Perspective—A New Viewpoint on the Mechanism of the Hydrogen Evolution Reaction on Various Transition Metal Electrodes

In the research for the catalytic activity of metals, the electronegativity (EN) and valence electronic configuration (VEC) of the atoms of metals have been considered as important factors. By comparing the catalytic activity of the hydrogen evolution reaction (HER) from various metals, we find that metals with high EN and containing two or more accessible partially filled orbitals (PFOs) can support high exchange current density i 0,H(A cm−2) for HER, however, metals with low EN and/or with just one or no PFOs are unable to support high i 0,H values. It is, therefore, concluded that the EN and the PFOs of the atoms of metals plays a decisive role in its catalytic behavior. Here, the EN and the VEC of the atoms of transition metals in relation to the catalytic activation for HER is discussed and a new type of reaction mechanism of HER on various metal electrodes is also suggested.

The hydrogen evolution reaction (HER, 2H + + 2e − → H 2 ) is a cathodic process to produce green H 2 in electrochemical water splitting, and this reaction can occur on normal conductive electrodes (such as bare glassy carbon) when high potential applied.To improve the energy efficiency, catalysts are usually applied on the surface of cathode.In the past few decades, a significant amount of work has been put into developing effective catalysts and understanding the catalytic reaction process.Some transition metals, such as platinum and nickel, have been confirmed to be effective for catalytic HER, but the real catalytic process remains a source of debate.In this paper, we wish to provide a new insight into the mechanism of the HER on various metal electrodes.

Current Status
The process of the catalytic HER is often regarded as the Volmer-Tafel (V-T) and the Volmer-Heyrovsky (V-H) mechanisms.Both mechanisms involve electrochemical hydrogen adsorption, hydrogen atoms were adsorbed on active atoms of the catalyst to form adsorbed H • (Volmer reaction), then followed by the combination of two adsorbed hydrogen atoms to produce H 2 molecule (Tafel reaction) as shown in Fig. 1a or the reaction between one adsorbed hydrogen and a solvated proton from the water layer to form a H 2 molecule (Heyrovsky reaction) as shown in Fig. 1b. 1,2If both mechanisms are correct, we need to know underlying factors which dictate the selection between both mechanisms on the surface of a given metal, but it remains in ambiguity in this area.
In addition, it is experimentally confirmed that the hydrogen molecules can form on the bare glassy carbon electrode (GCE) without addition of catalysts when high potential applied.Because the formation of adsorbed hydrogen on the surface of GCE is difficult, the mechanism of V-T or V-H seems impossible to unravel the real reaction process in this condition.Therefore, the both proposed V-T and V-H mechanisms fall short in providing an allencompassing interpretation of these experimental observations.
As hydrogen molecules are formed on the surface of the solid state materials in catalytic HER, it is accepted that the work function Φ, which is the energy to remove an electron from the surface of a solid to a point outside the solid, is suitable to correlate the electrochemical behaviour of a metal electrode during hydrogen evolution with its nature. 3,4In Trasatti's reports, 3 he complied literature log i 0,H values for HER at various pure metal electrodes and metal work functions, and found that the plots of log i 0,H against Φ are unable to yield a specific correlation, two parallel regression lines instead, and part metals still out far from two lines (such as Hg).To date, no suitable model is reported for catalytic behaviour of HER on various transition metal electrodes.

