Can dopants defend? Unraveling RuO₂ corrosion and reinforcement strategies for enhanced stability

Abstract

To advance sustainable green hydrogen production through water electrolysis, where ruthenium dioxide (RuO₂) is a promising catalyst for the oxygen evolution reaction (OER), we investigate the stability of RuO₂, focusing on corrosion resistance – a key challenge limiting its practical application. Using density functional theory (DFT), we analyze the thermodynamic stability and reaction pathways across various RuO₂ surface orientations, with a primary focus on the (110) surface. Specifically, we assess the impact of doping with Ta, W, Re, Ir, Ti, and Pt on the thermodynamic stability of the RuO₂(110) surface against dissolution of Ru surface atoms in the form of RuO₄. Our findings reveal that dopants Ir, Ti, and Pt in low oxidation states significantly enhance the resistance of the RuO₂(110) surface against corrosion, while Ta, W, and Re in high oxidation states destabilize the surface, promoting degradation. We also identify specific dopant sites, such as those next to or directly underneath the dissolving Ru atom, that contribute significantly to surface stability, providing a roadmap for optimizing RuO₂ catalysts. Additionally, we extend the investigation to reaction pathways towards the dissolution of the Ru atom by incorporating the effects of dopants, revealing that dopants not only alter the thermodynamic stability but also the reaction mechanism due to their different termination preferences. We establish a strong linear correlation between the Gibbs free energy of RuO₄ formation (ΔG_tot) and the free energy of the highest intermediate (ΔG_max), proposing ΔG_tot as a reliable descriptor for predicting the thermodynamic stability of doped RuO₂ surfaces against Ru dissolution. This allows for efficient computational screening of surface modifications, including dopant selection and surface orientation tuning, without requiring detailed knowledge of the entire stepwise mechanism toward the formation and removal of RuO₄. This insight enables efficient computational screening of dopants and surface modifications, providing a framework for optimizing RuO₂ catalysts to improve durability in electrochemical applications.

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1 Introduction

The transition towards sustainable energy sources has prompted intensive research into technologies capable of efficiently converting renewable electricity into storable and transportable forms. Among these technologies, water electrolysis is a promising avenue for producing green hydrogen, a clean and versatile energy carrier capable of decarbonizing various sectors, including transportation, industrial processes, and energy storage.¹ Polymer electrolyte membrane (PEM) electrolyzers (see Fig. 1), in particular, have gained traction due to their ability to catalyze hydrogen production at the cathode with high efficiency.² However, the sluggish kinetics of the oxygen evolution reaction (OER) at the anode pose a significant barrier to achieving optimal performance in water electrolysis systems.³

Fig. 1 A polymer electrolyte membrane (PEM) electrolyzer.

Addressing the challenges associated with the OER is paramount for advancing the commercial viability and widespread adoption of water electrolysis technology. Ruthenium dioxide (RuO₂) has emerged as a promising catalyst for the OER, owing to its high activity and favorable electrochemical properties.⁴ Despite its potential, the practical application of RuO₂ in water electrolysis is hindered by issues related to its stability under operating conditions.⁵ The dissolution of Ru from the RuO₂ structure leads to the formation of soluble RuO₄ species, compromising the long-term stability and performance of RuO₂-based catalysts.^6–8 This instability is particularly pronounced at surface defect sites and undercoordinated Ru atoms, where dissolution is more likely to occur. Understanding the atomic-scale mechanisms of RuO₂ degradation is therefore essential for developing more stable catalyst formulations.

Enhancing the stability of RuO₂ requires a fundamental understanding of the mechanisms governing its degradation and the development of effective strategies to mitigate corrosion. One promising approach is heteroatom doping, where the incorporation of stable elements such as Ir, Ti, and Pt can modify the electronic structure of RuO₂, suppress Ru dissolution, and improve overall durability. For instance, a Ru_0.5Ir_0.5 alloy achieves four times higher stability compared to other Ru–Ir OER materials by adjusting surface composition through segregation.⁹ In Ir–Ru mixed oxides, Ru dissolves more rapidly than Ir, leading to activity loss, while the corrosion resistance of Ir contributes to overall stability.¹⁰ Titanium substitution in RuO₂ at low concentrations (12.5% and 20% Ti) enhances catalyst stability and reduces Ru dissolution.¹¹ TiRuO₂ solid solutions improve selectivity towards cathodic electrochemical reactions (CER), such as the hydrogen evolution reaction (HER), rather than enhance OER activity.

