Hydrogen adsorption trends on various metal-doped Ni₂P surfaces for optimal catalyst design

Abstract

In this study, we looked at the hydrogen evolution reaction on Mg-, Mo-, Fe-, Co-, V-, and Cu-doped Ni₃P₂ and Ni₃P₂ + P terminated Ni₂P surfaces. The DFT calculated hydrogen adsorption free energy was employed as a predictor of the materials' catalytic HER activity. Our results indicate that doping can substantially improve the catalytic activity of the Ni₃P₂ terminated surface. In contrast, the Ni₃P₂ + P terminated one seems to be catalytically active irrespective of the type of doping, including in the absence of doping. Based on our doping energy and adsorption free energy calculations, the most promising dopants are iron and cobalt, whereas copper is less likely to function well as a doping element.

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1 Introduction

Due to the broad-ranging detrimental climate effects associated with the burning of fossil fuels, the impending rise in the global population, and the consequent increase in energy demand, the development of cleaner energy sources has become a top priority within the scientific community.^1–3 However, the intermittent nature of solar and wind energies means that an efficient storage system is required to realise their potential.^1,2 The absence of carbon emissions during conversion, high energy density, long-term storage capability, and flexibility of use both in mobile and stationary applications make hydrogen an appealing energy depository.⁴ One of the most promising candidates for large-scale hydrogen production is water-splitting through electrolysis, which enables the clean conversion of water into hydrogen and oxygen gases.^3,5

The hydrogen evolution reaction (HER) occurs at the cathode of a water-splitting cell, while the four-electron oxygen evolution reaction (OER) takes place at the anode. Hydrogen production through reduction (i.e., ) is a two-step process where two alternative reaction pathways are typically considered.⁶ Both pathways start with the Volmer reaction, where hydrogen adsorbs on a surface site symbolised by an asterisk *:

H⁺(aq) + e⁻ + * → *H. (1)

This is followed either by the Tafel reaction, where two surface-adsorbed hydrogens join together

*H + *H → H₂(g) + 2*, (2)

or by the Heyrovsky reaction, where the second proton arrives directly from the solution

*H + H⁺(aq) + e⁻ → H₂(g) + *. (3)

Reactions (1)–(3) summarise HER in acidic solutions.

Irrespective of the exact reaction mechanism, efficient catalysts are mandatory for turning the dream of a hydrogen energy economy into reality. While noble metals like Pt are some of the best HER catalysts, their high cost and scarcity hinder large-scale application.³ Thus, recent studies have looked at HER on various non-precious materials like heteroatom-doped nano-carbons,^7–10 together with nitrides, oxides, carbides, selenides, and sulfides of transition metals,⁷ which could replace platinum as the principal HER catalysts.

Compared to the other transition metal compounds, phosphides like MoP, CoP, and Ni₂P display HER activities on par with the best transition metal catalyst like MoS₂.^7,11–13 Generally speaking, phosphides possess advantages either in terms of synthesis routes or catalytic performance over the other classes of transition metal compounds. For example, MoS₂ needs to be nanostructured into nanosheets to yield catalytic properties comparable to MoP,^7,14 which can show high HER ability even in its bulk state.¹⁵ Particularly, nickel phosphide nanostructures like nanosheets and -particles have emerged as promising materials for HER catalysis under acidic conditions.^{7,11,12,16–18}

Chemical doping provides a novel way of enhancing the catalytic activity of many of the non-noble metal catalysts.⁷ In the case of Ni₂P, transition metal dopants such as Mo,¹⁹ Al,²⁰ Mn,²¹ W,²² and Fe^23,24 have been experimentally demonstrated to improve the HER activity. On the computational side, in our previous density functional theory (DFT) study of transition metal doping of a MoS₂ surface, we showed that the H-adsorption strength in the Volmer step depends on the microscopic structure of the surface and the nature of the dopant.²⁵ A similar result regarding the microscopic nature of the surface was observed in our computational study of aluminium doping on Ni₂P.²⁶