Future Needs and Prospects
It seems to us that before considering the mechanisms of catalytic HER, we firstly need to know every elementary step of this reaction without the addition of catalysts, as well as which step is ratedetermined step (RD-step).For HER(2H + +2e − →H 2 ) on bare GCE, as it is impossible to form adsorbed H • radicals on the surface of GCE, it seems that the initial elementary step is electron-transfer step (H + +e − →H • ) on cathode forming atomic hydrogen radical (H • ) by a single electron-transfer to proton from GCE, then followed by radical-dimerization step (H • +H • →H 2 ) to give a H 2 molecule by dimerization of two free H • radicals.
There are two elementary steps: electron-transfer step and radical-dimerization step, which step is RD-step?It is known that introducing suitable catalysts, the RD-step can be modified, and the total rate of reaction will be boosted.Thus, identifying the RD-step of HER is very important before understanding the mechanism of HER with metal-catalysts adding and the property of various metals as catalysts.As the electrodes are conductive, positively charged protons might be easy to achieve electron-transfer forming H • radicals on cathode surface under negative potential.Thus, it seems to us that the RD-step in HER may presumably is radical-dimerization step because H • radicals are extremely reactive and may react with H 2 O or other species, this might lead part of them to lose its reactive property before encounter of two H • radicals to form a H 2 molecule.And this might be the main reason that causes the low energy efficiency during hydrogen evolution.
From the foregoing, an interesting inference is that an active site of catalysts for H 2 formation may have a potential to in situ chemically bond two H • radicals after electron-transfer step, which may support the formation of H 2 molecule and avoid the reaction of free H • radicals with H 2 O or other species during the process of catalytic hydrogen formation.
When we consider the strength of a chemical bond between two atoms, it is widely accepted that bond strength is strongly dependent on the electronegativity (EN), 5,6 which is the power of an atom in a molecule to attract electrons to itself.Although there seems to be a specific linear relationship between electronegativity and work function, 7 the former is the intrinsic physicochemical property of elements and all atoms have the same EN in pure single-or polycrystal metal, the latter is the physical property of solid materials that z E-mail: yysunzjut@outlook.comECS Advances, 2024 3 010503 is dependent on crystal structure, crystal face and contamination. 8hus, there is a lack of accuracy and certainty in the value for work function of metals when used to study the strength of surface chemically bonding with other species.The EN of each atom within the different crystal structure or crystal face are the same in pure single-or poly-crystal metals comparing to the work function, therefore, the EN might be more suitable to be used to study the strength of bond between H • radical and surface atom of metal.
In addition, the formation of a chemical bond is generally due to that unpaired electrons on reactants are desperate to be paired up again.Therefore, the valence electrons configuration (VEC), which is the electrons configuration on the outermost shell of metal atom, is also a primary physicochemical property for chemically bonding with other species.To gain a decisive insight into the intrinsic mechanism of chemically bonding two H • radicals on surface atoms of metal catalysts for the formation of H 2 molecule, here both physicochemical properties (EN and VEC) of transition metals are used to correlate the electrochemical behavior of metal electrodes during HER with its nature.
][11][12] Firstly, It is observed that with both partially filled s-orbitals (PFSO, there is an unpaired electron on s orbital) and partially filled dsuborbitals (PFDOs, there are one or more unpaired electrons on dsuborbitals), those elements with high EN can support higher log i 0,H values than metals with low EN (Fig. 2b).Similarly, the same behaviour is observed on the metals with just PFDOs (Fig. 2c).These observations suggest that the catalytic activity of transition metals is strong dependent on the electronegativity: metals with high EN can support high i 0,H for catalytic hydrogen evolution.
However, it seems not feasible that if we just consider that those metals with high EN will support high log i 0,H values for HER.In the case of transition metals in Group 11 and 12 (no or only one PFSO exposed on the surface of their atoms), all of them are unable to support high log i 0,H values, although most of them have high EN as showed in Fig. 2d.In particular, Gold with EN of 2.4, which is higher than almost all transition metals, but are unable to support a high log i 0,H value, which is identical to that supported on metals of Ag and Cu, and far lower than that supported by metals with two or more PFOs, such as Os, Ir, Ru, Rh and Pt.
In addition, in case of metals with the same of EN, we found that metals with two or more PFOs (there are at least two unpaired electrons on the outermost shell of an metal atom) can support higher log i 0,H values than metals with just one or no PFO.As showed in Fig. 2e, EN of Re, Co and Ni is 1.9, identical to that of Cu, Ag and Hg, yet, Re, Co and Ni can support higher log i 0,H values when compared with Cu, Ag and Hg.All these observations imply that besides EN, VEC of metal atoms is another the major factors for catalytic HER.Therefore, knowing the relationships between VEC of transition metal atom and its catalytic activity of HER may also be critical for completely understanding the mechanism of catalytic hydrogen evolution.
Furthermore, it is also noted that with the same EN, metals with PFSO and PFDOs can support higher log i 0,H values than those metals with just PFDOs.For instance, although the EN of metals of Pt, Rh, Os and Ir are the same (2.2), the log i 0,H values supported by Pt and Rh are higher than that supported by Os and Ir as showed in Fig. 2f.This indicates that metals with PFSO and PFDOs are more active as catalysts for HER than those metals just with PFDOs.To date, the reason on this difference is untouched in this area.
As suggested previously, two formed H • radicals (with a PFSO) from electron-transfer step might be in situ chemically bonded on active sites of catalysts to avoid free H • radicals reacting with H 2 O or other species during the process of catalytic hydrogen evolution.Therefore, if we assume that on the ground of above analysis, an active site of catalyst for catalytic HER must have an ability to link two H • radicals on its surface via orbital interactions-two H • radicals can be linked to an active site by interactions of PFSO on atomic hydrogen with PFSO and/or just PFDO on atom of catalyst, we can obtain an illuminating explanation of the difference of various metals for catalytic HER.
In discussing the high log i 0,H values are supported by the metals with high EN as shown in Figs.2b and 2c.It is our opinion that low EN leads to the orbital interactions between H • radicals and the surface atoms of metals too weak to occur, and high EN is essential to successful interactions.Thus, metals with low EN, such as Ta, Ti, Mn, W, Fe, Nb, Cr and Mo, are unable to bond two H • radicals on atom of their metal surface, this makes them difficult to support high log i 0,H value for HER.
As formation of one H 2 molecule requires two H • radicals, in our treatment two or more PFOs (unpaired electrons) accessible on an active site are essential to link two H • radicals via orbital interactions.Atomic valence orbitals of these elements (in Group 11 and 12) are fully occupied or only one partially occupied left, it might be, therefore, difficult that the surface atom of these metals chemically bonds two H • radicals via orbital interactions.Thus, all of them are unable to support higher log i 0,H values when compared with metals with two or more PFOs and high EN (Fig. 2d).With a higher EN (2.4) than Pt (2.2) and Co (1.9), a lack of two PFOs might be the primary factor that gold metal are unable to support higher log i 0,H value for HER.In addition, it seems understandable that with the same EN, a lack of two PFOs on their atoms makes Cu, Ag and Hg metals unable to support high log i 0,H value when compared with metals of Re, Co and Ni (Fig. 2e).
As observed previously and showed in Fig. 2f, with the same EN, the metals with both PFSO and PFDOs can support higher log i 0,H values than those with merely two or more PFDOs.It is known that the d-orbital on a sub-shell has multiple spatial orientations (

