroscopy, and liquid-phase transmission electron microscopy to elucidate the nature of active sites of P-doped CoSe 2 in alkaline media under HER conditions [28]. The authors found that P-substitution facilitated the formation of defects, which exposed active, metallic Co sites for the HER.
Besides determining the true nature of the catalyst, operando measurements can be used to gain greater insight into the reaction pathway. Wang et al used operando nuclear magnetic resonance spectroscopy to elucidate the mechanism for the HER at anatase TiO 2 decorated with Pd nanoparticles [37]. Their study, which was supported by DFT calculations, yielded a detailed description of the key proton transfer steps involved in the HER, using methanol as a sacrificial hole scavenger.
In situ and operando spectroscopies continue to gain considerable traction in the study of catalysis and developments in this area have been the subject of recent reviews [25,26]. These considerations should serve to embolden rather than dishearten. As the tools at our disposal increase the breadth of our understanding, so too will they inform refined computational models and fabrication methods for the rational design of new photocatalyst materials.
In this review, we describe non-oxide catalysts that show significant promise in the search for cheap, abundant, and efficient alternatives to noble metals for the HER. This is not an exhaustive review of all materials, but instead we focus on a selection of key catalyst materials and results that best highlight advances in this field, particularly from the perspective of how composition and structure can be used to promote the HER. We also include some results from DFT and machine learning that have been employed in deepening the understanding of HER materials.
As part of this discussion, we note that while metal oxides are perhaps the most widely studied class of materials for photocatalytic applications, e.g. TiO 2 or Fe 2 O 3 , they are unsuitable as HER catalysts as hydrogen binds too strongly to oxygen sites in the surface, thereby forming an unreactive hydroxyl layer. These catalysts, therefore, need a co-catalyst, such as Pt, or a sacrificial agent to consume electrons. Thus, the focus for HER is on non-noble transition metals and their compounds with elements from groups 13-16 of the periodic table. In this regard, we pay particular attention to the chalcogenides (S, Se, and Te) and phosphides, which have recently emerged as interesting candidates for HER catalysts.

Hydrogen evolution reactions on metal chalcogenides
Metal chalcogenides, particularly layered transition metal dichalcogenides (TMDs) containing sulfur or selenium, have generated great interest for their catalytic activity toward HER. As they are useful for hydrodesulfurization (HDS) chemistry [38,39], they are also of great interest for HER given that the key reaction steps are similar between both chemistries. Perhaps the most widely studied of these materials is MoS 2 . While bulk MoS 2 [7,40] and the basal planes [41] were found to be inactive, other studies have examined the catalytic performance of MoS 2 supported on substrates [42,43]. MoS 2 dispersed at an NiS x surface promoted HER and inhibited degradation of the catalyst; the MoS 2 pigmented catalysts operated with overpotentials 50-100 mV below that recorded for bare NiS x [42]. MoS 2 supported on silica also exhibited good hydrogen evolution properties [43]. Drawing inspiration from these studies and noting  similarities with the active site of nitrogenase, an enzyme which efficiently catalyzes the HER, Heinemann and colleagues presented a now widely cited computational investigation of MoS 2 as a HER catalyst [44]. This paper can be considered as the beginning of the high level of activity in discovering sulfides for the HER. The authors identified low-coordinated S-sites of the MoS 2 edge as active sites with ∆G H comparable to that computed for Pt, as shown in figure 3. WS 2 has the same layered structure as MoS 2 , and has also been studied for its hydrogen evolution properties and corrosion resistance [45]. Silica-supported WS 2 was shown to be an active and stable catalyst for HER; 0.2 mg of the WS 2 /SiO 2 catalyst yielded in excess of 0.2 ml h −1 , with a small drop in performance after 2 h [45]. Conversely, the Pt/SiO 2 catalyst produced 0.1 ml in the first hour, but only 0.04 ml in the second hour. A combined experimental and computational study of MoS 2 and WS 2 nanoparticles found WS 2 to be almost as active as MoS 2 [46]. Tafel slopes of 120 mV dec −1 and 135 mV dec −1 were recorded for MoS 2 and WS 2 catalysts, respectively. The authors also reported promotion of HER after incorporation of Co into the S-edges of both materials. The Tafel slope decreased to 101 mV dec −1 and 132 mV dec −1 for Co-promoted MoS 2 and WS 2 . The computational results of this paper are summarized in table 1.
A subsequent study of MoS 2 and WS 2 by the same group adopted a more thorough approach and examined the effects of S-and H-coverage [47]. Consequently, the computational results for ∆G H were revised and these results are also presented in table 1. The authors found that H binding was too strong at the S-edge of MoS 2 , even at the highest possible coverage. They concluded that active sites for HER were present at the Mo-terminated edge. Conversely, H adsorption at both W-and S-terminated edges of WS 2 was close to thermoneutral.
Selenium is one period below sulfur in the chalcogenides, and consequently has similar chemical properties. A combination of these similarities and some important distinctions have generated significant interest in selenium containing materials for the HER. These distinctions include: (1) more pronounced metallic character with respect to sulfur, suggesting enhanced conductivity; (2) a larger ionic radius for Se, and (3) lower ionization energy relative to S [7]. The high lying p state of the anion in these non-oxide materials, where the energy of the np states is in the order O 2p < S 3p < Se 4p means that materials with S and Se show a more metallic character compared to oxides and this is important for promoting the optimum adsorption free energy of hydrogen.
A DFT study of the active sites of MoSe 2 and WSe 2 showed that, similar to their sulfide analogues, the basal planes of these materials are inert, with the active sites being present along the edges [47]. Some results from this work are included in table 1. A systematic computational study of layered TMDs of the form MX 2 (M = Ti, V, Nb, Ta, Mo, W, Pd, Pt; X = S, Se) identified some key trends with implications for practical implementation of such materials as HER catalysts [48]. The authors assessed the HER activity and stability of these materials based on computed values of ∆G H and ∆G HX , respectively. The latter quantity is the free energy of HX adsorption and an inverse relationship exists between H and HX binding. This implies that optimizing the HER activity can have detrimental effects on the stability of the catalyst. The authors considered ranges of chalcogen and hydrogen coverages, which can vary in a real system depending on the operating conditions. In general, hydrogen binding weakened with increasing hydrogen coverage. Moreover, through nudged elastic band (NEB) calculations, the authors concluded that the Volmer-Heyrovsky pathway is most likely for these materials, as prohibitively high activation barriers impede the Tafel step.
A study comparing the catalytic performance of electrodes consisting of porous arrays of MX 2 nanosheets (M = Mo, W; X = S, Se, Te), found a clear hierarchy in activity, following: selenides > sulfides > tellurides. MoSe 2 out-performed all other materials, which was attributed, in part, to a low Tafel slope of 77 mV dec −1 . The authors also postulated that diselenide sites have a higher intrinsic activity relative to equivalent disulfide and ditelluride sites.
Common among these studies that aim to use computational methods and experiment, to determine the origin of the activity of TMDs, is the identification of edges as active sites [49][50][51]. Computationally, this conclusion is drawn from the comparison of ∆G H for edge and basal sites. In one experiment, samples of MoS 2 nanoparticles of different sizes on Au (111) were prepared and the electrocatalytic activity correlated linearly with the number of MoS 2 edge sites [51].
Bentley and colleagues implemented SECCM to create spatially resolved measurements of the HER activity at basal and edge sites of bulk MoS 2 [32]. Combining SECCM data with topographical information from scanning electron microscopy (SEM) and atomic force microscopy (AFM), showed enhanced activity at defects, steps, and crevices. The authors followed up this study with additional measurements of HER at MoS 2 , with improved temporal and spatial resolution [33]. The results indicated a uniform activity in the basal plane and that the enhanced activity at the edges scaled with the step height.
These results indicate the necessity to engineer TMD-based catalysts that maximize the exposure of edge sites. However, strategies also exist for activating the basal plane. These and other considerations will be discussed in what follows.

Engineering edge sites
Nanoparticles are characterized by a high specific surface area and an abundance of low-coordinated surface sites and therefore, nanostructuring of TMDs is an approach to enhance the HER activity. TMDs consist of 2D layers that interact via van der Waals forces and various methods exist for exfoliating these layers to produce nanosheets or nanoflakes [52][53][54]. One such method involves applying adhesive tape to bulk TMD to peel off layers before transfer to a substrate material. This mechanical exfoliation technique was first employed by Novoselov and colleagues to isolate 2D single layers of graphene [55]. This method has since been used to deposit single-and few-layer nanosheets of TMDs onto SiO 2 coated Si substrates [56]. Another technique, described as similar to 'drawing chalk on a blackboard' , was employed by Novoselov et al to transfer single layers of BN, graphite, and TMDs to an oxidized silicon wafer [57]. While this approach is low-cost, it does not afford precise control or uniformity of the exfoliated layers and is further hindered by a low yield.
Exfoliation of TMDs has also been achieved by irradiation with a high-power femtosecond laser [58]. The resulting flakes were a few layers thick with feature sizes of 100-200 nm, see figure 4.