In this article, we expand our previous investigation of the impact of Al doping on the HER activity of Ni₂P²⁶ to include the dopants Mg, Mo, Fe, Co, V and Cu. As before, we focus on the two most stable Ni₂P surface terminations: Ni₃P₂ and phosphorised Ni₃P₂ + P.^27,28 We utilise the typical hydrogen adsorption free energy (ΔG_H) approach for HER activity, which has also been employed in previous Ni–P studies.^26,29 In this approach, ΔG_H on the electrode surface is used as a descriptor for predicting the catalytic activity with respect to a molecular H₂(g) reference.⁶ In line with Sabatier's principle, a value ΔG_H ≈ 0 indicates that the hydrogen neither binds too weakly nor too strongly to the surface, and corresponds to good HER activity.³⁰ As, for example, the choice of DFT functional affects the ΔG_H values,²⁶ following Greeley et al.³⁰ we consider sites with |ΔG_H| < 0.1 eV as optimal. Our primary goal is to understand how different dopants and doping induced surface structures impact HER activity and to suggest doping schemes that result in improved catalysts.

2 Systems and methods

2.1 Computational details

All our DFT calculations utilised the QUICKSTEP module³¹ of the publicly available CP2K simulation suite.³² The package employs the hybrid Gaussian/plane wave method where the wave functions are represented in a Gaussian-type basis and an auxiliary plane-wave basis is used for the electronic density. As in our previous Ni₂P and MoS₂ studies,^25,26 the Perdew–Burke–Ernzerhof (PBE) functional³³ was used with the Kohn–Sham orbitals expanded in the molecularly-optimised double-valence polarised basis set (MOLOPT-SR-DZVP) and the core electrons represented by the Goedecker–Teter–Hutter pseudopotentials (GTH).^34–36 In all calculations, the plane-wave kinetic energy cut-off was set to 700 Ry and the cutoff for the reference grid to 60 Ry. The force convergence criterion of the geometry optimisations was left to its default value of 0.023 eV Å⁻¹. The Poisson equation for the electrostatic potential was solved with periodic boundary conditions.

The Ni₂P bulk lattice parameters were taken from our previous study,²⁶ where a supercell of 4 × 4 × 4 unit cells was allowed to relax under a 0.1 kbar pressure tolerance. The system relaxed to a nonferromagnetic state with cell parameters a = b = 5.860 Å and c = 3.332 Å. For the calculation of the atomic reference energies of Ni, Mg, Mo, Fe, Co, Cu, and V in the crystalline phase, we employed a supercell of 10 × 10 × 10 units with the PBE lattice parameters taken from the literature.^37–40 Our original Ni₂P calculation employed the orbital transformation method, whereas in the reference energy calculation the diagonalisation method was used with the Fermi temperature set to 75 K. The effect of increasing this temperature to 300 and 400 K was studied but the impact on the energy/atom was less than 0.02 eV in all cases.

Our surface calculations used the same diagonalisation method with a 75 K electronic smearing but included the Grimme D3(BJ) dispersion corrections.^41,42 Of the different surface structures for Ni₂P, we focused on the Ni₃P₂ termination of the (0001) surface because it is the preferred bulk-like termination in the Ni₂P stability region.^27,43 At around pH = 0, which corresponds to the typical experimental conditions for HER in acid, this surface phase dominates at potentials U > −0.21 V vs. the standard hydrogen electrode.²⁸ Below this region, there is both experimental and computational evidence that the surface becomes enriched by phosphorus.^{27,28,44–49} Specifically, the Ni₃P₂ + P termination predominates within the potential region −0.21 V ≥ U ≥ −0.36 V, whereas below this range the pristine Ni₃P₂ surface becomes passivated by H atoms on the Ni₃ hollow sites.²⁸ Hence, both Ni₃P₂ and Ni₃P₂ + P surfaces were included in this study.

Based on our previous hydrogen adsorption free energy test calculations on 5, 7, 9, 11, and 13 layer slabs,²⁶ we modelled our two surfaces with a seven layers deep symmetric slab where the atoms at the bottom layer were fixed to their bulk positions. At least a 10 Å wide vacuum layer was used on both sides of the slab. For Ni₃P₂ + P, the extra phosphorus atom was added to the Ni₃ hollow site of the Ni₃P₂ structure, as depicted in Fig. 1. In both cases, 5 × 5 × 1 Monkhorst–Pack k-points were utilised.

