TiO₂-coated rutile oxide catalysts for acidic oxygen evolution: a design principle

Abstract

Green hydrogen production through water electrolysis under acidic conditions is limited by the efficiency of the anodic oxygen evolution reaction (OER). In this study, we outline a design principle for developing active and potentially stable rutile oxide electrocatalysts for acidic OER. Using density functional theory, we find that the adsorption energies for Ti, Sn, and Zr active sites correlate with the position of the Fermi level relative to the oxygen 2s states as the surrounding oxide composition is varied. This trend is not observed for platinum-group elements. We attribute this difference to the inability of Ti, Sn, and Zr active sites to access oxidation states above the 4+ of the rutile structure, according to changes in geometry and charge. Ti emerges as an adsorption site of special interest, since varying the composition of the surrounding rutile oxide allows titanium sites to reach theoretical overpotentials as low as 0.14 V. We then demonstrate tunable activity for TiO₂-coated conductive rutile substrates. Based on literature evidence that TiO₂ coatings improve stability under acidic OER conditions without substantially compromising activity, we suggest that a TiO₂ overlayer can serve as both an active site and corrosion protection. We propose a composition-based model that successfully finds Ir and Ru free compositions (W_xPt_1−xO₂, W_0.46Pd_0.54O₂) that can activate the applied TiO₂ overlayer.

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Broader context

Proton-exchange membrane water electrolysers offer significant advantages over alkaline water electrolysers in the production of green hydrogen, including higher current densities, a high-purity hydrogen gas and a compact device design. As catalysts for the anodic oxygen evolution reaction (OER), oxides based on Ir offer the best compromise between activity and stability, however, the scarcity of Ir limits the industrial scalability of this technology. Earth-abundant alternatives are usually either active but unstable under acidic conditions, or stable but not sufficiently active. This work outlines a design principle for the fabrication of active and stable TiO₂-coated rutile oxide catalysts for the acidic OER. Our calculations demonstrate that the activity of a Ti site correlates with the position of the Fermi level of the surrounding oxide. By choosing the right surrounding oxide composition, Ti sites can be activated to achieve low OER overpotential. The same principle is found to apply for TiO₂ overlayer(s) which can then act as both active site and corrosion protection. The Fermi level energy of the host oxide can be predicted based on the composition, making it possible to construct Ir- and Ru-free catalysts with predicted high OER activity.

Introduction

Practical strategies for storing electricity from renewable energy sources, e.g. in the form of chemical fuels, are crucial to reduce dependence on fossil fuels. Molecular hydrogen is a suitable fuel in this context, since it can be efficiently generated through water electrolysis (WE).¹ Alkaline WE is a well-established technology relying on transition metal based catalysts,^2,3 however proton exchange membrane water electrolysis (PEMWE), which operates under acidic conditions, offers several advantages over the alkaline setup, including higher current densities, purer product gas and more compact devices.⁴ The oxygen evolution reaction (OER), occurring at the anode, is recognised as the kinetic bottleneck in both alkaline and acidic water electrolysis.⁵ The limitation arises because the OER consists of four proton-coupled electron transfer steps, e.g. for the conventionally assumed adsorbate evolution mechanism (AEM, see Section S1 in the SI for illustration):

* + H₂O(l) → *OH + H⁺ + e⁻ (1)

ΔG₁ = ΔG_*OH − eU_RHE

*OH → *O + H⁺ + e⁻ (2)

ΔG₂ = ΔG_*O − ΔG_*OH − eU_RHE

*O + H₂O(l) → *OOH + H⁺ + e⁻ (3)

ΔG₃ = ΔG_*OOH − ΔG_*O − eU_RHE

*OOH → * + O₂(g) + H⁺ + e⁻ (4)

ΔG₄ = ΔG_O2 − ΔG_*OOH − eU_RHE

where * denotes the active site and U_RHE is the potential of the electrode relative to the reversible hydrogen electrode (RHE). Ideally, the free energy of all four steps (ΔG₁, ΔG₂, ΔG₃, and ΔG₄) should be equal to the thermodynamic potential of 1.23 V, but in practice the universal scaling relations relate the adsorption free energies of *OH and *OOH (ΔG_*OOH ≈ ΔG_*OH + 3.2 eV), which implies that a minimum potential of 1.6 V must be applied for all steps to have a negative free energy.^6,7

Within this limitation, oxides based on Ir and Ru are the most efficient catalysts for acidic OER.^8–14 IrO₂ is less active than RuO₂, but IrO₂ is substantially more stable.^8,10 Both IrO₂ and RuO₂ are metallic conductors,¹⁵ facilitating electron transport in the anode catalyst and offering low electronic resistance. However, the low abundance of Ir and Ru precludes industrial upscaling of this technology.¹⁶ Materials based on earth-abundant elements are usually either stable but inert or active but unstable under acidic OER conditions. Research on catalysts based on earth-abundant elements has therefore often followed one of two approaches: activating stable materials or stabilising active materials.^17,18