Exfoliation of layers from bulk materials can also be achieved by various methods applied to suspensions of bulk powders in solvents [52,53,61]. These techniques include sonication, whereby the crystals suspended in an appropriate solvent are broken apart by exposure to ultrasonic waves. This approach has been used successfully to isolate flakes of layered materials such as TMDs and BN [62]. Sonication can be combined with intercalation, wherein molecules or ionic species are incorporated into the space between layers, weakening interlayer interaction and increasing layer spacing.
The preceding methods are examples of top-down techniques, beginning from bulk materials and deconstructing them by one means or another to obtain nanostructures. Bottom-up strategies involve building layers of materials on a substrate from their constituent parts. Chemical vapor deposition (CVD) is  an example of a bottom-up technique. In CVD, a heated substrate is exposed to volatile chemical precursors that react to deposit a layer of desired material. Tuning of operational parameters, such as temperature, the composition of the substrate and precursors, allows for control of the topography of the deposited material [63]. Nanotubes and fullerene-like nanoparticles of MoS 2 were obtained via reacting MoO 3 and S in an argon atmosphere [64].
Dendritic monolayers of MoS 2 were deposited on SrTiO 3 and subsequently transferred intact to Au foil [65]. The fractal-like geometry of these samples expose a wealth of active sites for HER and Tafel slopes of 73-85 mV dec −1 were reported. This compares favorably with values of 140-145 mV dec −1 measured for multi-layer MoS 2 grown on glassy carbon electrodes. The authors reported exchange current densities of 5-25 µA cm −2 , depending on preparation temperature, and durability tests showed a reproducible polarization plot after 1000 voltammetry cycles. Shi and coworkers deposited hexagonal TaS 2 flakes on Au foil via CVD [66]. The authors measured Tafel slopes in the range 33-42 mV dec −1 for 2H-TaS 2 /Au samples, which compare with 31 mV dec −1 for Pt. The overpotentials, η 10 , of the 2H-TaS 2 samples were between 65 and 150 mV and the exchange current densities were 100-179 µA cm −2 .
Hydrothermal and solvothermal synthesis are other bottom-up techniques, which for TMDs, typically involve the reaction of transition metal salts in aqueous/organic solutions at moderate to high temperatures (80 • C-240 • C) [52,67,68]. These methods allow for considerable control over the product by tuning preparation parameters, and morphologies such as nanorods, nanosheets, and nanoflowers of MoS 2 have been achieved in this way [67]. Such techniques have been used to grow MoS 2 on TiO 2 [69,70] and carbon [71] nanotubes and reduced graphene oxide (rGO) [72]. Tafel slopes of 42 and 38 mV dec −1 and η 10 of 98 and 95 mV were measured for MoS 2 grown on TiO 2 and Si doped TiO 2 nanotubes, respectively [69]. Li and colleagues measured a slope of 41 mV dec −1 for MoS 2 on rGO [72]. The value for η 10 was ∼150 mV and durability tests indicated negligible losses in HER current after 1000 cycles.
These are but a few of the techniques which have been implemented to deposit nanostructured TMDs on substrates and a comprehensive overview of other methods is provided in ref. [52]. A common feature of these techniques is that the nanostructured TMD lies flat on the substrate surface [7,59,60] which minimizes the surface energy [73]. One consequence is that this orientation exposes the inactive basal plane. Secondly, electrons must transfer from the substrate to the active sites of the outermost layer, and in doing so, overcome the interlayer potential barrier; see top panels in figure 5.
He and coworkers addressed this issue by constructing edge-on MoS 2 /TiO 2 heterostructures [60]. This was achieved in a two-step process wherein a hydrothermal preparation of MoO 2 on TiO 2 was followed by sulfurization by CVD and a schematic of this process is shown in the bottom half of figure 5. The core idea of this approach is that sulfurization is faster parallel to the basal plane, owing to the weak inter-layer interaction. A similar effect was achieved for MoS 2 on a carbon fiber paper (CFP) substrate by Hu et al using a microwave hydrothermal method [74]. By altering the reaction time, the researchers could control whether the exposed edges of MoS 2 were stepped or flat with respect to each other. The authors measured Tafel slopes of 121, 69, and 59 mV dec −1 for samples with randomly oriented, flat edged, and stepped edge MoS 2 , indicating that stepped edges promote HER activity. Stepped edge samples required η 10 of 104 mV and exhibited an exchange current density of 200 µA cm −2 . The cathodic overpotential to maintain 10 mA cm −2 decreased from 104 to 95 mV after 24 h, indicating good stability for the stepped edge MoS 2 catalyst.
CoS 2 was the subject of a combined theoretical and experimental study [75]. The group reported on the controlled fabrication of hierarchically mesoporous CoS 2 microspheres on CFP. The microspheres are terminated by vertical arrays of CoS 2 sheets with an abundance of exposed sulfur sites. The authors reported a Tafel slope of 67 mV dec −1 and a low overpotential of 90 mV at 10 mA cm −2 . DFT analysis of free energies of hydrogen adsorption at different CoS 2 facets, at a coverage of 1/8, monolayer showed computed values for ∆G H in the range 0.04-0.06 eV.
Wang et al reported Tafel slopes of 60 and 77 mV dec −1 for MoSe 2 and WSe 2 films grown vertically on a CFP substrate [73]. The authors concluded that the curvature and roughness of the substrate enhanced the exposure of active sites. This lead to values for η 10 of 250 and 300 mV for MoSe 2 and WSe 2 on CFP, respectively. Moreover, the performance of both catalysts improved slightly after 15 000 cycles at 50 mV s −1 .

Activating the basal plane
Before describing approaches to increasing the activity of basal plane of TMDs we first note that these materials exist predominantly in two polymorphs, denoted 2H and 1T. The 2H phase exhibits tetrahedral coordination while the 1T phase is characterized by octahedral coordination, as shown in figure 6. For bulk group 6 TMDs, such as MoS 2 and WS 2 , the 2H phase is thermodynamically favored over the metastable 1T phase, although this is not true for all TMDs [48]. The electronic properties of these materials depend on the structural geometry. For example, the basal plane of MoS 2 is semiconducting in the 2H phase and becomes metallic in the 1T phase. In addition to enhanced conductivity, the 1T phase has active sites for HER in the basal plane [7,48,76,77]. This was deduced from measurements of the activities of 2H-and 1T-MoS 2 samples after oxidation; the activity of 2H-MoS 2 decreased after oxidation of edge sites whereas the activity of 1T-MoS 2 was undiminished, implying the presence of active sites in the basal plane.
This suggests a strategy for promoting the activity of TMDs might be to promote their metallic phase. The 2H-1T phase transition has been shown to occur in samples of MoS 2 upon exfoliation via Li intercalation [16,76,77]. Tafel slopes of 40 [76] and 43 [77] mV dec −1 were measured for 1T-MoS 2 samples prepared in this manner. As mentioned above, metallic 2H-TaS 2 deposited on Au foil (Tafel slopes: 33-42 mV dec −1 ) showed HER activity comparable to that of Pt (31 mV dec −1 ) [66], and similar results were found for 1T-MoS 2 decorating TiO 2 nanotubes (38-42 mV dec −1 ) [69]. Voiry and colleagues also used Li intercalation to isolate metallic 1T-WS 2 and obtained a Tafel slope of 60 mV dec −1 , compared with 110 mV dec −1 for 2H-WS 2 [79]. Durability tests entailed 10 000 cycles and monitoring of current density over 100 h of continuous operation at −0.3 V and the results indicated a stable performance with no loss of 1T phase.
Using hydrothermal synthesis and varying the temperature and the ratio of reactants, Yin and coworkers isolated 1T-MoSe 2 nanosheets for which they measured a Tafel slope of 52 mV dec −1 and η 10 of 152 mV [80]. Formation of 1T phase was achieved during synthesis with a large excess of the NaBH 4 reductant. The catalyst stability was assessed by cycling the electrodes 1000 times, which showed negligible losses in current density. Kong and coworkers produced a nanoparticulate CoSe 2 film on CFP via selenization of a cobalt oxide layer with Se vapor [81]. The resulting electrode consisted of CoSe 2 nanoparticles with dimensions of tens of nanometers. X-ray diffraction (XRD) analysis revealed the presence of predominantly cubic pyrite phase with some evidence of marcasite and amorphous phases. The metallic property of CoSe 2 contributed to the high HER activity, as shown by a Tafel slope of 40 mV dec −1 and η 10 of 137 mV. At an overpotential of 155 mV, the current density remained stable at ∼20 mA cm −2 for over 60 h.
It is also possible to activate the basal plane of semiconducting 2H-MoS 2 . This was first achieved by Li and colleagues through combinations of S-vacancies and strain, see figure 7 [82]. 2H-MoS 2 flakes were grown by CVD on a Si/SiO 2 wafer before transfer to a gold substrate and S-vacancies were introduced by exposure to argon plasma. The combination of S-vacancies and strain could be tuned such that the optimal condition of ∆G H = 0eV was satisfied. The authors identified S-vacancies as active sites and DFT calculations revealed defect gap states that could be shifted toward the Fermi level by application of strain, which would promote the adsorption of hydrogen. Experimentally, this manifested as measured Tafel slopes of 60 mV dec −1 for the strained sample with S-vacancies; a value of 98 mV dec −1 was measured for the sample without strain or vacancies.