Fig. 1 A surface representation of the Ni₃P₂ and Ni₃P₂ + P terminations of Ni₂P. In this and all remaining figures, the hydrogen atoms are indicated by white, the phosphorus atoms by yellow-brown, the Ni atoms by deep blue, and the metal atoms by teal. The phosphorus adatom is marked by P_ad.

2.2 HER activity model

Our analysis of the H-coverage and differential Gibbs free energies of the H-adsorption followed the self-consistent scheme proposed by Nørskov et al.⁶ and Skúlason et al.⁵⁰ According to this scheme, the relevant H coverage at a particular chemical potential μ is determined by the minimum of the total adsorption energy Δ_totG_H(n):

Δ_totG_H(n) = G(n) − G(0) − nμ (4)

where G(n) is the free energy of the surface with n hydrogen atoms attached and G(0) is the free energy of the bare surface. The chemical potential of hydrogen is given by²⁹where G(H₂) is the free energy of molecular hydrogen in the gas phase and U is the cathode potential. For comparison of different adsorption sites, the differential Gibbs free energy of adsorption

ΔG_H(n) = G(n) − G(n − 1) − μ, (6)

plays a crucial role. By using a factor of 0.24 eV to account for all the differences in entropic and zero-point energy contributions between the products and reactants at pH = 0,^6,29,51 this equation simplifies intowhere E(n) is the total energy at 0 K with n hydrogen atoms attached to the surface. It is directly obtained from DFT calculations. The minimum overpotential to adsorb hydrogen at a given H coverage n iswhere the minimum is taken over the different surface sites studied. In our calculations, we used a set of 14 initial positions for the hydrogen above the slab. Because our previous test calculations for charged pristine and Al-doped surfaces failed to show any charge trapping,²⁶ we consider only the neutral states in this article, i.e., where U = 0 V.

3 Results and discussion

As illustrated in Fig. 2, the Ni₃P₂ terminated Ni₂P surface has alternating Ni₃P₂ and Ni₃P layers.^52,53 The dopant atoms were restricted to the top four layers. To identify the different doping schemes, the notation lxdy is used where x is the layer of the dopant atoms (i.e. x ∈ {1, 2, 3, 4}) and y is their number (i.e. y ∈ {1, 2, 3}). In cases where dopants were present in two layers, we employ the simpler notation lx₁lx₂, where x₁ and x₂ tell the layers of the two dopant atoms, respectively, since we only investigated cases with one dopant atom per layer.

Fig. 2 The slab model for the Ni₃P₂ and Ni₃P₂ + P terminated Ni₂P surface. In the figure, the third layer is doped by a single metal atom which corresponds to an l3d1 doping scheme.

3.1 Doping energies

Ni₃P₂ termination. The doping energies for the Ni₃P₂ termination of Ni₂P are shown in Fig. 3. As can be seen, regardless of layer, most metals show a linear trend as the number of dopants in the layer increases. For Co this trend is always strongly negative, implying that thermodynamically the lattice structure is very susceptible to cobalt doping, due to it's high reactivity and comparable size to Ni. In contrast, the doping energy is always positive for the less reactive Cu. For other dopants, the sign and steepness of the slope depend on the layer. For V and Mo, the doping energies are positive or near zero and generally increase with increasing number of dopants for the 1st and 3rd layers, and negative and decreasing for the 2nd and 4th layers. In contrast, for iron, the doping energies are positive and increasing only for the first layer and then negative and decreasing for the other three.

Fig. 3 Doping energies (E_F) for Mg, V, Fe, Co, Cu, and Mo for the four topmost layers of the Ni₃P₂ termination of Ni₂P.