Stable materials that are based on low-cost elements have been doped to enhance their OER activity. For example, TiO₂ is stable in acid,¹⁹ but it is a poor OER catalyst because it is a semiconductor.²⁰ Both experimental and theoretical studies have demonstrated that the catalytic activity can be enhanced by doping.^21–24 The dopant introduces new states in the band gap, which determine the Fermi level. In particular, introducing one or two subsurface layers of SrRuO₃ into inert SrTiO₃ enhanced the experimentally measured OER activity under alkaline conditions, which was attributed to new electronic states introduced by the dopant.²⁵ In a later computational study, this concept was extended by introducing a single subsurface layer of different transition metals into SrTiO₃, SrZrO₃, TiO₂, and ZrO₂, and a correlation between the Fermi level and catalytic activity was established.²⁶ Since the catalytic activity is influenced by the energy position of the dopant states in the band gap, it is desirable to be able to tune these states, which is difficult to achieve with a single dopant. Co-doping with both n-type (electron-donor) and p-type (electron-acceptor) dopants has therefore been investigated, demonstrating that the OER activity of TiO₂ and SrTiO₃ can be tuned.^20,21 As an extreme case of the co-doping strategy, Ti atoms incorporated in a conducting high-entropy oxide (HEO), i.e. an oxide containing five different metals, were theoretically predicted to be highly active.²⁷

Protecting active but unstable catalysts by coating or enriching them with a stable oxide such as TiO₂ is an alternative strategy for improving catalyst performance. Dimensionally stable anodes (DSAs), used in the commercial production of chlorine, employ this strategy.²⁸ DSAs consist of a mixture of active precious-metal oxides such as RuO₂ and IrO₂, together with TiO₂, which offers stability. Such mixtures have therefore been extensively studied, and it has been shown that the formation of an ultrathin TiO₂ coating on oxide nanoparticles consisting of Ru, Ti, and Nb resulted in improved stability during chlorine evolution.²⁹ Thin TiO₂ coatings have also been formed on active catalysts such as MnO₂ and Co₃O₄, resulting in improved stability without significant loss of activity.^30,31 Such coatings can be readily made by atomic layer deposition (ALD),^30,32 thermal diffusion,²⁹ sputter deposition,³¹ and electrodeposition.³³

The catalytic activity for OER on oxides can be estimated computationally by calculating the free energies of the individual steps along the reaction pathway (eqn (1)–(4)). Correlations between catalytic activity and the adsorption energies of reaction intermediates are often represented by volcano plots.^34,35 In particular, ΔG₂ has been proposed as a universal descriptor of OER activity.⁷ It is attractive to relate these adsorption energies to electronic properties of the material to provide an understanding of the adsorption process and reduce the effort required to predict the catalytic activity of new materials.³⁶ A range of electronic descriptors have been widely studied in the literature, inspired by the success of the d-band model from Hammer and Nørskov. They showed that the binding energy on metal surfaces is linearly dependent on the energy difference between the center of the metal d-band and the Fermi level of the material.^37,38 This approach has been less successful in describing the adsorption energies on oxides. In contrast, the positions of the O_2p band, t_2g band, the occupancy of the e_g orbital, and the vacuum level relative to the Fermi level have all been identified as alternative descriptors for different systems.^{22,26,39–43}

Here, guided by the fundamental ideas from these previous efforts, we outline a new design principle for developing active and potentially stable electrocatalysts for the OER under acidic conditions. We first study Ru, Rh, Ir, Os, Pd, Pt, Ti, Sn, and Zr “guest” atoms substituted at surface sites in rutile oxide slabs (“host”) with a range of element compositions. Using density functional theory (DFT), we show how the adsorption energies of *OH and *O intermediates on these guest sites change as the host composition, and therefore its Fermi level, is varied. For Ti, Sn, and Zr guests, the adsorption energies show a pronounced variation that correlates with the host Fermi level, whereas Ru, Rh, Pd, Pt, Os, and Ir guests show only low variations, which are independent of the Fermi level. By studying changes in the geometry and the charge at the adsorption site, we show that this difference is related to the inability of the Ti, Sn, and Zr guest elements to access oxidation states higher than the 4+ oxidation state of the rutile structure. Ti is particularly interesting, as it spans binding energies corresponding to OER overpotentials as low as 0.14 V. Motivated by this, we further extend the concept from single Ti sites to TiO₂ overlayers applied as coatings on conductive rutile oxides (substrates). The overpotentials on TiO₂ overlayers coating substrates of various compositions showed trends similar to those for single Ti sites. Finally, we show that a simple linear model can successfully predict the Fermi level of the TiO₂-coated system from the composition of the underlying substrate oxide. Thus, substrate oxides with a Fermi level that optimally activates the TiO₂ overlayer for the OER can be designed from combinations of metal oxides that are not necessarily active or stable by themselves, making it possible to avoid Ru and Ir entirely. As an example, our model accurately predicts W_xPt_1−xO₂ and W_0.46Pd_0.54O₂ substrate compositions that, when coated with TiO₂, exhibit calculated OER overpotentials as low as 0.39 V.