Another approach involves oxygen vacancy engineering, where dopants such as W and Er increase the formation energy of oxygen vacancies, effectively improving the structural integrity of RuO₂ and reducing dissolution in acidic PEM electrolyzers.¹² Furthermore, surface modifications, such as atomic layer deposition (ALD) of protective coatings and the formation of mixed-metal oxide layers, have been shown to enhance RuO₂ stability, with submonolayer IrO_x on RuO₂ significantly suppressing Ru dissolution and improving durability in PEM electrolyzers.¹³ Meanwhile, Ru nanoparticles exhibit severe corrosion and instability during OER, whereas Ir nanoparticles show improved durability, indicating their potential as effective nanoscale OER catalysts.¹⁴ Dispersing RuO₂ over defective TiO₂ enhances acidic OER performance by lowering the *OOH formation barrier and improving stability.¹⁵

In this study, leveraging Density Functional Theory (DFT) calculations in the computational hydrogen electrode model,^16,17 we investigate the thermodynamic stability and reaction pathways of RuO₂ catalysts in water electrolysis. We examine surface defects across various orientations, including (110), (100), c(2 × 2)-reconstructed, and step edge configurations, to gain insights into the influence of surface morphology on RuO₂ stability against corrosion. Additionally, we explore the effects of support materials like M = (Ta, W, Re, Ir, Ti, and Pt), selected based on their stability in oxidative environments, electrochemical properties, and structural compatibility with RuO₂ due to their ability to form MO₂ rutile structures, thereby potentially forming stable solid solutions and interfaces with RuO₂. These elements are known to influence corrosion resistance, making them ideal candidates for this study. Their effects, either as a substrate or sublayer, on RuO₂ surface composition and stability are examined. Finally, we investigate how doping with a selection of these elements influences the thermodynamic stability of the RuO₂(110) surface against corrosion.

In order to study the connection between thermodynamics and kinetics of corrosion, represented by the overall Gibbs free energy of RuO₄ formation (ΔG_tot) and the free energy of the highest intermediate (ΔG_max), we delve into the reaction pathways of RuO₄ formation at the bridge site of the (110) surface. Here, we focus on how different dopants alter the corrosion mechanisms and overall stability of RuO₂ surfaces. By detailing these reaction pathways, we aim to identify opportunities for optimizing RuO₂ catalysts to enhance their performance in water electrolysis. Finally, we demonstrate that ΔG_max is highly correlated with ΔG_tot for a large variety of modified surface structures, enabling the use of the Gibbs free energy of reaction as a descriptor in the optimization of the surface stability.

Ultimately, this study aims to advance sustainable energy technologies by developing robust and cost-effective catalysts for water electrolysis through knowledge-based proofing of the anode material against corrosion, facilitating the efficient use of renewable energy resources for green hydrogen production.

2 Computational details

Our investigation, grounded in DFT calculations, utilizes the Vienna ab initio simulation package (VASP)^18,19 employing the Perdew–Burke–Ernzerhof (PBE) functional.²⁰

For surface computations, a (4 × 2 × 1) k-point mesh is employed for (2 × 2) superstructures of the (110) surface, with a constant k-point density in reciprocal space for larger surface configurations. These asymmetric slabs comprise five RuO₂ trilayers, with two fixed and three fully relaxed trilayers. The relaxed bulk lattice parameters used in the calculations are optimized for RuO₂, IrO₂, and TiO₂. Specifically, the lattice constants for RuO₂ are a = b = 4.497 Å and c = 3.105 Å, for IrO₂ they are a = b = 4.499 Å and c = 3.146 Å, and for TiO₂ the parameters are a = b = 4.589 Å and c = 2.958 Å. A vacuum layer of 17.359 Å is employed. An energy cutoff of 450 eV and convergence criteria of 10⁻⁶ eV for energy during structural optimization is specified. Pseudopotentials are utilized for various elements including Ru, Ti, Ir, W, Re, Pt, Ta, O, and H^19,21 designated as Ru_sv, Ti, Ir, W, Re_pv, Pt_pv, Ta_pv, O, H.