The role of gap states in the HER activity was also investigated by Li and coworkers in their study of MoS 2 films grown on a Mo substrate [83]. A combination of S-vacancies and Pt-doping introduces gap states, which promote the HER activity. The authors reported a Tafel slope of 38 mV dec −1 for the Pt/MoS 2 /Mo heterostructure, which is compared with 68 mV dec −1 for MoS 2 /Mo. Values for η 10 of 58 and 198 mV were recorded for Pt/MoS 2 /Mo and MoS 2 /Mo, respectively, further highlighting a crucial role for Pt in the catalytic activity. Moreover, the authors found no decrease in activities after 1000 CV cycles.
A comprehensive study of active sites of MoS 2 reported a maximum in catalytic activity for S-vacancy concentrations in the range of 7%-10% [84]. The crystalline quality near the vacancy also strongly affected the activity of the vacancy. Dong and colleagues described morphological control of MoS 2 flakes prepared via CVD, and as a consequence of this method, control of the abundance of S-vacancies [85]. The authors reported enhanced HER activity for hexagonal MoS 2 flakes on glassy carbon with a Tafel slope of 53 mV dec −1 ; the hexagonal samples also exhibited an exchange current density of 91 µA cm −2 and η 10 of 104 mV. After a slight improvement in performance after 3000 cycles, the performance remained stable from 3000 to 6000 cycles. S-vacancies have also been introduced to the basal plane of MoS 2 by electrochemical desulfurization as a viable alternative to Ar plasma exposure [86]. Desulfurization decreased the Tafel slopes from 151 to 102 mV dec −1 (after iR correction). Stability was assessed over 8 h, over which the current remained the stable.
Gao et al reported a method for heterostructuring defect-rich MoS 2 nanoflakes on exfoliated MoS 2 /WS 2 scaffolds, via a hydrothermal approach [87] and measured Tafel slopes of 81 and 73 mV dec −1 for the flakes on MoS 2 and WS 2 , respectively. There was negligible variation in polarization curves after 3000 cycles. Geng and colleagues approached activating the basal plane by fabricating porous MoS 2 [88]. This was achieved by preparing Al-doped MoS 2 , followed by submersion in NaOH solution to remove Al. The resulting porous MoS 2 yielded a Tafel slope of 62 mV dec −1 . The measured η 10 was 201 mV and no differences were observed in polarization curves before and after 3000 CV cycles. A systematic study of the impact of phase, edge sites and S-vacancies on the HER activity concluded that phase is the major determining factor [89]. The 1T-MoS 2 samples consistently outperformed the 2H phase. Mesoporous 1T-MoS 2 , prepared via liquid-ammonia-assisted lithiation and with an abundance of S-vacancies yielded the best activity with a Tafel slope of 43 mV dec −1 and η 10 of 154 mV. The current density yielded by this sample decreased by <7% after 1000 cycles.

Amorphous TMDs
Amorphous MoS x has also been investigated as a HER catalyst, with reports of activities rivalling those of 1T-MoS 2 [90,91]. One advantage of amorphous MoS x is the ease and economy with which it can be synthesized; simple, wet chemical techniques, requiring no high-temperature processing, have been reported in the literature [92,93]. Merki et al prepared amorphous MoS 2 films using electro-polymerization procedures and reported high current densities at low overpotentials with a Tafel slope of 40 mV dec −1 and η 15 of 200 mV [90].
A study by Wu and colleagues attributed the high activity of amorphous MoS 2 to similarities with 1T-MoS 2 in terms of bonding character and electronic structure [91]. The authors identified a short Mo-Mo bond, common to 1T-phase and amorphous samples, as a crucial feature for the HER activity. Tafel slopes of 65, 58, and 42 mV dec −1 were measured for 2H, 1T-and amorphous MoS 2 , respectively. Wang et al fabricated copolymer hybrid films consisting of polypyrrole and amorphous MoS x (x ∼ 5) [94]. This was achieved via electrochemical copolymerization of pyrrole and (NH 4 ) 2 MoS 4 and the result exhibited a HER activity comparable to that of commercial Pt/C catalysts with a Tafel slope of 29 mV dec −1 ; however, a clear decrease in current was observed after 5000 s at a potential of −0.05 V (vs. RHE).
A strategy to further enhance the HER activity of amorphous MoS x via doping with first row transition metals was investigated by Merki et al [95]. The Tafel slopes for all samples of M-MoS 3 (M=Mn, Fe, Co, Ni, Cu, Zn) were in the range 39-43 mV dec −1 . The authors found that Fe-, Co-, and Ni-doping promoted growth of the MoS 3 film, resulting in higher surface area and catalyst loading, and consequently, enhanced HER activity. However, the authors also concluded that the improved activity was not attributable solely to morphological effects and that the dopants increased the intrinsic catalytic activity. The impact on activity was pH-dependent, with Fe-and Co-doping performing best under acidic and neutral conditions, respectively.
The use of MoS x -coated carbon electrodes in microbial electrolysis cells (MECs) under operating conditions was investigated by Kokko and colleagues [96]. MECs can renewably produce H 2 while simultaneously treating wastewater. Three different carbon supports were considered: activated carbon cloth, electrospun carbon, and buckypaper (BP); in combination with three deposition methods: electrodeposition, drop coating, and impregnation followed by heat treatment. The best performing MoS x electrodes exhibited onset potentials only slightly higher than that of a platinum electrode and Tafel slopes were in the range of 40-100 mV dec −1 . The values for η 10 were in the range 130-250 mV. Importantly, the catalytic efficiency improved over time whereas the Pt electrode was slowly deactivated. This latter result is common for amorphous MoS x electrodes and is attributed to structural changes induced under HER conditions.
Amorphous MoSe x has also been reported as an efficient catalyst for the HER [97]. To obtain amorphous MoSe 3 , Nguyen et al employed the same strategy as described by Benck and coworkers to prepare MoS 3 [93]. While the as-prepared amorphous MoSe 3 nanopowder was inactive, exposure to HER conditions rendered the catalyst active. This was attributed to the development of structures with composition close to that of MoSe 2 . The active catalytic material was more robust than its MoS x analogue and operated in a wider range of pH solutions. In a pH 0 electrolyte MoSe x displayed a Tafel slope of 60 mV dec −1 and η 10 of 270 mV.
Amorphous CoSe x films were deposited electrochemically onto planar Ti supports under ambient conditions [98]. The films were mesoporous with pore sizes estimated to be ∼20 nm in diameter and exhibited a Tafel slope of 60 mV dec −1 and η 10 of 135 mV. The catalyst performance remained stable after >16 h of operation at −10 mA cm −2 .

Heterostructuring
Heterostructuring consists of interfacing two or more materials of different composition or phase. In this way, it is possible to combine the qualities of each phase and moreover, capitalize on novel properties which emerge at the interface.
Wang and coworkers grew MoS 2 on CoS 2 decorated carbon cloth (MoS 2 /CoS 2 /CC) and investigated the activity of this sandwich-structured electrode for HER [99]. The CoS 2 was deposited on the carbon cloth (CC) electrochemically prior to growth of MoS 2 via a hydrothermal method. The interplay between the MoS 2 and CoS 2 phases was shown to play a crucial role in both the HER activity and stability of the electrode. This was established by comparing the performance of MoS 2 /CoS 2 /CC, MoS 2 /CC, and CoS 2 /CC, for which Tafel slopes of 37, 50, and 60 mV dec −1 were measured, respectively. MoS 2 /CoS 2 /CC exhibited η 10 of 118 mV and showed no decay in performance after 4000 CV cycles. Further stability tests, conducted via continuous HER at a constant overpotential, indicated a decrease in activity to 80% of the initial current density in the first 60 h, after which the activity plateaued and remained at 80% up to 83 h. The enhanced activity was attributed to optimal adsorption of hydrogen at interfacial S-sites; strong bonding interactions between MoS 2 and CoS 2 were the origin of the superior stability, compared to the individual materials.
In their 2016 paper [100], Staszak-Jirkovský and colleagues established that, while amorphous CoS x is more active than amorphous MoS x , as measured by HER activity in acidic and alkaline media, the latter is more stable, and this observation informed the rational design of a low-cost CoMoS x chalcogel catalyst. The resulting catalyst consisted of Mo 3 S 13 clusters interconnected by CoS 8 octahedra capped by polysulfide oligomers in a compact structure and was highly active and stable, irrespective of pH. In alkaline media there was a large difference in activity, following: MoS x ≪ CoMoS x ≪ CoS x ; whereas, in acid solutions the  differences were less significant, with MoS x < CoS x ≤ CoMoS x , as shown in figure 8. Moreover, the authors noted that less active crystalline MoS 2 and CoS 2 were more stable than their amorphous analogues by a factor of 10, which implies an important role for the density of defects in the relationship between activity and stability.