The large deviations from linear behaviour for Mo and Mg in the third layer are accompanied by radical surface reconstructions. For example, in the double and triple doping for Mg and the triple doping in Mo, one of the P atoms moves away from the third Ni₃P₂ layer, creating a vacancy and a surface structure that resembles the Ni₃P₂ + P one. In most cases, the introduction of dopants causes no substantial changes in geometry. For Fe and Co, it results in a slight contraction of the slab with the magnitude generally depending on the number of dopants, and for the other metals a slight expansion. Interestingly, for first layer Mg doping, the Mg atoms lift up from the surface, staying more than 0.6 Å above the corresponding Ni atoms. Similarly, for the triple Mo doping of the first layer, the atoms of the two topmost layers of the Ni₂P surface lift up from the surface, while the P atom from the first layer moves down to the second one.

Ni₃P₂ + P termination. The doping energies for the Ni₃P₂ + P termination are shown in Fig. 4. As in Fig. 3, most energies behave linearly with respect to increasing number of dopant atoms within a given layer. The clearest trends are observed for Cu and Co. In the case of Cu the formation energy of the doped lattice is always positive and increases with the number of dopant atoms. For Co, the energies are always strongly negative and decrease with the number of dopants. As before, in some cases like l3d3 for Mo, significant deviation from linear behaviour is observed due to radical restructuring of the surface.

Fig. 4 Doping energies (E_F) for Mg, V, Fe, Co, Cu, and Mo for the four topmost layers of the Ni₃P₂ + P termination of Ni₂P.

Comparing the linear trends of different dopants in Fig. 3 and 4, one sees that for Mo, V, Co, and Fe the doping energies are higher for the first layer for Ni₃P₂ termination whereas for Cu, and Mg the energies are lower. Unsurprisingly, in the lower layers, the doping energies are similar. Based on the figures, we predict that Ni₂P should be readily dopable by Co, Fe, V, Mg, and Mo. In contrast, for Cu, the doping is clearly energetically unfavourable in all cases, and according to our test calculations inserting two Cu atoms to different layers does not remedy the situation.

3.2 Hydrogen adsorption free energies

Ni₃P₂ termination. The hydrogen adsorption free energies predicted with eqn (7) are summarised in Fig. 5 for the Ni₃P₂ terminated Ni₂P. The full data is provided in pictorial form in the ESI.† In the calculations, first one hydrogen was placed in one of fourteen random locations above the surface, as described in Section 2.2. The lowest adsorption free energies from these calculations are shown as black triangles in Fig. 5, and with the exception of the l2d3-doped Mg, these lie clearly below the optimal range of ±0.1 eV.

Fig. 5 Hydrogen adsorption free energies (ΔG_H) for Mg-, V-, Fe-, Co-, Cu-, and Mo-doped Ni₃P₂ terminated Ni₂P. The triangles indicate ΔG_H values for the first hydrogen adsorption, whereas the squares signify ΔG_H values for the second hydrogen adsorption. The deep yellow band highlights the ±0.1 eV region around the optimal ΔG_H = 0 value.

Aligned with previous studies on pristine and Al-doped Ni₃P₂ surfaces,^26,28,54 we find a strongly binding Ni₃-hollow site together with a number of more weakly binding sites. In most studied surfaces, the first hydrogen is found in the Ni₃ deep site with the exception of Mg where it is located on the Ni–Ni bridge of the Ni₃ site. In these three bridge configurations, the closer the hydrogen is to the centre of the Ni₃ site (or in the case of Mg (l1d1) the Ni₂Mg site) the lower the ΔG_H-value. In addition to the Mg-doped cases, also the l1d2 Co doping had the hydrogen localise to a Co–Co bridge site for the lowest free energy configuration. As the H also moved towards the Ni-atoms from the centre of the Ni₃ site for the l1d1 doping with Cu and Mo, we conclude that the prevalent adsorption pattern of H on the strongly binding Ni₃ hollow site is most perturbed by substitutional doping of the first layer, at least in low doping conditions. This is in agreement with the results of Hakala and Laasonen who observed that low Al doping of the surface layer effectively weakened the hollow site's binding energy, resulting in H coordination by just two Ni atoms.²⁶

Recently, Wexler et al.⁵⁵ were able to show that the effect of nonmetal surface doping of the P atoms surrounding the Ni₃ site on a Ni₃P₂ surface can be explained through a chemical pressure-like effect.⁵⁶ Consequently, the hollow site Ni–Ni bond length works as a good predictor of the ΔG_H value. We also looked at the correlation between these two quantities, but it was not significant in our data, likely because the electronic character of the dopants is more significant at least in the first layer, where the Ni atoms of the hollow site are directly substituted.