For Ti, a Hubbard coefficient U_H of 8 eV is implemented in the Generalized Gradient Approximation (GGA) calculation to accurately describe the localized nature of Ti d-electrons in the semiconductor, thereby improving the characterization of its electronic structure.^22–24 Other elements in the system did not require a U_H correction, as their electron interactions were sufficiently well-described by conventional DFT.

The reactions investigated in this study include the oxygen evolution reaction at the anode, represented by the following reaction:

The corrosion reaction at the anode is:

RuO₂ + 2H₂O → RuO₄ + 4H⁺ + 4e⁻.

At the cathode, the hydrogen evolution reaction is represented by:

4H⁺ + 4e⁻ → 2H₂.

Our computational approach is based on the total free energy equation, following methodologies detailed in previous studies.^16,17,25 The free energy change for a particular configuration i, denoted as ΔG_i(U_SHE,_pH), is calculated using the following expression:

The reason RuO₄ was chosen in eqn (1) is that, at the potential corresponding to the dissolution threshold (around 1.21 V), RuO₄ is typically the dominant solvated species. At higher potentials, ruthenium tends to stabilize in its higher oxidation state, often as RuO₄. In this equation, ΔG_i(U_SHE,_pH) represents the free energy change for configuration i as a function of the applied potential relative to the standard hydrogen electrode (SHE), U_SHE, and the pH of the environment. The term E^DFT_i is the electronic energy of the system in configuration i, while E^DFT_ref is reference energy, typically the energy of the initial state of the RuO₂ system, obtained from density functional theory (DFT) calculations. The numbers n_RuO4, n_e⁻,_i, n_H2O,i, n_H2,i, and n_O2 represent the number of RuO₄ units involved in the reaction or transformation for configuration i, the number of electrons transferred in the electrochemical process associated with configuration i, the number of adsorbed water molecules involved, the number of hydrogen molecules, and the number of oxygen molecules, respectively. The constant 0.059 eV represents a unit conversion factor at room temperature. U_SHE is the applied potential relative to the standard hydrogen electrode.

G _RuO4,aq is the free energy of RuO₄ in an aqueous solution, which can be determined using its entropy, S_RuO4,aq ≈ 104.55 J (K⁻¹ mol⁻¹). G_H2 and G_O2 represent the free energies of hydrogen and oxygen molecules, respectively. The free energy of liquid water, G_H2O,l, is determined by the expression

where S_H2O,g = 188.8 J (K⁻¹ mol⁻¹) is the entropy of gaseous water, calculated at room temperature T = 298.15 K, and 0.035 bar represents the vapor pressure of water.

At U_corr, which is the thermodynamic corrosion potential where the system is in dynamic equilibrium, and the net current of oxidation (corrosion) and reduction reactions on the surface is zero, indicating no net electron flow. When pH = 0, indicating an acidic environment, the total free energy at the corrosion potential is given by:

ΔG_i(U_corr) = E_i − E_ref + n_RuO4G_RuO4,aq − n_e⁻,iU_corr − n_H4OG_H2O,l + n_H2G_H2 + n_O2G_O2 = 0 (3)

This equation is essential for understanding the stability and reactivity of RuO₂ under different electrochemical conditions, providing insights into the factors influencing its performance as an oxygen evolution reaction (OER) catalyst.