−
), we make here an assumption that this angular  dependence on the d-sub-orbitals has a significant impact on the catalytic behaviour.In metal, ratio of accessible valence d-suborbitals exposed on surface atom is different, part of them may be blocked by neighbouring atoms.We assume that an atom situated on the inner basal plane of surface of metal has only one of the outermost d-sub-orbitals accessible for orbital interaction.However, there are two or more valence d-sub-orbitals accessible when an atom is situated on the edge and corner sites.Hence, for those metals that only possess PFDOs, the maximum accessible PFDOs of the atoms situated on the inner basal plane is only one, this indicates that these sites can bond only one H • radical via orbital interactions, thus they are inactive for catalytic HER.The atoms situated on the edge and corner sites of crystal have a potential to expose two accessible PFDOs, might bond two H • radicals via orbital interactions and be active for catalytic HER.As a result, metals with just PFDOs may require to be made in nanoscale to exposure more the edge and corner for chemically bonding two H • radicals.As we discussed above, there might be one outermost d-suborbitals accessible when atoms lying on the inner basal plane.For metals possessed PFSO and PFDOs, as s-orbital is independent from the d-orbital and no angular dependence, the atoms lying on the inner basal plane might still expose two accessible PFOs (one PFDO and one PFSO).Thus, each surface atom of this type of metal can bond two H • radicals via orbital interactions and will be active for catalytic HER.Yet, for metals with just PFDOs, the atoms only situated on the edge and corner of crystal are active for catalytic hydrogen evolution.This might be the main reason that with the same EN, Pt and Rh metals can support higher log i 0,H values than Os and Ir (Fig. 2f).
There is no angular dependence on s-orbital, we assume that valence s-orbital is accessible whenever the atom situated on the inner basal plane of crystal or the edge and corner.It is our opinion, furthermore, that palladium ([Kr]4d 10 ), with an empty valence 5sorbital and high EN(2.2),have a potential to interact with two H • radicals via orbital interactions even if they are located on the inner basal plane of crystal, therefore, high log i 0,H value, identical to Pt metal, is experimentally supported by Pd catalyst as well in Fig. 2a (centre of figure, green colour).
In our treatments so for disclosed the relationship between difference of various metal catalysts and their catalytic properties for HER, the reaction process of producing a H 2 molecule from H + ions on various electrodes are left untouched.We shall try here to add some discussion on how the HER occurs on several typical electrodes.
We start with bare GCE without addition of catalysts.As the chemical inertness of GCE, H • radical probably is impossible to bond to its surface.We assume, therefore, that two free H • radicals are initially produced via electron-transfer steps, followed by a diffusion process to collide each other dimerizing to yield an H 2 molecule in the vicinity of bare GCE electrode in Fig. 3a.We also assume that the rate of H 2 production is governed by collision frequency of free H • radicals in this condition, the formation of one H 2 molecule requires a diffusion of a lot of free H • radicals for a successful collision, and free H • radicals in this diffusion process might react with other species causing low energy efficiency.
As we discussed above that an active site for catalytic HER has a potential to bond two H • radicals via orbital interactions.When it is assumed, in an effective catalytic HER, that two H • radicals formed from electron-transfer step are in situ bonded to one active site and then directly undergo a combination step to yield a H 2 molecule, the diffusion step of H • radicals is eliminated from the whole process and the reaction of H • radicals with H 2 O or other species is avoided as well, hence it can be expected that the formation of H 2 can take place with low energy losing.In Figs.3b and 3c, the new suggested mechanism of HER on active catalytic sites is illustrated.For metals with high EN and two PFOs (PFSO and PFDOs), represented by Pt, Rh and Ru, each atom on the crystal surface has potential to bond two H • radicals via orbitals interaction and is active for catalytic HER (Fig. 3b).Yet, for metals with high EN and two PFOs (just PFDOs), the atoms within inner basal plane of crystal might be impossible to bond two H • radicals via orbital interactions, only the edge and corner sites have a potential to achieve this for catalytic HER (Fig. 3c).Due to nanoscale particles exposed with a high ratio of the edge and corner sites, hence, those metals with high EN and just PFDOs, represented by Co, Ni, Os and Ir, might obtain a boosting rate of catalytic H 2 production when made within nanoscale.
As to the metals with low EN or with only one or no PFO, it might be difficult for the sites on the surface of crystal (neither sites of inner plan nor edge and corner sites) to bond two H • radicals via orbital interactions.Thus, the actual reaction process on these types of metals is identical to that on bare GCE, still requiring the diffusion of a lot of free H • radicals for formation of one H 2 molecule (Figs.3d and 3e).This might be attributed to the fact that these metals are unable to support high log i 0,H value for HER.