The coloured squares in Fig. 5 represent the best, i.e., closest to zero ΔG_H values for the second hydrogen adsorption with the H-atom corresponding to the lowest adsorption free energy already on the surface. The colour indicates the number of geometrically different sites that fall into the ideal ΔG_H-region. We see that for the Ni₃P₂ termination, Fe and Co doping seems to be particularly effective with plenty of sites in the optimal region for the tested doping schemes. These findings agree with the experimental results on the activating effects of Fe doping.^23,24 In concordance with the predictions of the doping energies of Fig. 3, Cu seems to be rather ineffective as a catalyst while the rest of the studied dopants fall somewhere in between. Looking at the V (l4d1) and Mg (l2l4) cases, one sees that inserting dopants to the fourth layer has minimal impact on the adsorption energies. Unsurprisingly, the doping effects on the adsorption free energies generally increase when one moves from the third layer to the second and first ones.

As for the first hydrogen, a number of different adsorption patterns were observed for the second hydrogen. In most cases, the initial hydrogen occupied the hollow Ni₃ site whereas the second hydrogen was located on a nearby Ni–P bridge site. This bonding pattern agrees with the findings of Liu and Rodriguez⁵⁴ for the pristine surface. For Mo- and Mg-doped materials showing ideal sites, both hydrogens were located on bridges. In the l1d2-doped Co, we also encountered an energetically favourable configuration where a hydrogen molecule was formed on top of one of the surface Co atoms. The different bonding patterns are illustrated in Fig. 6 for Co (l1d2).

Fig. 6 Sample hydrogen adsorption patterns observed in the Co (l1d2) surface: (A) H₂ formation, (B) Co–Co and Co–P bridge site hydrogens, and (C) Co₂Ni hollow site and Co–P bridge site hydrogens.

Because Hakala and Laasonen²⁶ found that increasing the supercell surface area did not impact the H-adsorption energies, its effect was not investigated in this study. They also tested how changing the PBE functional to RPBE⁵⁷ and turning off the van der Waals interaction affected the ΔG_H values, and found that while the RPBE slightly weakened H binding, the effect of the van der Waals correction was minuscule.²⁶

Ni₃P₂ + P termination. Analogously to Fig. 5, the ΔG_H values for the Ni₃P₂ + P terminated Ni₂P are summarised in Fig. 7. In addition to the first and second hydrogen adsorptions depicted by triangles and squares, respectively, for calculations where the second hydrogen adsorption energy was lower than or very similar to the first ΔG_H, free energy values for a third hydrogen adsorption were also calculated. These calculations are indicated by circles and are in all cases with the exception of Fe (l1d3) clearly higher in energy than the other two. Again, for the optimal hydrogen adsorption, i.e., the one with ΔG_H values closest to 0, colours are used to indicate the number of distinct adsorption patterns within the optimal energy region. In cases like Co (l1d1), where all the first H adsorption free energies are above −0.1 eV and some of the ΔG_H values for the second H adsorption lie within the optimal ±0.1 range, the coloured symbol is reserved for the adsorption with the larger number of distinct adsorption patterns within the optimal region. As before, it indicates the best free energy value. Finally, the black symbols correspond to the lowest ΔG_H value obtained from the 14 geometry optimisations.

Fig. 7 Hydrogen adsorption free energies (ΔG_H) for Mg-, V-, Fe-, Co-, Cu-, and Mo-doped Ni₃P₂ + P terminated Ni₂P. The triangles indicate ΔG_H values for the first hydrogen adsorption, the squares signify ΔG_H values for the second hydrogen adsorption, and the circles show ΔG_H values for the third hydrogen adsorption. The deep yellow band highlights the ±0.1 eV region around the optimal ΔG_H = 0 value.