Methodology

DFT (cf. Section S2 in the SI for computational details) is used to calculate the adsorption energies of the reaction intermediates *OH, *O + Hb, *O, *OOH, *O₂ + Hb, and O₂(g) + Hb, where Hb is a hydrogen atom adsorbed on a bridging oxygen atom adjacent to the adsorption site (*). These calculations are carried out for a range of adsorption site elements (guests) and surrounding oxide compositions (hosts), as illustrated in Fig. 1a. More specifically, Ru, Rh, Ir, Os, Pd, Pt, Ti, Sn, and Zr have been considered as guests, while both pure oxides of these elements (except for ZrO₂, which does not have a rutile polymorph),^44,45 and high entropy oxides have been employed as hosts. More details and structural illustrations of this dataset are provided in Sections S2 and S4 of the SI.

Fig. 1 (a) Schematic representation of the host–guest data, illustrating the two parts of the structure; the element of the adsorption site (guest) and the composition of the surroundings (host). Ru, Rh, Ir, Os, Pd, Pt, Ti, Sn, and Zr were studied as guests. For the host compositions, pure rutile oxides of these elements (except for ZrO₂) along with high entropy oxides were examined. (b) Top and side view of the rutile (110) surface model utilised in this study. (c) Illustration of of the Fermi level calculated by DFT (E_Fermi,DFT), relative to the oxygen 2s band on the DOS of pure RuO₂. The blue line corresponds to the E_Fermi,DFT, the red peak corresponds to the projected DOS of the oxygen 2s band of the oxygen atoms, and the black dashed line corresponds to the centroid of this band (E_center,O2s). Occupied levels are shaded.

We focus on the (110) surfaces of rutile structures because RuO₂, IrO₂, RhO₂, OsO₂, PdO₂, PtO₂, SnO₂, and TiO₂ are all known to form a rutile polymorph.^15,46,47 Rutile is the preferred crystal structure for TiO₂,⁴⁸ RuO₂, IrO₂, OsO₂,⁴⁹ and SnO₂,⁵⁰ under standard conditions. PtO₂ prefers a distorted rutile structure,⁵¹ rutile RhO₂ is possibly only a high-pressure phase,⁵² while PdO₂ appears to have been synthesised by only one group and is unstable under standard conditions.⁴⁷ The (110) surface is the rutile facet that preserves the highest coordination number for surface atoms, and for TiO₂ it is calculated to have the lowest surface energy.⁵³ Furthermore, corrosion measurements on RuO₂ single crystals⁵⁴ and IrO₂ crystalline films⁵⁵ demonstrate low dissolution rates from the (110) facets, which indicate increased stability compared to other facets.

In our analysis, we included previously published adsorption energies for *O and *OH on the rutile (110) surface of near-equimolar HEOs consisting of Ru, Ti, Ir, Os and Rh (details about the HEOs dataset are provided in Sections S3 and S4 in the SI).²⁷ Similar HEOs in the IrOsPdPtRu, IrOsPtRhRu, AuOsPdPtRu, and AuIrOsPdPtReRhRu composition spaces have been prepared as nanoparticles using microwave solvothermal synthesis, and their OER activities were studied under acidic conditions.⁵⁶

The surface model (Fig. 1b) consists of three coordinatively unsaturated sites (cus). One of these is the adsorption site and the other two are either bare or occupied with a pre-adsorbed oxygen, depending on the O* affinity of the adsorbing metal element (details are provided in Section S2 in the SI).

The adsorption free energies of the catalytic intermediates (ΔG_intermediate) are calculated as:

ΔG_intermediate = ΔE_DFT + ΔZPE − TΔS (5)

where ΔE_DFT is the DFT calculated adsorption energy (computational details are provided in Section S2 in the SI), ΔZPE and TΔS account for changes in zero-point energy and entropy upon adsorption, respectively, and are taken from ref. 6. From the adsorption free energies, we can then calculate ΔG₁, ΔG₂, ΔG₃, and ΔG₄ at U_RHE = 0 V and employ the computational hydrogen electrode (CHE)³⁵ to evaluate the overpotential, η:⁵⁷η represents the additional potential beyond the thermodynamic 1.23 V that is required to make all four reaction steps thermodynamically downhill (ΔG_i ≤ 0). We plot −η such that higher positions on the volcano correspond to lower overpotentials (higher activity).