Conclusions
In present paper, we initially assume that on the analysis of HER occurring on electrode without addition of catalysts, the RD-step is radical-dimerization step.A diffusion of free H • radicals formed by electron-transfer step is involved in this step for H 2 molecule formation, this may lead to low rate of hydrogen evolution.In addition, the reaction of H • radicals with H 2 O or other species may occur during the process of diffusion, this might cause a losing of the energy.
To reveal the intrinsic property of transition metals as catalysts for improving the rate of HER and the efficiency of energy, we found that EN and VEC existed on the atom of metals exist a certain correlation with their catalytic behavior in the course of HER.It is assumed that there is a type of orbital interactions occurring between atomic hydrogen and the catalytic active atom, and this type of orbital interaction might be a type of covalent bond, the strength of which is strongly dependent on high EN of metals: bonding H • radical on surface atom of metal requires high EN on surface atoms.As the formation of one H 2 molecule requires two H • radicals, at least two accessible PFOs on a surface atom of metal are required as well.Two H • radicals are chemically bonded to an active site via orbital interactions as a transition state for supporting the formation of H 2 molecule, this can eliminate the diffusion step of H • radicals from the whole process and avoid the reaction of H • radicals with H 2 O or other species, making H 2 formed under a high rate of reaction and low losing of energy.Based on our assumptions, a new mechanism, which is different from previous proposed V-T and V-H mechanisms, is discussed for HER on various electrodes.Here we hope that our assumptions may be useful to some investigator in this research area.