Zhang and coworkers prepared polymorphic CoSe 2 with mixed orthorhombic and cubic phases by calcining amorphous CoSe x , fabricated by electrodeposition [101]. The authors described polymorphic CoSe 2 (p-CoSe2) as a highly active HER catalyst with activities exceeding those of amorphous CoS x , cubic CoSe 2 and CoSe. The phase and morphology of the samples were tuned via the calcination temperature. At 300 • C the sample presented as mixed orthorhombic and cubic phases. Calcination at 450 • C and 600 • C produced cubic CoSe 2 (c-CoSe 2 ) and CoSe, respectively. The measured Tafel slopes were 38, 31, 39, and 55 mV dec −1 for CoSe x , p-CoSe 2 , c-CoSe 2 , and CoSe, respectively. The corresponding values for η 10 were 180, 150, 200, and 270 mV, indicating that the polymorphic sample had the best activity. The value of η 10 was found to increase by 8 mV for p-CoSe 2 after 40 h of galvanostatic measurement.

Ternary TMDs
Ternary TMDs (TTMDs) have also been considered in the pursuit for active and stable HER catalysts [102]. TTMDs have the general formula M 1 z M 2 1−z X 2 or MX 1 2z X 2 2(1−z) , where M 1 , M 2 and M are transition metals (M 1 ̸ = M 2 ) and X 1 , X 2 and X = S, Se or Te (X 1 ̸ = X 2 ). The properties of TTMDs can be tuned by altering the composition and the molar ratio, z.
Kiran and coworkers found that MoS 2z Se 2(1-z) alloys possessed higher HER activity compared to MoS 2 and MoSe 2 [103]. The authors systematically studied the structure-activity relationship by varying the composition and found that MoS 1 Se 1 presented the highest HER activity among the catalysts under study.  The alloys were prepared via a high temperature solid-state reaction technique followed by exfoliation to obtain catalysts of a few layers. The authors measured Tafel slopes in the range 50-60 mV dec −1 , compared to 96 and 95 mV dec −1 for MoS 2 and MoSe 2 , respectively, and attributed the higher activity of MoSSe to improved electronic conductivity. Exchange current densities, j 0 , of 320, 36, and 45 µA cm −2 were measured for samples of MoS 1 Se 1 , MoS 2 , and MoSe 2 , indicating facile HER kinetics for the TTMD, for which negligible differences were found in the performance after 1000 cycles.
Konkena et al studied MoSSe interfaced with rGO [104]. The composite catalyst was constructed via self-assembly, owing to the electrostatic attraction between the oppositely charged nanosheets. The authors reported that the nanocomposite heterostructures were active and stable electrocatalysts for HER. They measured a Tafel slope of 51 mV dec −1 and η 10 of 155 mV. Stability tests showed no decrease in performance after 5000 cycles.
Liu et al grew CoS 2z Se 2(1−z) (z = 0.67) nanowires on flexible carbon fiber [105]. This composite material exhibited high catalytic activity and stability. A Tafel slope of 44 mV dec −1 for CoS 2z Se 2(1−z) compared with values of 69 and 46 mV dec −1 for CoS 2 and CoSe 2 nanowires, respectively. The authors measured η 10 of 130 mV, with no decrease in activity after 1000 cycles. Xu et al synthesized high-quality WS 2 and WSe 2 nanotubes on carbon fibers via CVD, see figure 9 [106]. The authors also reported synthesis of WS 2z Se 2(1−z) with systematic control of the S/Se ratio through optimization of growth conditions. The WS 2 , WSe 2 , and WS 2z Se 2(1−z) (z = 0.48) nanotubes exhibited Tafel slopes of 113, 99, and 105 mV dec −1 and values for j 0 of 12, 3, and 29 µA cm −2 . The enhanced activity of these TTMD catalysts is due to improved conductivity, which results from incorporation of Se into the WS 2 lattice, as evidenced by analyses of the electronic structure.
Zhang and colleagues implemented CVD techniques to grow dendritic WS 2z Se 2(1−z) flakes on a SrTiO 3 substrate by sulfurization and selenization of WO 3 powder [107]. The flakes, with a morphology that produces an abundance of active edge sites, were transferred to Au foil to measure their HER capability. The WS 2z Se 2(1−z) on Au electrode, with an S to Se ratio of 19 to1, presented a Tafel slope and η 10 of 67 mV dec −1 and 156 mV which were lower than those measured for dendritic WS 2 (87 mV dec −1 and 310 mV). Moreover, the TTMD catalyst exhibited excellent stability, with negligible decay in performance after 1000 cycles. Other studies of WS 2z Se 2(1−z) inferred that active sites are present on the basal plane of the TTMD due to lattice strain arising from the different atomic radii of S and Se atoms [108,109].
Xia et al prepared Ni z Co (1−z) Se 2 (z = 0.33) solid solutions by selenization of a nickel cobalt precursor [110]. The resulting Ni z Co (1−z) Se 2 catalyst consisted of mixed cubic and orthorhombic phases. Through temperature dependent measurements of the conductivity, the authors described the metallic-like electrical conductivity of the TTMD solid solution. The room-temperature conductivity of Ni z Co (1−z) Se 2 was three times that of CoSe 2 . DFT calculations indicated that incorporation of Ni into the CoSe 2 lattice lowered the free energy of hydrogen adsorption at edge sites. Ni z Co (1−z) Se 2 operated under both acidic and alkaline conditions and measurements in an acidic electrolyte yielded a Tafel slope of 35 mV dec −1 and η 10 of 65 mV, with no loss of performance after 24 h of electrolysis.
Lie et al prepared 3D Ni (1−z) Co z Se 2 mesoporous nanosheet networks with tunable stoichiometry (z = 0-0.35) which operated as HER catalysts with excellent stability over a wide pH range [78]. A schematic of the fabrication process is shown in figure 10. The TTMD samples were prepared on nickel foam and by varying the Ni:Co ratio the authors identified Ni (1−z) Co z Se 2 (z = 0.11) as the optimal configuration. DFT calculations revealed that Ni 0.89 Co 0.11 Se 2 was metallic with high electrical conductivity. The electronic structure that resulted from substitutional doping of Co into the NiSe 2 lattice led to favorable adsorption free energies of H and H 2 O at the surface. This result indicated that Ni 0.89 Co 0.11 Se 2 could operate with high HER activity in all pH environments. Tafel slopes of 0.39, 0.78, and 0.52 mV dec −1 were measured for Ni 0.89 Co 0.11 Se 2 operating in acidic, neutral, and alkaline conditions, respectively. The corresponding values for η 10 were 52, 82, and 85 mV. Performance data for selected sulfur-and selenium-based HER catalysts are presented in tables 2 and 3, respectively, which can be found at the end of this review.

Metal phosphides
Metal Phosphides are another group of non-oxide materials that are seeing significant interest in HER. Similar to chalcogenide catalysts based on NiMo, Mo 2 C and MoS 2 , phosphide materials are HDS catalysts and are therefore potentially active for HER. Among phosphides, Ni 2 P, CoP, Fe 2 P, and MoP and ternaries have been studied as HDS catalysts [111][112][113][114]. Figure 11 shows the atomic structure of a range of metal phosphides, namely the Ni 2 P (001) surface (figure 11(a)) Co 2 P surface facets in figure 11(b), CoS 2 in figure 11(c), and CoSP in figure 11(d). These structures are taken from references [115][116][117][118].

Pure phosphorous materials
Phosphorous has been explored as a non-noble metal photocatalyst. Hu et al showed that fibrous phase red phosphorus functions as a semiconductor photocatalyst for visible-light-driven hydrogen evolution [122]. The fibrous phosphorus was prepared by loading onto photoinactive SiO 2 fibers or treating single phase fibrous phosphorous ultrasonically. Red P is useful as it is inexpensive and of low-toxicity and is more stable than Si in water under irradiation because it is not deactivated by surface oxidation. Fibrous P is a direct band gap semiconductor with a very high conduction band minimum of −0.9 V vs. NHE. This is higher than the theoretical potential of hydrogen evolution (0 V vs. NHE) and the previously reported values for Hittorf red P (−0.25 V) and Si (−0.2 to −0.35 V); this indicates that fibrous P is more favorable for water reduction than red P or Si.
The yield of hydrogen from photocatalytic water splitting was evaluated by using methanol as a sacrificial reagent and Pt as a cocatalyst. Hydrogen generation over time was evaluated at intervals of 1 h under visible light irradiation (wavelength > 420 nm). The resulting catalyst displayed steady hydrogen evolution rates of 633 and 684 µmol/g/h. These values are much higher than for amorphous P and Hittorf Phosphorous, for which H 2 evolution rates of 0.6 and 1.6 µmol/g/h were obtained.
Zhu et al prepared a binary nanohybrid composed of nanoflakes of black phosphorous interfaced with carbon nitride nanosheets (BP/CN) which was studied for H 2 evolution in the presence of methanol as a hole scavenger [123]. Trace amounts of H 2 were evolved using the single components. The optimum H 2 evolution for 1.5 mg of BP/CN reached 1.93 µmol for 3 h under >420 nm light irradiation without any metal elements. This catalyst also exhibited generation of H 2 (0.46 µmol) under >780 nm radiation for 3 h. The improvement in hydrogen evolution is proposed to arise from the strong interfacial interaction between BP and CN and the resulting efficient charge transfer at the interface that inhibits the recombination of photogenerated charges. The optimal ratio of BP:CN was 1:4, which resulted in a H 2 evolution rate of 427 µmol/g/h. Tian et al demonstrated that amorphous cobalt phosphide (CoP)-supported black phosphorus nanosheets exhibit robust hydrogen evolution from pure water (pH = 6.8), without bias [124]. The apparent quantum efficiency is 42.55% at 430 nm and the energy conversion efficiency is over 5.4% at 353 K. This was attributed to the extremely efficient utilization of solar energy (∼75% of incident light) by black phosphorus nanosheets and the high-carrier separation efficiency induced by the interface with amorphous Co-P.