As a descriptor for the adsorption free energies, we investigate the Fermi level, which was previously observed to correlate with the adsorption energies of OER intermediates for doped SrTiO₃ and TiO₂.²⁶ In that study, the vacuum level was used as a reference to compare DFT-calculated Fermi levels (E_Fermi,DFT) across different oxides; here, we adopt the approach in ref. 58, where E_Fermi,DFT values are aligned using a sharp low-energy peak in the density of states (DOS) as a reference. In our case the oxygen 2s band centroid (E_center,O2s) is used as the reference point, because it is common to systems studied, lies at relatively low energies (approximately −18 eV), and generally exhibits a sharp, non-interacting peak as illustrated in Fig. 1c for RuO₂ (see Section S5 in the SI for the DOS of all pure oxides studied). In the case of RuO₂, the E_Fermi,DFT relative to the oxygen 2s band center is 18.6 eV (E_Fermi,RuO2) and we use this value to normalise the Fermi level energies of all systems in this study

E_Fermi = [E_Fermi,DFT − E_center,O2s] −E_Fermi,RuO2 (7)

All the E_Fermi are calculated on the bare surface of each structure.

In addition to the host–guest dataset described above, we studied TiO₂ overlayers applied as coatings on conductive rutile oxides (substrates). We modelled pure RuO₂, RhO₂, IrO₂, OsO₂, PdO₂, and PtO₂ substrates, as well as substrates containing 89%, 78%, and 56% of each oxide, with the remainder being a random mixture of the other five oxides. To study the effect of increasing the coating thickness, the substrate oxides were investigated with both one and two TiO₂ overlayers. We also studied TiO₂-coated rutiles of W_xPt_1−xO₂ (W = tungsten, x = 0.04, 0.08, 0.12, 0.17, 0.21, and WO₂) and W_0.46Pd_0.54O₂, as Ir and Ru free OER candidates. For each W_xPt_1−xO₂ composition, we construct two distinct rutile slabs covered with one TiO₂ overlayer and calculate adsorption energies at all six Ti cus sites. The lattice constants of all TiO₂-coated doped structures were set to the composition weighted averages of the lattice parameters of the constituent pure oxides. More details on the TiO₂-coated dataset are provided in Sections S2 and S4 of the SI.

GGA functionals such as RPBE are known to over-delocalise electrons and to underestimate band gaps. To assess how this affects our E_Fermi descriptor and the band gaps of the systems in our study, we benchmarked the E_Fermi (as defined in eqn (7)) and the band gaps using the HSE06 hybrid functional.⁵⁹ We perform non self-consistent calculations, which have shown good agreement with self-consistent hybrid calculations⁶⁰ and are widely used,^61–63 while avoiding the computationally too demanding self-consistent HSE06 calculations for large surface slabs.

The HSE06 E_Fermi values calculated for the TiO₂-coated systems are on average 0.08 eV lower than the RPBE E_Fermi values, although there are significant outliers (Fig. S9 in the SI). We also compared the band gaps between HSE06 and RPBE for the bare surface slabs of the pure oxides (Table S4). HSE06 band gaps remain in the metallic, near-metallic regime for RuO₂, IrO₂, OsO₂, RhO₂, and WO₂, in agreement with resistivity measurements.¹⁵ PdO₂ is also calculated to be metallic, and ref. 64 shows that Pd doping in RuO₂ improves OER activity, suggesting that Pd incorporation is unlikely to severely diminish electronic conductivity. TiO₂ and SnO₂ show much larger HSE06 band gaps than RPBE, consistent with the known GGA underestimation on semiconductors. In Fig. S8, the RPBE band gaps of the bare surface slabs for the mixed oxides studied in this work indicate metallic or near-metallic behaviour (band gap range around 0–0.15 eV).

We also studied the D3 dispersion correction⁶⁵ in the RPBE calculations for the TiO₂-coated systems. D3 introduces an approximately constant shift of 0.25 eV in ΔG₂ but the E_Fermi − ΔG₂ trend remains essentially unchanged (Fig. S16 in the SI).