Figure 1 .
Figure1.The previous proposed mechanism for catalytic HER: (a) Volmer-Tafel (V-T) process, hydrogen atoms formed by electron transfer were adsorbed on active atoms of the catalyst to form adsorbed H • radical, then followed by the combination of two adsorbed hydrogen atoms to produce H 2 molecule, (b) Volmer-Heyrovsky (V-H) process, one hydrogen atom formed by electron transfer was adsorbed on active atoms of the catalyst to form adsorbed H • , with a further electron transfer, then reacts with a solvated proton from the water layer to form a H 2 molecule.

Figure 2 .
Figure 2. (a) Selection of previous experimental values of exchange current density i 0,H for the electrolytic evolution of hydrogen on polycrystal metals.Here, the value of log i 0,H in acidic media were collected from previous literature, and reported by various authors for some metals.3,[9][10][11][12]The electronegativity was collected from literature.10 (b-c) those metals with high EN can support higher log i 0,H values than metals with low EN.(d) although most of metals in group 11 and 12 have high EN, they are unable to support higher log i 0,H values for HER, in particularly, Au with high EN (2.4) fails to support high log i 0,H value when compared with metals with two or more PFOs (e) With the same EN(1.9),Cu, Ag and Hg metals with only one or no PFOs are unable to support higher log i 0,H values than metals of Re, Co and Ni with two or more PFOs.(f) With the same EN(2.2),Pt and Rh with PFSO and PFDO(s) can support higher log i 0,H values for HER than Os and Ir with just PFDOs.

Figure 3 .
Figure 3.The reaction process proposed for HER in this work.The black arrow represents the process of new species formation, solid harpoon arrow represents electron movement and dashed harpoon arrow represents the diffusion process of H • radicals for H 2 formation.(a) solid black square represents conductive electrodes, H 2 is formed on electrode without addition of catalysts, involving diffusion of a lot of H • radicals after electron-transfer step, (b) green balls represent metals with high EN and two PFOs (PFSO and PFDOs), each surface site can in situ bond two H • radicals after electron-transfer step, and then directly forming a H 2 molecule from this type of bonding (c) pink balls represent metals with high EN and two PFOs (just PFDOs), only edge and corner sites can in situ bond two H • radicals after electron-transfer step for H 2 formation, sites in inner basal plane of crystal can bond only one H • radical and inactive for catalytic HER (d) blue balls represent metals with high EN and only one PFSO, surface atoms can bond only one H • radical, all surface sites are inactive for catalytic HER, H 2 formation involves a diffusion of a lot of H • radicals after electron-transfer step.(e) brown balls represent metals with low EN and/or no PFO, the reaction process is identical to (d) involving a diffusion of a lot of H • radicals after electron-transfer step for H 2 formation.