3 Results

Our results are structured into two main parts: overall thermodynamic stability of Ru sites at the surface against RuO₄ formation and reaction pathways toward the dissolution of Ru in the form of RuO₄. This approach allows for a comprehensive analysis of RuO₂ surface corrosion, exploring both the inherent stability of various doped configurations and the specific mechanisms through which corrosion occurs. Finally, we examine the suitability of ΔG_tot as a descriptor for the stability of sites at the RuO₂(110) surface against corrosion by quantifying the correlation between ΔG_tot, representing the overall thermodynamic stability of a specific site, and ΔG_max, representing the least stable intermediate in the full corrosion mechanism.

3.1 Thermodynamic stability

In our investigation of the thermodynamic stability and corrosion susceptibility of various pure RuO₂ surfaces, we examined different orientations (110, 100, c(2 × 2)-reconstructed (100), and RuO₂(110)/RuO₂(100) step edge) to discern their relative stability against corrosion. Subsequently, we examine the influence of dopants, as well as the direct and indirect effects of the catalyst support.

3.1.1 Different RuO₂ surface facets. The (110) surface of this material presents a nuanced picture with two distinct types of Ru atoms: coordinatively unsaturated sites (cus) and bridge sites (br). Fig. 2a and b show the free energy of corrosion as defined by eqn (3) as a function of the potential.

Fig. 2 Thermodynamic corrosion potentials and structures of (a and b) different Ru sites at the (110) surface. Corrosion potentials are 1.21 V, 1.277 V, and 1.488 V, calculated at pH = 0. Colors: sky blue: Ru_bulk, blue: Ru_cus, black: Ru_br, red: O.

Positive free energies indicate that corrosion is not thermodynamically favored, implying that the surface is thermodynamically stable against corrosion. The potential at which the free energy turns negative will hereafter be referred to as the corrosion potential (U_corr), which indicates the lowest potential at which corrosion is thermodynamically preferred. Examining the corroded potential as a stability metric reveals variations in the stability of both atom types. The Ru_br site involves the removal of one Ru_br atom and one of its O_br atoms, while the other O_br atom relocates to the top of the nearest Ru_br atom, which then becomes Ru_5f. The corrosion potential of 1.277 V for the Ru_br site is higher than the bulk corrosion potential of 1.21 V (the bulk corrosion potential refers to the total conversion of bulk RuO₂ to RuO₄), indicating that the site remains stable, as corrosion is not thermodynamically favored at this higher potential.

The Ru_br–O site, formed by further removing the remaining O atom from the Ru_br site (which previously moved to the nearest Ru_br atom), transforms the nearest Ru_br atom into a Ru_4f atom without any termination on top. This site is identified as the most stable on the surface, with a corrosion potential of 1.488 V.

In contrast, the Ru_cus site is the least stable, indicating a higher susceptibility to corrosion. Its stability is comparable to that of bulk material, with a corrosion potential of 1.21 V. However, the instability of the Ru_cus site affects its neighboring Ru_cus atom, leading to the elongation of the underlying bond after metal dissolution, from 2.03 Å to 2.27 Å, as shown in Fig. 2b (top). In this specific case, our analysis reveals that the neighboring Ru_cus atom has a higher corrosion potential (1.291 V) compared to the initial Ru_cus site (1.214 V), making it less susceptible to dissolution.

We uncovered distinct dissolution behaviors and stabilities by extending our analyses to the (100) surface and step edge between the (100) and (110) facets. In each case, we examined the dissolution of different Ru sites with different oxygen terminations in the initial and final structures. Fig. 3 presents the summarized results, displaying the least stable site for each of the facets. Details for each of the facets can be found in Fig. S1–S3 in the ESI† for the (100), c(2 × 2)-reconstructed (100) and (100)/(110) step edge, respectively. For instance, Fig. S1 in the ESI† illustrates the dissolution behavior of the (100) surface, revealing the formation of a tetrahedral Ru_4f structure post-dissolution and highlighting its comparatively lower stability: the least stable site on the (100) surface corrodes at a potential of 0.901 V, differing by 0.3 V compared to bulk RuO₂.