Results and discussion

The adsorption free energies of *OH (ΔG_*OH) and *O (ΔG_*O) intermediates on the pure oxides as a function of the E_Fermi of the bare surface slabs are shown in Fig. 2a and b, demonstrating clear linear correlations. Looking at the individual guest elements in the host–guest systems, two significantly different trends in the adsorption free energies are observed (Fig. 2c–f). For Ti, Sn, and Zr guests, a notable variation in the adsorption free energies that correlates with the variation in E_Fermi is observed (Fig. 2c and d), indicating that the adsorption energy is primarily determined by the host composition. In contrast to this, the adsorption energies for the other guest elements (Ru, Rh, Ir, Os, Pd, Pt) span a much smaller energy range and are not correlated with E_Fermi (Fig. 2e and f), indicating that, in these systems, the adsorption energy is primarily determined by the guest element. We note that the data corresponding to SnO₂ and TiO₂ hosts are excluded from Fig. 2e and f, because their semiconducting electronic structure leads to a significantly different behaviour. Analysis of the trends in ΔG_*O and E_Fermi, as the guest element is varied for each pure-host composition (including data where TiO₂ and SnO₂ are hosts) can be found in Section S6 in the SI.

Fig. 2 Correlation between adsorption energies of the *OH and *O intermediates and the E_Fermi of the bare surface slabs for the pure oxides (a) and (b), the Zr, Ti, and Sn guests data (c) and (d), the Ru, Rh, Os, Ir, Pd, and Pt guests data (e) and (f). Markers represent different host compositions and colours correspond to different guest elements, as described in the legend.

In ref. 27, a model based on the local atomic environments could predict ΔG_*OH and ΔG_*O adsorption energies. The model worked very well for Ru, Rh, Ir, and Os sites, but less well for Ti sites. We now know that *OH and *O adsorption on Ti sites depend strongly on E_Fermi, which was completely missing from the developed model.

To further understand the interactions between the adsorbates and the surface, we derived the scaling relation ΔG_*O = aΔG_*OH + b, where a is the slope and b is the intercept, for each of the guest elements under study (see Section S7 in the SI). Ti, Sn, and Zr exhibit strong correlations (R² = 0.85–0.99) with slopes approaching 2 (a = 1.5–1.9). A relationship between OH and O adsorption energies with a slope of around 2 has been observed on metals,⁶⁶ which have multiple electrons at the Fermi level, and on oxides, except when the computational cell only contains one dopant,⁶⁷ i.e. when there is only one electron at the Fermi level.

To investigate the origin of the two different trends in the adsorption energies, we conducted Bader charge analysis⁶⁸ on the structures before and after the adsorption of *OH and *O. The Bader charge difference of the adsorption site atom upon adsorption of A (Δq_*A, A = OH or O) is calculated as the difference between the Bader charge of that atom in the bare surface (q_*) and the charge when the adsorbate is added (q_*A):

Δq_*A = q_*A − q_* (8)

Using the HEO dataset, we collected the Δq_*A and Δq_*O values of Ru, Rh, Ir, and Os adsorption sites in one distribution and the corresponding values for the Ti adsorption sites in another distribution. Each set was plotted as a probability histogram, normalising each by the number of data points so that its total area equals one. The resulting plots, shown in Fig. 3a and b, demonstrate that the Ti sites exhibit a small change in charge upon OH and O adsorption. This suggests that the charge transferred to the adsorbate is supplied by the surrounding oxide rather than by the Ti adsorption site itself. This behaviour is consistent with Ti already occupying its highest oxidation state (4+) in the rutile structure. Therefore, further oxidation of the Ti site is unfavourable, and the additional charge must be supplied by the host. In contrast, Ru, Rh, Ir, and Os sites show larger changes in charge upon adsorption, indicating that electrons are, to a large extent, taken locally from the adsorption site. This is consistent with these platinum group elements being able to access oxidation states higher than 4+, making further oxidation of the metal center feasible. The trends observed for Sn, Zr, Pd and Pt adsorption sites are consistent with these conclusions, i.e. Sn and Zr, which also have a maximum oxidation state of 4+, behave like Ti, while Pd and Pt behave more like the other platinum group elements (see Section S8 in the SI for details).

Fig. 3 Probability distributions of the Bader charge difference (Δq_*A) at the adsorption site atom in the RuRhIrOsTi high entropy oxides dataset after (a) *OH, and (b) *O adsorption. (c) Probability distributions of the change in the distance (Δd_*A) between the adsorption site atom and the oxygen atom underneath after *OH and (d) *O adsorption. Data for Ru, Rh, Ir, and Os adsorption sites are aggregated into a single distribution for comparison with the distribution based on data for Ti sites. (e) Schematic figure of the proposed explanation for the different adsorption energies trends observed for Ti, Sn, and Zr guests and Ru, Rh, Ir, Os, Pd, and Pt guests.