The H 2 -evolution rate was assessed for 40 mg of catalyst dispersed in 150 ml. The as-prepared BP nanosheets yielded 1.2 µmol h −1 of H 2 and after supporting amorphous CoP nanoparticles (P:Co ratio of 3:1), the H 2 -evolution rate increased to 15 µmol h −1 . This is due to the low recombination of electron-hole pairs induced by formation of the interface with the amorphous Co-P cocatalyst. The highest H 2 -evolving activity was at a mass ratio of P:Co of 8:1; 40 mg of this catalyst produced 29.4 µmol h −1 of H 2 . However, increasing the ratio of P to Co decreased activity due to a decrease in light absorption.
The catalyst showed high stability over 40 h activity under cycling and in a pH range from 2 to 13. The STH efficiency in this CoP/BP system was obtained via loading 40 mg of Co-P/BP catalyst in 150 ml pure water under AM1.5 G simulated sunlight illumination (100 mW cm −2 ). After 2 h of irradiation, 160 umol of H2 was generated, giving an STH efficiency of 0.66% at room temperature. Activation energy for hydrogen evolution was 32.8 kJ mol −1 . This is smaller than from acidic or basic solutions.

Nickel phosphides
In 2005, early work from Liu and Rodriguez proposed that Ni 2 P could be a practical catalyst for HER based on DFT calculations [115]. Their calculations on the (001) surface showed favorable H-binding together with the stability of a solid catalyst. They found that the Ni concentration was diluted by introduction of P elements, which made Ni 2 P(001) behave like hydrogenase rather than the pure metal surface. In the HER process, hydrogen binds strongly at Ni hollow sites, but with the inclusion of P, the hydrogen is less strongly bound so that H 2 could be removed from Ni 2 P(001) surface. Ni 2 P nanoparticles were deposited onto a Ti foil substrate, which was followed by an annealing treatment [125]. The Ni 2 P/Ti electrode exhibited excellent HER activity with an exchange current density of 33 µA cm −2 and a Tafel slope of ∼46 mV dec −1 . Figure 12(a) shows a comparison of polarization curves for three individual Ni 2 P electrodes, along with glassy carbon, Ti foil, and Pt. However, further work showed that the stability of electrode was not satisfactory.
Kucernak and Sundaram examined the interplay between activity and corrosion resistance for varying phosphorous content in NiP samples [126]. Metal rich phosphides show high electronic conductivity but suffer from reduced stability in acidic medium compared to phosphorus rich materials; so the key is to find a balance between the metal and phosphorous content while enhancing the HER activity.
Nickel phosphide alloys show higher corrosion resistance than pure Ni metal. There are three important aspects contributing to the corrosion resistance of these phosphides: • Metal dissolution is thermodynamically less favorable in a metal alloy with phosphorus.
• Metal phosphides form amorphous films that are less susceptible to oxidation at grain boundaries.
• On oxidation, phosphorus oxidises to phosphate, which is much less soluble than other ionic species that can form during metal dissolution.
This work showed that nickel-based phosphides, namely Ni 2 P and Ni 12 P 5 with 33 and 29 at% P can be used for HER in an acidic medium. Ni 2 P samples were prepared via ball-milling commercially purchased Ni 2 P from 2-9 h and Ni 12 P 5 was prepared hydrothermally. The corrosion behavior was examined in two overpotential regimes: low (0 to −140 mV) and high (−140 to −450 mV). The lower potential regime is more typical of practical HER conditions and under these conditions the possibility of metal corrosion is minimized due to the low electrochemical potential.
A higher phosphorus content produced higher HER activity, as measured by lower Tafel slopes and higher exchange current densities. The Tafel plots in figure 12(b) are shown for the as-received Ni 2 P, Ni 2 P after ball-milling for 6 and 9 h, and Ni 12 P 5 . In the low potential regime, the Ni 2 P electrocatalysts showed Tafel slopes of 79-84 mV dec −1 , depending on the duration of ball milling, whereas a slope of 108 mV dec −1 was recorded for Ni 12 P 5 . Recognizing that suitable hydrogen evolution catalysts should show low corrosion current densities but high exchange current densities, the results of this work showed that Ni 2 P samples ball-milled for 6 h best met this demand. Although initially highly active, the Ni 2 P catalysts displayed a decay in current or loss in stability over time. By contrast, the Ni 12 P 5 electrocatalyst, although giving a lower electrocatalytic activity, showed better stability over time. It would appear that the metal-rich Ni 12 P 5 phase is less intrinsically active than Ni 2 P but is more stable in terms of hydrogen production with a lower corrosion current.

Cobalt phosphides
Popczun et al first reported in 2014 that CoP is a highly active and acid-stable HER catalyst [119]. CoP is a known HDS catalyst and is structurally different and compositionally distinct from Ni 2 P. CoP particles are single-crystalline with observed lattice spacings of 2.4 Å, consistent with closely spaced (102) and (111) planes of MnP-type CoP.
Multi-faceted, hollow CoP nanoparticles were synthesized via reaction of Co nanoparticles with thioctylphosphine. CoP/Ti electrodes were constructed by depositing CoP nanoparticles on a Ti support, followed by annealing. Figure 13(a) shows the polarization curve for CoP nanoparticle electrodes in acidic medium and the Tafel plots. The HER activity was consistent among ten different CoP/Ti samples. The electrodes exhibited a value for η 20 of 85 mV and Tafel slopes of 50 mV dec −1 . The catalysts showed stability in 0.5M H 2 SO 4 for 24 h with no change in activity over 400 CV sweeps. The value for η 20 changed to ∼90 mV after 400 cycles. This demonstrated high stability under strongly acidic conditions. The chemistry of CoP was described with a mechanism in which the bond strength of adsorbed hydrogen is strong enough to promote optimal hydrogen coverage but is not so strong to impede desorption of H 2 .
Liu and coworkers pioneered a low-temperature toptotactic transformation preparation of metal phosphide nanostructures [127]. CoP nanocrystals were decorated on carbon nanotubes (CoP/CNT). This was prepared by a low-temperature phosphidation process of Co 3 O 4 /CNT precursor with NaH 2 PO 2 . The catalyst displayed high HER activity, with a reported η 10 of 122 mV and a Tafel slope of 54 mV dec −1 .
Using a similar synthesis approach, the same group grew nanoporous CoP nanowire arrays on CC [128]. The resulting CoP/CC catalyst sustained hydrogen production for 80 000 s in acidic media and showed a Tafel slope of 51 mV dec −1 and η 10 of 67 mV. This group has developed this novel approach to prepare binder-free 3D metal phosphide arrays [129] and nanowires [130] on Ti plates. The Ti-supported CoP nanosheet arrays exhibited a Tafel slope of 43 mV dec −1 and η 10 of 90 mV while the CoP nanowires on Ti showed a Tafel slope of 65 mV dec −1 and η 20 of 95 mV.
Saadi et al synthesized an amorphous CoP film on Cu through cathodic deposition from a solution of Co 2+ in boric acid and H 2 PO 2− [120]. Figure 13(b) shows the J-V curves for CoPS Tafel plots and stability over more than 30 h. After measuring HER, the Co:P ratio was 1:1, suggesting that the initial high-valent Co and P species present in the original catalyst are removed under HER conditions. This in situ film purification yields an active electrocatalyst, which displayed a Tafel slope of 50 mV dec −1 and η 10 of 85 mV.
Caban-Acevedo et al predicted that HER catalytic activity of metal chalcogenides can be improved by tuning the hydrogen adsorption free energy through modifying the composition of CoS 2 , figure 14(a), while preserving the pyrite structure [117]. The crystal structure of the resulting CoPS is similar to CoS 2 but shows dumbbells with a homogeneous distribution of P 2− and S − anions. CoPS has one less valence electron than CoS 2 and is a semiconductor isoelectronic to iron pyrite. Since the Co octahedra in CoPS have P 2− ligands with higher electron-donating character than S − ligands, this pyrite can show higher HER catalytic activity than CoS 2 . DFT was used to compute ∆G H on the (100) figure 13(c). The catalysts also showed long-term operational stability beyond 36 h with little change in the film morphology.
CoPS was compared with CoP (which included a minor CoP 2 impurity) and showed that the catalytic HER performance of CoPS electrodes is attributable to the ternary pyrite-type compound instead of CoP impurities or anion-substituted doping on surface of CoPS.
Huang et al prepared Co 2 P nanorods which exhibited values for η 20 of 167 mV in acid solution and 171 mV in alkaline solution [131]. The Faradaic yield of H 2 production was close to 100% and the HER process followed the Volmer-Heyrovsky reaction, with a Tafel slope of 51.7 mV dec −1 in acidic conditions. Co 2 P nanorods are stable in both acidic and alkaline solution during H 2 production. The importance of the crystal structure of Co 2 P (orthorhombic) was highlighted. Co and P in Co 2 P are similar to hydride and proton acceptors in Ni 2 P. Similarities in the electronic nature of Co and P implied that the catalytic mechanism for HER would be the same in Co 2 P and in Ni 2 P.