Because the strongly binding Ni₃ site is occupied by the P adatom in Ni₃P₂ + P, for some doping schemes in Fig. 7, the first hydrogen adsorption already results in the best observed ΔG_H value as indicated by the coloured triangle. Within the accuracy of the DFT calculations, this agrees with the pristine Ni₃P₂ + P results indicated by the dashed lines and implies that the surface hydrogen coverage is often lower for this termination.

As expected, doping of the fourth layer in V (l4d1) has virtually no effect on the ΔG_H values when compared to the pristine case. Following the trends found in Fig. 5, doping of the Ni atoms in layer 3 generally impacts the adsorption free energies less than doping at the second or first layers, although the effects become large also at the third layer when the number of dopants increases. Most studied systems in Fig. 7 have adsorption energies within the optimal range, indicating that the P adatom leads to surface activation, again in agreement with the pristine case. There does not seem to be a clearly superior candidate for doping material for the Ni₃P₂ + P termination. Rather, all the systems function roughly on par with the undoped surface within the optimal region.

In terms of the adsorption geometries for the optimal sites, only the first layer l1d3 Mg doping that is accompanied by a surface reconstruction possesses more than 2 geometrically different active sites for the 1st H adsorption within the energetically optimal region. In most cases, the hydrogen is located on top of the P adatom but in some cases, like V (l2d1) also adsorption on the Ni atoms surrounding the P adatom is observed. With 2 hydrogens adsorbed on the surface, typically at least one of them is located on top of the P adatom. Often, such as in Co (l2d2), both hydrogens are on top of the P adatom, but are oriented in symmetrically non-equivalent directions as illustrated in Fig. 8 for Co (l2d2). Similarly to Wexler et al.²⁸ and Hakala et al.,²⁶ we find that the P adatom can adsorb up to three hydrogens. However, in all cases where hydrogen adsorption of three hydrogens was considered, spontaneous H₂ formation was also observed during some of the geometry optimisations, underlining the high reactivity of these surfaces.

Fig. 8 Sample hydrogen adsorption patterns observed in the Co (l2d2) surface: (A) Hydrogens on top P adatom and (B) hydrogens on top P adatom with different orientation.

4 Conclusions

In this study, we have looked at HER on metal-doped Ni₃P₂ and Ni₃P₂ + P terminated Ni₂P surfaces. The catalytic HER activity of the studied materials was predicted through DFT calculations by using the hydrogen adsorption free energy as a predictor following the self-consistent scheme proposed by Nørskov et al.⁶ and Skúlason et al.⁵⁰ Our calculations indicate that doping can substantially improve the catalytic activity of the Ni₃P₂ terminated Ni₂P surface, in agreement with experimental studies. Particularly iron and cobalt emerged as promising dopants. In contrast, the Ni₃P₂ + P termination seems to be catalytically active irrespective of the type of doping and even in the absence of doping.

In addition to the ΔG_H values, we also looked at the formation energies of the doped materials to investigate their stability. We predict that the surface should be readily dopable by Co and Fe, for example, whereas for Cu all the energies were unfavourable. Based on our results, the most promising candidates for doping material are iron and cobalt, whereas copper is less likely to function well as a dopant. The rest of the studied metals, V, Mg, and Mo, are predicted to be roughly equal in their applicability.

For the doping geometries, in most cases on Ni₃P₂ the first hydrogen is adsorbed to the strongly binding Ni₃ hollow site, although in some cases it preferred a bridge site on the hollow's edge. In Ni₃P₂ + P, the Ni₃-site is filled by a P adatom. Consequently, for the second hydrogen in the Ni₃P₂ case and the first, second, and third hydrogen adsorptions in the Ni₃P₂ + P case, a number of highly active geometrical arrangements were identified with large variations between dopants and doping schemes. In line with previous studies, we find that the P adatom can adsorb up to three hydrogens. However, spontaneous H₂ formation was observed during some of the geometry optimisations in all adsorption calculations involving three hydrogens, which underscores the high reactivity of the Ni₃P₂ + P surfaces.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The work was supported by the European Union's Horizon 2020 research and innovation programme (CritCat Project, grant agreement no. 686053). We are grateful for the generous computing resources from CSC – IT Center for Scientific Computing including the Grand Challenge project CritCat.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c8cp06143b

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