To further elucidate the distinct trends in adsorption behaviour, we calculated the change in the distance between the adsorption site atom and the oxygen atom beneath it upon adsorption of A (Δd_*A, A = OH or O):

Δd_*A = d_*A − d_* (9)

Again, the results for Ru, Rh, Ir, and Os are combined, while the Ti data are collected separately. The normalised distributions are shown in Fig. 3c and d, demonstrating that the Ti atoms are significantly displaced from their original position when an adsorbate is added. This observation qualitatively shows that Ti cannot form additional bonds, and to create a new bond (with the adsorbate) it therefore must weaken the bond with the oxygen atom underneath. In contrast, Ru, Rh, Ir, and Os show smaller displacement, indicating that the increased number of bonds and the associated increase in the oxidation state can be accommodated. The observed trends for Sn, Zr, Pd, and Pt in the host–guest data generally align with these findings (see Section S9 in the SI for details). Fig. 3e summarizes that Ru, Rh, Ir, Os, Pd, and Pt sites can offer charge locally to the adsorbate, whereas Ti, Sn, and Zr sites cannot, and therefore draw charge from the surrounding oxide, while the bond between the adsorption site and the oxygen atom underneath weakens.

To evaluate the impact of the different adsorption behaviour on the OER activity, the theoretical overpotential (η) for OER has been calculated using eqn (6). We have considered both the adsorbate evolution mechanism (AEM) given in eqn (1)–(4), along with alternative pathways which have previously been studied for rutile oxides, where the proton of the *OH and *OOH intermediates is transferred to a neighbouring bridging oxygen atom to form *O + Hb and *O₂ + Hb (eqn (S1)–(S4)).^27,69–72 Additionally, we considered the pathway in which molecular oxygen desorbs from the surface already in the third step, represented as O₂(g) + Hb. Further details of the reaction pathways and illustrations of the intermediates can be found in Section S1 in the SI.

Volcano plots of the calculated theoretical overpotential based on the minimum energy pathway as a function of ΔG₂ are shown in Fig. 4. Ti, Zr, and Sn guests (Fig. 4a) exhibit a significant variation in the overpotential compared to the Ru, Rh, Ir, Os, Pd and Pt sites (Fig. 4b) in accordance with the corresponding trends in the adsorption energies. The Ti ensemble is particularly remarkable, because it includes the high-activity region near the peak of the volcano plot. Notably, many Ti sites demonstrate activities beyond the conventional volcano (as low as η = 0.14 V), due to the absence of the known scaling relation ΔG_*OOH ≈ ΔG_*OH + 3.2 eV (see Fig. S14b). In particular, O₂(g) + Hb and *O₂ +Hb intermediates are found to be thermodynamically more stable than *OOH. Meanwhile, high catalytic activity is only marginally achieved at Zr sites, and not at all at Sn sites, due to the weak binding of the *O intermediate across the entire E_Fermi range. Among the platinum group elements, the Os guest data covers the widest activity range. This could be attributed to OsO₂ having the highest E_Fermi among the studied oxides (Fig. 2), resulting in electrons donated by Os adsorption sites having similar energies to the electrons at the E_Fermi.

Fig. 4 Negative theoretical overpotentials (−η) of the Ti, Sn, and Zr guests (a) and the Rh, Ru, Ir, Os, Pd, and Pt guests (b) as a function of the free energy of the second catalytic step (ΔG₂) of the OER. The volcano plot line is generated by employing the known scaling relation ΔG_*OOH ≈ ΔG_*OH + 3.2 eV. Markers represent different host compositions and colours correspond to different guest elements, as described in the legend.

Inspired by the tunable activity observed for Ti guest sites across different host compositions (Fig. 4a), we now extend this single-site concept to a more advantageous catalyst design by considering TiO₂ coatings on conductive rutile oxide substrates. Previous studies have shown that a TiO₂ coating can be applied on conductive oxides, often with a minor decrease in the activity and improvement of the stability under acidic OER conditions.^30–32 The feasibility of producing TiO₂ coatings of one or two monolayers is supported by ref. 29, where an ultrathin protective TiO₂ layer was formed by annealing RuO₂ nanoparticles on a Nb-doped TiO₂ support. The thickness of the TiO₂ layer was ∼4.4 Å, compared with ∼4.0 Å for a single TiO₂ monolayer. Moreover, the atomic layer deposition (ALD) technique has demonstrated exceptional control for fabricating TiO₂ coatings on IrO₂, RuO₂, and F-doped SnO₂ films.³² In ref. 32, the average growth rate of TiO₂ was estimated via profilometric and scanning electron microscopy measurements to be 0.50–0.65 Å per ALD cycle. It is also possible that thicker TiO₂ coatings can be used for OER catalysis without strongly compromising activity, since ref. 30 reports that TiO₂ coatings up to 5.5 nm on Co₃O₄ increase durability without significantly affecting the activity relative to bare Co₃O₄.