Pan et al prepared a range of CoP-based electrocatalysts, including Co 2 P, CoP, heterostructures interfaced with CNTs and with N-doped CNTs (NCNTs) via a thermal decomposition approach [132]. The catalytic activity followed the order CoP/NCNTs > Co 2 P/NCNTs > CoP/CNTs > Co 2 P/CNTs > CoP > Co 2 P. The higher activity of CoP compared to Co 2 P is related to the difference in coordination environments for Co and the higher phosphorous content in CoP. In addition, the strong interactions between CoP and carbon materials, and the doping of N atoms in the NCNTs further enhance the activity in the heterostructured materials. Furthermore, the high surface area in the CoP catalysts (44.2 m 2 g −1 ) compared to Co 2 P (26.9 m 2 g −1 ) catalysts also promoted HER activity. Differences in the catalyst morphology were discussed. The rod-like morphology of CoP can enhance the efficiency of interfacial electron transfer, for example. The as-synthesized CoP/NCNTs catalysts exhibit the best electrocatalytic activity for HER in 0.5M H 2 SO 4 . A low onset overpotential of 32 mV, a small Tafel slope of 49 mV dec −1 , a high j 0 of 320 µA cm −2 , and η 20 of 97 mV were reported. Stability was tested by CV scanning over 1000 cycles, at a scan rate of 50 mV s −1 , after which the LSV curve was unchanged from the first cycle.
Sumboja et al prepared CoPs for HER, in acidic and alkaline media [121]. Samples of CoP were synthesized using precursors containing acetate (labeled CoP I) or acetylacetonate (labeled CoP II). CoP I had a higher Co x P content (92.5 wt%) compared to CoP II (63.5 wt%), to which was attributed the enhanced HER activity of CoP I in acid. However, both catalysts were active for HER in neutral and alkaline conditions. Figure 13 Cobalt oxides present in the Co-material were proposed to also be beneficial for the HER activity in alkaline conditions. The CoO x is supposed to promote the dissociation of water due to the affinity of OH − to Co 2+ and Co 3+ . Values for η 10 of 160 and 169 mV were found in acidic electrolyte for the higher and lower CoP content materials, respectively. These overpotentials are comparable to other forms of CoPs measured in acidic electrolytes-urchin-like CoP, 105 mV [133]; CoP nanowires, 110 mV [134]; CoP nanosheets, 164 mV [134]; CoP microparticles, 202 mV [135]; CoP nanoparticles, 221 mV [134]; and CoP microspheres, 226 mV [127].
In alkaline media the values for η 10 were 175 and 188 mV fpr CoP I and CoP II, respectively, indicating that larger overpotentials are required to drive the HER in alkaline conditions. This compared to FeP 2 nanowires, 189 mV [136]; FeP nanowires, 194 mV [136]; and MoP nanoparticles, 276 mV [137]. Due to Tafel slopes in excess of 40 mV dec −1 for the CoP catalysts in both acidic and alkaline media, the authors concluded that HER is most likely to proceed via a Volmer-Heyrovsky mechanism.
In acid the CoP catalysts showed degradation of no more than 15.5% during 13 h of stability tests, which was better than the degradation of the Pt/C catalyst. In alkaline electrolyte, CoP shows only 4% degradation after 13 h of testing, compared to 19% for Pt/C catalyst.
Wu et al studied the pyrite structured ternary compound CoPS as an earth-abundant catalyst for photoelectrochemical hydrogen production in acidic environment [118]. Large single crystals of CoPS, with selectively exposed (100) and (111) facets, were synthesized and the corresponding HER activities were measured. Tafel slopes of 109 and 86 mV dec −1 were recorded for the (100) and (111) facets, respectively. The CoPS (100) surface contains intact PS 3− dimer dumbbells that are electron rich compared to S 2 2− in CoS 2 , owing to the lower electronegativity of P compared to S. These electron-rich P sites provide strong H-binding sites. The adsorption of H onto a P site results in the reduction of Co 3+ to Co 2+ , which was proposed as a new site for subsequent facile H adsorption. The CoPS (111) with S-and P-terminations were considered. These (111) surfaces lack intact PS 3− dumbbells, but expose four symmetry-unique Co atoms, three of which are 4-coordinated and one of which is 3-coordinated. The electron rich 3-coordinated site preferentially adsorbs H atoms compared to the 4-coordinated Co sites, for both S-and P-terminated surfaces.
DFT computations of the free energies of H adsorption show that adsorption of the first H atom on the (111) facet is endergonic, while on the (100) facet this is exergonic, as shown in figure 14(b). The same is found for the second adsorbed H atoms so that the coverage of hydrogen appears to be an important factor in the activity of these catalysts.
In the low potential region (<0.35 V), the HER activity of (100) facet is superior to the (111) facet, which is reversed in the high potential region (>0.35 V). The differing HER activities are proposed to arise from differences in the energetics of H atom adsorption and the barriers to H-H recombination on these facets. At low potentials, the H adsorption process is rate limiting so the (100) facet is more active, while with increasing potential, H 2 recombination and desorption is the limiting step and the (111) facet shows lower desorption barriers.

Molybdenum phosphides
Molybdenum phosphide (MoP) is a well-known HDS catalyst [138]. DFT calculations showed that MoP can display properties similar to the platinum group metals, particularly the near zero free energy of hydrogen adsorption at certain H coverages [139]. The authors prepared bulk MoP and Mo 3 P through tuning key synthesis parameters, including reaction temperature, and demonstrated the efficient HER activity of MoP, compared to Mo or Mo 3 P. Tafel slopes of 54, 147, and 92 mV dec −1 were recorded in acidic medium for MoP, Mo 3 O, and Mo, respectively. A Tafel slope of 48 mV dec −1 was measured for MoP in alkaline conditions. For MoP, the onset of hydrogen evolution was observed at ∼50 mV and the current density reached 30 mA cm −2 at a potential (η 30 ) of 180 mV. This demonstrates that phosphorization can modify the properties of Mo and tuning the degree of phosphorization has a strong impact on the HER activity and stability of the resulting catalysts. The catalytic activity of MoP persisted for 24 h, indicating good stability. The high HER activity was proposed to result from the presence of a closely interconnected network of MoP nanoparticles in the structure.
Kibsgaard et al incorporated sulfur into the surface of MoP, producing an MoPS (molybdenum phosphosulfide) catalyst [140]. The introduction of sulfur was achieved by post-sulfidation treatment of MoP in an atmosphere of H 2 S. XRD showed that the crystal structure of MoP is not altered by introduction of sulfur. In acidic environment, this catalyst shows high activity and stability for HER, figure 15(a). A value for η 10 of 86 mV for MoPS compared with 117 mV for MoP, for approximate loadings of ∼1 mg cm −2 . Increasing the loading of MoPS to ∼3 mg cm −2 reduces the η 10 to 64 mV. Both MoP and MoPS exhibited similar Tafel slopes of ∼50 mV dec −1 . It was proposed that sulfur incorporation into MoP mitigates surface oxidation of the phosphide.
The stability of MoP and MoPS was assessed by 1000 continuous CV cycles, figure 15(B). The accelerated durability test was designed to represent the cycling expected for water (photo)electrolysis powered by  intermittent renewable resources. MoP showed a slight decrease in activity with increased potential cycling. MoPS exhibited enhanced stability in this durability test, with overpotentials increasing by no more than 1 mV even at current densities larger than 100 mA cm −2 .
Sultana and Mullane reported on the HER activity of amorphous MoPS in both acidic and alkaline media [141]. The electrodeposited MoPS films contained oxygen and exhibited Tafel slopes of 36 mV dec −1 and 122 mV dec −1 in acidic and alkaline conditions, respectively. The authors reported that phosphorous was crucial to the alkaline HER activity and the samples remained stable after 20 h of electrolysis at 10 mA cm −2 . Huang et al deposited MoP nanoparticles on hierarchical carbonaceous scaffolds, MoP/NC [142]. This was followed by treatment with H 2 S in Ar to create ultra-dispersed MoPS nanoparticles on the carbonaceous support, MoPS/NC. The authors measured values for η 10 of 92 and 158 mV, for the S-containing catalyst, in acidic and alkaline media; this compared with values of 120 and 170 mV for the MoP/NC catalyst. Tafel Controlled phosphorus doping was used to modify the electronic configuration of nanostructured Mo 2 C [143]. Shi and coworkers controlled P-doping of Mo 2 C by using MoO x -phytic acid-polyaniline hybrids with tunable composition as precursors. The resulting catalysts consisted of hierarchical nanowires composed of P-doped Mo 2 C nanoparticles integrated with conducting carbon and were denoted P-Mo 2 C@C. The incorporation of P into Mo 2 C increases the electron density around the Fermi level of Mo 2 C. This weakens Mo-H bonding and improves the HER kinetics. With optimal doping, a ∆G H approaching 0 eV presents a balance between the Volmer and Heyrovsky/Tafel steps in the HER kinetics. The optimal P content in P-Mo 2 C@C nanowires was found to be 2.9 wt% and this catalyst delivered η 10 of 89 mV and a Tafel slope of 42 mV dec −1 in acidic electrolytes. By contrast, pure Mo 2 C@C presented a Tafel slope of 64 mV dec −1 . The highest exchange current for 2.9% P-doped Mo 2 C@C was 180 µA cm −2 , which is very close to that of Pt/C (J 0 = 540 µA cm −2 ). The Faradaic efficiency of 2.9% P-Mo 2 C@C is close to 100%.