Fig. 3 Comparison of different RuO₂ surface facets based on potential calculations at pH = 0, identifying the least stable sites for each surface. The least stable sites are: 110: RuO₂-Ru_cus, 100: RuO₂-Ru_surf-2O, 100-c(2 × 2): RuO₂-Ru_6f + O_ot/Ru_4f, and step edge: RuO₂-Ru_cus-O.

Similarly, Fig. S2 in the ESI† elucidates the dissolution behavior of the (100)-c(2 × 2) surface, revealing corrosion potentials of 1.285 V for Ru_4f (reported by Hess and Over)²⁵ and 1.255 V for Ru_6f (according to our investigation). Ru_4f, Ru_5f, and Ru_6f denote distinct Ru crystallographic sites with fourfold, fivefold, and sixfold coordination, respectively, affecting the material's electronic structure and bonding.

Moving on to the dissolution behavior of step edge surfaces, Fig. S3 in the ESI† reveals corrosion potentials and stability characteristics. Notably, the step edge surface exhibits decreased stability compared to the bulk material, particularly evident in the least stable site (Ru_cus–O), with a corrosion potential of 0.858 V. The corrosion potentials for the least stable site on each facet are summarized in Fig. 3. This highlights the step edge as the least stable site among all examined, while the 110 surface emerges as one of the most stable surfaces. Consequently, we direct our further investigations towards the 110 surface.

3.1.2 RuO₂(110) surface with different dopants. To explore the potential improvement in stability against the RuO₂(110) surface corrosion, we investigated the impact of various dopants (Ta, W, Re, Ir, Pt, Ti) on its stability. The dopants were chosen based on their ability to form rutile-type structures, representing different groups of 3d and 5d transition metals. To isolate the effect of dopants from strain due to variation of the lattice parameter issues, we used the RuO₂ lattice parameter. Two models were constructed: (1) in the first model, a sublayer of dopants was placed in the middle of the RuO₂ layers, with the two bottom layers fixed (atoms in the vertical direction were constrained), while the remaining layers were allowed to relax in all directions, (cf.Fig. 4b), and (2) random arrangement of dopants M_0.21Ru_0.79O₂ (M = Ir, W) on the metal sites. This approach allows us to solely observe the influence of dopants on the corrosion of the RuO₂ surface without introducing strain.

Fig. 4 (a and b) Influence of different dopant sublayers on RuO₂ corrosion with a varied thickness (1L or 2L) of RuO₂; (c) influence of different M_0.21Ru_0.79O₂ (M = Ir, W) configurations on RuO₂ corrosion (cf. Fig. S4†). Potentials were calculated at pH = 0.

Furthermore, to distinguish the direct and indirect effect of the sublayer in RuO₂ corrosion, we deposited 1 or 2 layers of RuO₂ atop the dopant sublayer. In the case of 1 layer (1L), the corroded Ru atom is bonded to the sublayer via a single O_3f (direct effect), while with 2 layers (2L), only an indirect effect of the sublayer is probed, since surface Ru is not directly bonded to the sublayer. This approach enables us to investigate whether varying the thickness of the RuO₂ layer on the dopant sublayer affects the enhancement in stability against the RuO₂(110) surface corrosion.

Fig. 4a and b illustrate the corrosion potential of the sublayer containing different dopants within the two models (1L, 2L). In the 1L model (direct effect), Ta, W, and Re destabilize the Ru top layer, whereas Ir, Pt, and Ti stabilize it against corrosion, as indicated by their decreased and increased corrosion potentials, respectively. The dopant is exposed after RuO₄ dissolution, resulting in different surface stabilities of the final surface: W strongly prefers a higher oxidation state, making it the least supportive dopant for RuO₂ surface stability against corrosion. Ta and Re prefer high oxidation states but not as strongly as W. In contrast, Ir, Pt, and Ti prefer lower oxidation states, with Ir and Ti being the most supportive dopants for RuO₂ surface stability against corrosion The trends within the two groups persist in the 2L model, but the corrosion potentials for each of the dopants now scatter closely around the value for pure RuO₂, with Ta, Ir, and Ti now causing a weak stabilization. For the others (W, Re, Pt), the effect on stability is negligible.