To investigate whether TiO₂ coatings exhibit tunable activity, as observed for Ti guest sites, we calculated the adsorption energies and overpotentials on TiO₂-coated rutile oxides composed of the conductive elements studied above, namely Ru, Rh, Ir, Os, Pt, and Pd (see Methodology section). The ΔG₂ of these systems is plotted against the E_Fermi in Fig. 5a and b. A strong correlation is demonstrated (R² > 0.8), with the linear fit showing a consistent slope of around −0.8 for one TiO₂ and two TiO₂ overlayers, close to the slope obtained for the single Ti sites (−0.92). This demonstrates the robustness of the E_Fermi as a descriptor for the adsorption energies on both single Ti sites and TiO₂ overlayers. More details and illustrations of the slab structures in this dataset are provided in Sections S2 and S4 of the SI.

Fig. 5 Correlation between E_Fermi and ΔG₂ for rutile oxides coated with one overlayer (a) and two overlayers (b) of TiO₂. Black lines correspond to the best linear fits. Negative theoretical overpotentials (−η) as a function of the E_Fermi for the rutile oxides covered with one overlayer (c) and two overlayers (d) of TiO₂. The dashed horizontal line indicates the value of the overpotential at the apex of the activity volcano defined by the conventional scaling relation ΔG_*OOH ≈ ΔG_*OH + 3.2 eV. Markers represent different substrate oxide compositions and colours correspond to different number of TiO₂ overlayers as described in the legend.

The theoretical overpotential based on the minimum energy pathway is directly compared to the E_Fermi for these systems in Fig. 5c and d. From these plots, it is evident that TiO₂-coated oxides can be highly active if they have a suitable E_Fermi. Notably, a system with a E_Fermi close to 0 eV (compared to the E_Fermi of RuO₂), can yield low overpotentials beyond the conventional volcano (Fig. 5c). The shape of these distributions suggests a volcano-type activity trend. Adding a second TiO₂ overlayer increases the overpotential (Fig. 5d), consistent with experimental observations that thicker TiO₂ coatings on Co₃O₄ progressively decrease OER performance.³⁰ Scaling relations of the adsorption energies and conventional volcano plots for the TiO₂-coated oxides data can be found in the Section S11 of the SI.

To further expand the use of the E_Fermi as a descriptor, we propose a model (E_Fermi,model) which predicts the E_Fermi of TiO₂-coated oxides based on the composition of the substrate oxide (excluding the TiO₂ overlayer). Specifically, this model is a weighted average of the E_Fermi of the pure oxides,

where E_Fermi,i is the Fermi level of the bare surface slab of the pure oxide of the element i, N_i is the number of atoms of the element i and N_total is the total number of the metal atoms (we do not count the oxygen atoms) in the surface slab.

In Fig. 6a, E_Fermi,model values predicted by eqn (10) are plotted against the E_Fermi (calculated from eqn (7)) for the TiO₂-coated oxides with one TiO₂ overlayer. A strong correlation is observed (R² = 0.98 and MAE = 0.04 eV), showing that the composition of the substrate oxide is a straightforward way to engineer the E_Fermi of TiO₂-coated oxides. We note that while the model is clearly successful for mixtures primarily consisting of platinum-group elements, it may be too simplistic for some combinations of elements, for example, when mixing results in changes in oxidation states.

Fig. 6 (a) Correlation between the composition-based model (eqn (10)) and the real E_Fermi data obtained from DFT (eqn (7)) for oxides covered with one TiO₂ overlayer. The black line corresponds to the best linear fit. (b) The W_xPt_1−xO₂ and W_0.46Pd_0.54O₂ substrate compositions have been predicted based on the model (eqn (10)). (c) Correlation between E_Fermi and ΔG₂ for the W_xPt_1−xO₂ and W_0.46Pd_0.54O₂ substrate oxides. The semi-transparent data points and the linear fit (black line) correspond to the data shown in Fig. 5a. (d) Negative theoretical overpotentials (−η) as a function of the E_Fermi for the W_xPt_1−xO₂ and W_0.46Pd_0.54O₂ substrate oxides. The semi-transparent points correspond to the data shown in Fig. 5c. The dashed horizontal line indicates the value of the overpotential at the apex of the activity volcano defined by the conventional scaling relation ΔG_*OOH ≈ ΔG_*OH + 3.2 eV.

Based on the observation that the activity of TiO₂-coated rutile oxides can be tuned through the substrate oxide E_Fermi (Fig. 5), and that the E_Fermi of the TiO₂-coated systems can be predicted from the substrate oxide composition using the linear model in eqn (10) (Fig. 6a), we now apply this to predict Ir- and Ru-free OER candidates. We also exclude Rh and Os, because they are equally or even more scarce and expensive than Ru and Ir.¹⁶ Instead, we select TiO₂-coated PtO₂ as a representative system, whose activity is not yet optimal, and dope it with tungsten (W) to tune E_Fermi.