When the Mo 2 C (102) surface is P-doped, the P atoms occupy the vacant interstitial sites or replace the C atoms of Mo 2 C. With a larger atomic radius compared to carbon, the P atom prefers 4-fold hollow sites at the surface. It was proposed that the 1D nanostructure used in this work provides abundant space for H 2 bubble release and facilitates charge transfer in the axial dimension. Finally, as P doping was increased, an excess of phosphorous inhibits the HER activity, which highlights the importance of tunable control for optimal P-doping. Figure 16 shows the computed hydrogen binding energies (∆E H ) and free energies changes per H (∆G H ) for P-doped Mo 2 C with varying P-content.

Ternary phosphide materials
Fang et al prepared CoP/MoP hybrid materials by doping Co into MoP to increase the intrinsic activity of MoP [144]. The measured Tafel slopes decreased from 84 to 60.5 mV dec −1 with increasing the Co/Mo ration from 0 to 0.5. These values suggest that HER occurs via a Volmer-Heyrovsky mechanism in which the slow adsorption of proton dominates the kinetics. Samples of Co 0.5 Mo 0.5 P annealed at different temperatures were investigated for HER activity. For an annealing temperature of 650 • C, the authors reported the presence of hexagonal CoMoP 2 , h-CoMoP 2 . Increasing the annealing temperature to 1000 • C induced a change in phase from h-CoMoP 2 to CoMoP in which phosphorus is evaporated and the resulting CoMoP structure was less active than P-rich h-CoMoP 2 .
Values for η 10 of 250 and 283 mV were recorded for bulk MoP and CoP catalysts, respectively, compared with 50 mV for Pt foil. On adding Co to MoP, η 10 decreases from 250 to 165 mV. The Co 0.5 Mo 0.5 P catalyst showed an exchange current of 343 µA cm −2 , which is up to 6 and 16 times that of MoP and CoP catalysts. Figure 17(a) shows the Tafel plots for the CoMoP catalysts, together with the dependence of the Tafel slope on Co content ( figure 17(b)). After 1000 CV cycles, figure 17(c), the Co 0.5 Mo 0.5 P electrode showed a small increase of 11 mV in η 10 , which indicated the stability of the catalyst under typical operating conditions.
Guan et al prepared high performance catalysts through the direct growth of catalyst materials in the form of well-aligned Mo-doped CoP nanoarrays on current collectors [145]. In this work, hollow Mo-doped CoP nanoarrays were prepared on CC starting from a MOF precursor. Mo-CoP arrays were transformed in situ into Mo-CoOOH with good OER properties, providing a means for overall water splitting. The spaces between the nanoarrays facilitate electrolyte penetration and the release of evolved gas bubbles. The electrical/mechanical connections between the active catalyst and the current collectors promote efficient electron transfer paths, which can also deliver long-term stability.
These materials were tested against control samples with similar structures: hollow CoP nanoarrays, hollow Co 3 O 4 nanoarrays and noble metal based catalysts (Pt/C and Ir/C), all on CC. The Mo-CoP catalyst showed a small η 10 of 40 mV, which was lower than those of CoP (160 mV) and Co 3 O 4 (242 mV). The Tafel slope of Mo-CoP is 65 mV dec −1 , which is smaller than the corresponding Tafel slopes for CoP and Co 3 O 4 , which are 75 and 103 mV dec −1 , respectively. It appears that the overpotential can be reduced by phosphidation and formation of a ternary system through substitutional Mo-doping. At an overpotential of 100 mV, Mo-CoP exhibits a current density of 57 mA cm −2 , which is higher than the Pt/C catalyst, 47 mA cm −2 . Stability tests revealed that the Mo-CoP catalyst maintained 95% of the initial current density (∼54 mA cm −2 ) after 20 h of operation at 100 mV.
From DFT simulations, the origin of the superior Mo-CoP properties was proposed to be due to Mo doping giving lower free energy changes, ∆G H , for hydrogen adsorption, compared to CoP. The hollow nanoarray structure has numerous nanograins, which is confirmed by atomic resolution STEM meaning that this structure has many active sites. Performance data for selected phosphide-based HER catalysts are presented in table 4, which can be found at the end of this review.

Accelerating materials discovery
In the preceding sections, we have also highlighted the complementary role of computational methods, and particularly DFT, in identifying active sites and the origin of the activity of catalyst materials for HER. This is driven by the observation that the Gibbs free energies of H adsorption at active sites of Pt and hydrogen producing enzymes were close to thermodynamically neutral, i.e. ∆G H ≈ 0 eV, in accordance with the Sabatier principle [44,146]. Thus, ∆G H is considered an appropriate descriptor to assess the potential for a given material to catalyze the HER. This has paved the way for fast screening of candidate materials by computing ∆G H for various sites and hydrogen coverages at the surface of modes of the catalyst and has informed design and fabrication methods to maximize exposure of active sites. Establishing simple relationships between chemical concepts and HER activity is also of interest.
However, as mentioned in the introduction, care must be taken with the application and interpretation of computational models. Describing the complexity of the catalyst surface and its environment represents a considerable challenge for first principles simulations. The relevance of computational results depends on the accuracy with which the models approximate the real system. While free energy calculations are the workhorse of computational materials discovery, with demonstrable efficacy, there are efforts to bridge the gap between simple surface, vapor-phase models and the finite-temperature catalyst-solvent interface [147,148].
There are various strategies to account for the solvent and its role in the chemistry at the catalyst surface. The solvent can be incorporated implicitly, where the solvent is treated in an average way and described as a continuous medium, or explicitly, where the molecules that constitute the solvent are included in the computation [149].
Explicit solvation models can range in complexity from single to multiple layers of molecules at the catalyst surface [150][151][152]. Ping and coworkers examined the impact of water on the band positions of some common photocatalyst materials [150]. They compared results among approaches, including an explicit, single water layer, continuum solvation models (CSMs), and combinations of the two. The authors reported that, while CSMs were sufficient to account for the solvation shift in the band energies of hydrophobic surfaces, the inclusion of an explicit water layer was necessary to describe the stronger interactions at hydrophilic surfaces.
Skúlason and colleagues implemented a water bilayer in their model of the HER at Pt (111) [151]. By varying the number of H atoms in the bilayer, the authors could examine the effect of the electrode potential on the activation energies in the HER. This is because the H atoms were solvated in the bilayer-the protons remained in the bilayer while the electrons moved to the catalyst surface. In this way, their model described the Helmholtz double layer.
The treatment of such a system with DFT can be used to determine the effect of the solvent on the binding energies of reaction intermediates. However, DFT is a 0 K theory, and so cannot describe the temperature-dependent effects of a liquid solvent. Thus, an approach to modeling the solvent at finite temperatures is to implement molecular dynamics (MD). Classical MD simulations can be used to obtain an array of local minima in the solvent configuration, which are subsequently treated with DFT [149]. In classical MD, quantum effects and electronic degrees of freedom are neglected and molecule positions are determined by solving Newton's equations of motion. This necessitates the implementation of force fields, which must be parametrized for the system under study [153,154].
Another approach to modeling finite temperature solvents, explicitly, is ab initio MD (AIMD). AIMD differs from classical MD in that it is based on quantum, rather than classical, mechanics [155]. Kronberg and colleagues compared AIMD with NEB in their study of the Volmer-Heyrovsky mechanism for the HER at an N-doped carbon nanotube [156]. The authors reported substantial discrepancies between the activation and reaction energies computed with the two methods and highlighted the importance of explicitly including interfacial dynamics when studying the HER at the catalyst-electrolyte interface. Cheng and coworkers used AIMD to examine the role of charge trapping during deprotonation of a surface-bound hydroxyl at rutile TiO 2 (110) [157]. Gono et al found that the explicit inclusion of water molecules in their models affected the overpotential for water oxidation at rutile TiO 2 by up to 0.5 V [152].
Van den Bossche and coworkers approximated the solvent by a polarizable dielectric continuum in their study of the HER at Pt surfaces [158]. The authors maintained a constant electrode potential by varying the concentration of counterions in the electrolyte, in response to changes in the number of electrons during the reaction. The results of this implicit approach compared favorably with the more rigorous and computationally expensive, 'extrapolation' approach [159,160].
Chang et al used both implicit and explicit solvent models to examine the HER at sub-nm Au-Ag clusters [161]. In their implicit model, the authors computed the solvation energy of the nanoclusters and thereby adjusted the electron affinity to account for the water environment. The explicit model implemented AIMD to test the catalyst stability and introduce thermal effects.