Continuing our investigation into the effect of doping on the stability of RuO₂ against corrosion, we selected W from the group (Ta, W, Re) and Ir from the group (Ir, Pt, Ti), mixing them randomly with RuO₂ to create eight configurations comprising a mixture of M_0.21Ru_0.79O₂ (M = Ir, W). To maintain consistency and avoid lattice parameter issues, we fixed two layers of pure RuO₂ at the bottom, while three layers of (M_0.21Ru_0.79O₂ (M = Ir, W)) were allowed to relax (the considered dopant configurations are shown in Fig. S4†). Fig. 4c displays the corrosion potential of these configurations. In all configurations, Ir_0.21Ru_0.79O₂ consistently demonstrates superior stability against corrosion compared to W_0.21Ru_0.79O₂. The observed variations in stability among configurations are fairly consistent between the two dopants, suggesting that the positions of dopant atoms influence the corrosion behavior of the Ru_diss atom, particularly its nearest neighbors. The distribution of dopant atoms in the bridge atom sites of the surface significantly influences stability, particularly the nearest bridge atom of Ru_diss, as observed in configurations (3, 5, 7), where the bridge site next to Ru_diss is occupied with a dopant atom. The metal atom directly underneath the Ru_diss plays a similarly strong role: configuration 7 in Ir_0.21Ru_0.79O₂, where Ir is the metal atom underlying Ru_diss atom, is identified as the most stable configuration. Conversely, configuration 3 in W_0.21Ru_0.79O₂, where Ru acts as the underlying Ru_diss atom, demonstrates the highest stability among W_0.21Ru_0.79O₂ configurations. This consistency aligns with sublayer results, where W and Ir in the sublayer destabilize and stabilize the surface Ru atom, respectively. This trend is equally observed in the random configurations. Conversely, configurations where the dopant is not located in the bridge position, such as configurations 6 and 8 in W_0.21Ru_0.79O₂, which lack W bridge atoms, are the least stable. This analysis provides valuable insights into predicting the stability of the surface based on specific dopant sites.

Interestingly, while in the case of Ir, all configurations demonstrate a stabilization, W can provide both a stabilizing effect, if it is located directly at the surface, and a destabilizing effect, if it is located in the sublayer. The strong role of the dopant distribution is further emphasized if we further consider different dopant contents, only favoring the most stabilizing patterns identified from the above analysis: in this approach, we can achieve a corrosion potential of 1.457 V for an Ir content as low as 8% in the slab, only placing one Ir atom in the bridge position next to, and another directly underneath (cf. Fig. S5†). This represents a significant enhancement compared to the bulk corrosion of 1.21 V. By adding more Ir dopants in favorable positions, the corrosion potential can be further raised to 1.492 V at 21% Ir in the slab. This result highlights that a significant degree of stabilization can theoretically be achieved by doping very little Ir in just the right positions; however, experimentally achieving such selective doping remains a significant challenge. This result is significant because the price of raw Ir metal has been over 10 times as high as that of Ru consistently over the past three years.²⁶ If Ir was used to stabilize RuO₂-based anodes for OER, its content should be as low as possible to reduce the cost of raw materials. Our results presented herein enable a knowledge-based approach to achieve these goals, which remains to be tested by experimental model studies.

3.1.3 Influence of strain and layer thickness in RuO₂@IrO₂(110) and RuO₂@TiO₂(110). For further investigation, we selected Ir and Ti from the group (Ir, Pt, Ti) to create substrates of IrO₂ and TiO₂ (these being the most commonly used materials to modify RuO₂), aiming to explore additional parameters influencing the stability of the RuO₂(110) surface against corrosion. Here, we aim to elucidate the influence of a substrate on a pseudomorphically grown RuO₂ layer. In the substrate model, we focused on two aspects: first, the effect of RuO₂ thickness on its surface stability against corrosion of the RuO₂(110) surface, and second, the impact of strain due to the different lattice parameters on the stability against the RuO₂(110) surface corrosion. The lattice mismatch between RuO₂ and IrO₂ is approximately 0.839% along the [001] direction and −0.482% along the [1̄10] direction. Meanwhile, the mismatch between RuO₂ and TiO₂ is approximately −4.910% along the [001] direction and 2.496% along the [1̄10] direction, indicating that TiO₂ introduces a higher strain on RuO₂ compared to IrO₂.