In Fig. 6b, we show that the model (eqn (10)) successfully predicts the E_Fermi of the TiO₂-coated W_xPt_1−xO₂ data. The two distinct rutile slabs for each composition are found to have similar E_Fermi, indicating that E_Fermi is largely controlled by composition rather than the specific arrangement of metal atoms in the slab. In Fig. 6c, we see that the adsorption energies vary almost linearly with the E_Fermi, and the trend is shifted smoothly from the TiO₂-coated PtO₂ towards the TiO₂-coated WO₂ direction, as the amount of W increases. The observed scatter arises from an inequivalent local coordination environment associated with the distinct atomic configurations at the three different Ti-cus sites sampled on each composition. This indicates that E_Fermi is not a perfect descriptor, since all six adsorption sites (three Ti sites for each of the two atomic configurations) experience similar E_Fermi. In Fig. 6d, it is evident that these systems follow the expected volcano trend. The largest improvement in overpotential is observed for W_0.12Pt_0.88O₂ and W_0.17Pt_0.83O₂ (as low as 0.55 V), compared with the PtO₂ substrate composition (0.73 V), indicating that higher activity can be achieved while reducing precious-metal content. Increasing the W content further to 21 at% reduces the activity, indicating that the W_xPt_1−xO₂ substrate composition is optimal at x = 12–17 at%.

We applied the same design principle to predict active Pd-based catalysts. In Fig. 6, we show TiO₂-coated W_0.46Pd_0.54O₂ (purple star), which has a significantly lower overpotential (η = 0.39 V) than the TiO₂-coated PdO₂ (η = 0.96 V). Together with the TiO₂-coated W_xPt_1−xO₂ results, this demonstrates that tuning the substrate E_Fermi provides a robust route to designing Ru and Ir free catalysts.

Conclusions

In summary, our work presents a theoretical design principle for active and potentially stable OER electrocatalysts under acidic conditions. We find that elements which cannot be oxidised beyond the 4+ oxidation state in the rutile structure (Ti, Sn, and Zr) exhibit adsorption energies and activities that are correlated with the E_Fermi of the surrounding oxide, whereas this behaviour is not observed for Pt, Pd, Ir, Os, Ru, and Rh sites. Among these, Ti is found to be particularly special, as it spans a wide range of adsorption energies, many of which correspond to very low overpotentials (η = 0.14 V).

We then show that these observations on single Ti sites can be transferred to a more advantageous catalyst design by studying TiO₂ coatings on conductive rutile oxide substrates. For these systems, a volcano-type relationship is observed between activity and E_Fermi, demonstrating that a TiO₂-coated oxide with a suitable E_Fermi can be highly active and potentially stable under acidic OER conditions, consistent with experimental reports that TiO₂ coatings can preserve activity while improving stability in acid.^19,29–32 Furthermore, we show that a simple linear model can accurately predict the E_Fermi of TiO₂-coated oxides based on the composition of the substrate oxide. Using this model, we identify Ir and Ru free substrate compositions, W_xPt_1−xO₂ and W_0.46Pd_0.54O₂, with E_Fermi values that can activate the TiO₂ overlayer, illustrating a practical route to designing Ir and Ru free acidic OER catalysts.

Author contributions

J. R. supervised the whole project. G. K. S. performed the DFT calculations and data analysis supervised by K. L. S., H. H. K., and J. R. G. K. S., H. H. K., and K. L. S. wrote the manuscript. All authors discussed the results, provided insights and suggestions, and helped improve the manuscript.

Conflicts of interest

The authors have submitted a patent application (European application under number EP 25387103.2) covering this work.

Data availability

The data and analysis that support the findings of this study are openly available at https://www.erda.dk/archives/f73eb5ea1d7a1897bfa54659f714b3cd/published-archive.html.

Supplementary information (SI): reaction pathways for the OER; DFT calculations setup; RuRhIrOsTi high entropy oxide dataset; description of the model structures; Fermi level alignment using O 2s band centroid; trends in ΔG_*O and EFermi; scaling relations between adsorption energies; Bader charge differences in pure oxide hosts; change in distance between adsorption site and oxygen atom beneath in pure oxide hosts; conventional volcano plots for TiO₂-coated metal oxides; and D3-corrections. See DOI: https://doi.org/10.1039/d5ee07605f.

Acknowledgements

We acknowledge financial support from the Danish National Research Foundation, Center for High Entropy Alloy Catalysis (CHEAC) DNRF149, the European Union under ERC Synergy grant DEMI, GA no. 101118768, and V-Sustain: The VILLUM Centre for the Science of Sustainable Fuels and Chemicals (#9455) from VILLUM FONDEN.

Notes and references

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