Despite these advances in computational techniques to model the catalyst-electrolyte interface, descriptor-based approaches remain at the forefront of computation-driven design of new photocatalyst materials. Expanding on this theme and going beyond the usual application of DFT calculations to the HER, machine learning approaches are being investigated. In machine learning, the algorithm is trained on a known data set related to the catalytic descriptor of interest and the resulting machine learning function is then used to explore a wide range of potential materials at much lower cost than a full DFT-level simulation. In one example of this, Jäger and colleagues adopted a machine learning approach [146] in which they constructed a large data set of hydrogen adsorption energies on various sites of nanoclusters of MoS 2 and Au 40 Cu 40 , figure 18(a). This dataset was characterized by structural descriptors and used to train a model to predict the adsorption energy for an arbitrary site based on its description. The goal of this study was to establish how many data points were required to interpolate the potential energy surface and predict the hydrogen adsorption energy, ∆E H , to an accuracy of 0.1 eV. Datasets consisted of 10 000 single-point DFT calculations of ∆E H and comparisons were made between a number of structural descriptors: atom-centered symmetry functions [162]; many-body tensor representation [163]; and smooth overlap of atomic positions [164,165]. The authors concluded that each of the aforementioned descriptors performed satisfactorily well, provided they were given a training set of sufficient size, which is a key consideration in developing machine learning models.
Another computational descriptor that can be used to assess the active sites of a catalyst surface is the Fermi softness, S F [166]. This descriptor finds its analogue in frontier molecular orbital theory [167], which describes the spatial distribution of active sites of a molecule. The local Fermi softness at position r is defined as: where g (E, r) is the DOS projected at position r and f ′ T (E − E F ) is the derivative of the Fermi-Dirac distribution function at finite temperature. The negative of f ′ T (E − E F ) provides a weighting factor which reaches a maximum at E F and this is included to reflect the greater contribution to bonding of states near the Fermi level. Huang et al benchmarked this descriptor in a study of transition metal surfaces before examining active sites of a one-dimensional MoS 2 edge [166]. Based on analysis of S F (r), figure 18(b), and subsequently  . Highlighting the evolution of HER materials from metals, through low dimensional materials and phosphides to mixed cation catalysts and the role of modeling. The word cloud shows keywords used in this field. Adapted with permission from [15,48,116,144,166,170]. confirmed by NEB calculations, the authors identified a subtlety in the reactivity at the MoS 2 edge: an anisotropy exists which promotes the HER at intra-S-dimer bridge sites, relative to inter-S-dimer bridge sites.
Ran and colleagues established a relationship between the HER activity and bond electronegativity in a study of TMDs [168]. Citing a trial-and-error approach in existing endeavors to activating and optimizing catalysts for HER, the authors implemented a high-throughput first-principles strategy to identify a universal design principle. The study began with 2H-MoS 2 doped with other TMs and examined H adsorption at S-sites neighboring the TM-dopant. The authors presented a formula that describes the characteristic S-H bonding electron number, based on the local properties of the active site. The descriptor, Ψ, takes into account bond electronegativity, coordination numbers, and valence electrons, and was used to predict potential HER catalysts with high activities; although experimental confirmation is required to confirm the validity of such predictions.  Pt/np-Co0.85Se 55 10 35 [180] Hu et al explored the mechanism for HER on pristine CoP using first principles simulations [169]. The most stable surface facet on CoP is (011), followed by (110), (111), and (100). The (011) facet exhibits the highest surface packing density. From the DFT results, the Co bridge sites and P top sites are able to adsorb hydrogen atoms with a free energy change that is close to 0 eV. Importantly, and going beyond many studies where single H atom adsorption is studied and temperature/pressure are neglected, both the role of hydrogen coverage and ab initio thermodynamics were considered to make better contact with experimental set-ups.
In exploring coverage effects on the CoP (111) surface, which is claimed to be present in typical nanostructures of CoP, the authors showed that at a hydrogen coverage of 25% H atoms is strongly adsorbed at cobalt bridge sites, with computed ∆G H of ca. −0.6 eV. Upon increasing the hydrogen coverage beyond 25%, adsorption at cobalt bridge and phosphorus sites is possible and there are some dependencies of ∆G H on which sites are occupied. The value of ∆G H is close to zero for these coverages so that cobalt bridge sites and phosphorus top sites are active for HER on the (111) surface. For coverages up to 100% hydrogen, more than one H atom can adsorb on Co atoms.
From ab intio thermodynamics, extremely low hydrogen pressures result in the clean surface being the most stable. At typical ambient pressures, 75% hydrogen coverage is most stable. The authors conclude that the (111) surface of CoP is the most active facet for high and stable HER activity.
Liang et al presented DFT studies to show that the different surface facets in a catalyst can show very different HER properties [116]. They show that the surface stability of Co 2 P facets goes in the order: (112) > (010) > (113) >(101) > (001). To examine the HER activity, the usual Gibbs free energy of hydrogen adsorption, ∆G H was used to evaluate HER activity. The optimum ∆G H value for the five facets is in the following order: (113) L1 ≈ (001) L1 < (112) L1 < (101) L5 < (010) L5 < (010) L4, where L1, L3, L4, and L5 indicate specific adsorption sites. Given that the surface energy of the (113) facet is smaller than that of the (001) facet, Co 2 P catalysts that expose the (113) surface would be proposed as active catalysts for HER. The effect of the Co-H distance on the charge transfer from Co to adsorbed H can be examined. A shorter Co-H bond length induces larger charge transfer from Co to H. The 'Co s ' species has a stronger effect on ∆G H than other Co species. Considering the Fermi levels, these are found in a valley of the DOS for the (001) and (101) facets and on a hill for (112), which is in agreement with the proposed HER activity. Finally, a linear relationship between the Co-H bond lengths and the computed ∆G H was established.

Conclusions
The importance of the HER in both electrochemistry and renewable fuel is undeniable. It serves as both the key half reaction for production of high purity hydrogen from water splitting but also as a side reaction in other technologies. Noble metals have been widely studied for the HER and still act as a benchmark for any potential catalyst materials. However, recent years have seen an upsurge of interest in using chalcogens and phosphides for the HER reaction and there is a bewildering number of papers on this topic. In figure 19, we summarise what we see as the evolution from metals through the current high performance, low dimensional materials and phosphides. The future includes heterostructures, mixed cation catalysts and the important role of modeling in catalyst design.
However, despite all this work, there is still no ideal, scalable HER technology. One issue that should be addressed is the characterization and reporting of the HER catalysts and their activity, similar to the protocols for reporting solar cells, where standards have been adopted.
In this regard tables 1, 2, 3 and 4 present a compilation of data from HER studies referenced in this review and some additional references where metal sulfides, selenides, and phosphides were explored. If we consider the five characteristics presented in these tables, we can immediately see that not every study of HER presents and discussed these data. Tafel slopes tend to be most widely reported, along with overpotentials. These would be sensitive to details around composition, preparation, cycling, test conditions, etc, and it would be of significant benefit to report other characteristics such as exchange current density, H 2 evolution rate, H 2 evolution after a defined number of cycles or over a predetermined time; these latter two will be crucial for the large-scale performance of the HER catalyst. Reproducible preparation methodologies will also be needed so that results can be reproduced and the feasibility of scale-up of production can be assessed. In addition, there will also be a requirement to assess the cost/economic aspects and investigate the life cycle analysis of these catalysts. As one example, although cobalt is a promising metal cation for HER catalysts, e.g. CoSe 2 or CoP, it is a critical raw material with a huge demand from the battery sector and issues around its mining and extraction.
Despite the discussion above, the results of the papers discussed in this review show that chalcogenides and phosphides are extremely promising HER materials. Exploiting the advances in controlled synthesis, heterostructuring and characterization has allowed fine control of structure and composition, e.g. the amount of phosphorous or the relative amounts of two cations, which can be used to enhance the HER in these materials.
Key fundamental properties of these materials include the high lying electronic states with metallic character, which means that the free energy of hydrogen adsorption can be close to 0 eV and thus drive HER. In addition, the introduction of a second metal in a ternary structure, e.g. Mo/Co-containing catalysts can modulate the electronic structure and further promote the HER activity. Low dimensional structures show high surface to volume ratios, which can have a high density of active sites; however, of course, the 2D dichalcogenides have an inactive basal plane, so strategies to activate the exposed areas or facets are also valuable. Heterostructures can tune light absorption for photochemical HER, as well as tuning the density of active sites and charge localization. Finally, we have to ensure that the catalyst is stable under the desired use conditions, e.g. acid environment, applied voltage, expected number of cycles or time under which it is used.
As we drive toward the dream of clean, efficient hydrogen production, advances in multiple areas will only help to bring us closer to a usable HER catalyst. In synthesis, using atomic layer deposition to deposit well controlled amounts of finely dispersed active materials will be an extremely valuable advance, producing highly active materials, but using small amounts of valuable metals. In characterization, advances in microscopy and operando methods will allow a deeper understanding of HER catalysts and give key insights into the features that drive a good catalyst. Finally, the power of computational modeling will drive rapid screening of a multitude of candidate materials, allowing only the most suitable to be prepared and tested, giving significant savings in time and cost while growing our understanding of the fundamentals of HER catalysts.