Using the lattice parameter of IrO₂, Fig. 5a and b depict the corrosion potential of different thicknesses of RuO₂ on two IrO₂ substrate models consisting of either 3 or 4 layers (3L, 4L). We observe that there is a significant scatter in the U_corr for even and uneven numbers of RuO₂(110) layers. Similarly, we observe slightly different corrosion potentials for 3 and 4 layers of IrO₂ substrate. Both models consistently show that odd layers of RuO₂ stabilize the surface more strongly against even layers, and the corrosion potential converges around 6–7 layers to around 1.23 V for both models. According to these calculations, odd layers of RuO₂ grown on the IrO₂ clearly show a higher stabilization. Still, this behavior is likely significant only for very thin epitaxially grown layers not exceeding 4–5 layers. However, the lattice strain introduced due to IrO₂ as a substrate led to an overall stabilization of the RuO₂(110) surface by shifting the U_corr from 1.21 V (pure RuO₂(110)) to 1.23 V.

Fig. 5 (a and b) Influence of IrO₂(110) substrate with different thicknesses of RuO₂ on the stability of RuO₂ against corrosion (calculated with IrO₂ lattice parameter). Configurations include 3 or 4 layers of IrO₂ with 1–7 layers of RuO₂. (c) Influence of lattice parameters on the stability of RuO₂(110) against corrosion. Potentials were calculated at pH = 0.

Such odd-even oscillations have been described previously for TiO₂(110),^27,28 and upon closer examination, we attribute it to the layer stacking in the (110) direction of the rutile lattice, which comprises two different types of atoms, Ru_cus and Ru_br stacked in an A–B–A–B sequence on the substrate. For odd and even layers, corrosion occurs in an A and B layer, respectively, which may explain the observed oscillation, although the exact reason for this behavior is still unknown. This observation prompted us to reinvestigate the (100) surface, composed solely of A layers, as depicted in Fig. S6.† In this model, the oscillation of the U_corr between odd and even layers is not observed. On a (100) surface, it is in steady observed that increasing thickness of strained RuO₂ on top of IrO₂, destabilizes the surface against corrosion, from 1.13 V (1L) to 0.84 V (7L). This indicates that strain can introduce a significant stabilizing effect in an otherwise inherently unstable facet like (100) and may be employed in addition to targeted doping to enhance the durability of RuO₂-based OER catalysts. On the other hand, in the more stable (110) facet, the effect of strain is negligible if IrO₂ is employed as a substrate.

To validate these conclusions, the corrosion potentials for RuO₂ layers grown on top of IrO₂ without strain (i.e., employing the RuO₂ lattice parameter) are shown in Fig. 5c. Here, we observe the same odd-even oscillations; however, for thick RuO₂ layers, the corrosion potential converges to the value of pure RuO₂(110), confirming that the stability of the RuO₂ surface is enhanced due to the strain introduced by the IrO₂ substrate. The oscillations, on the other hand, are not a result of strain, but occur in thin RuO₂(110) layers regardless of strain. We emphasize that, despite these oscillations, the strain induced by the IrO₂ substrate enhances stability of RuO₂(110), regardless of thickness.

For the TiO₂ substrate, we utilized the same model as for the 3L IrO₂ model. Fig. S7† depicts the corrosion potential of different thicknesses of RuO₂ on a 3L TiO₂ substrate with varying lattice parameters. The odd-even oscillation behavior occurs here as well, but with a lower intensity. Interestingly, when using the TiO₂ lattice parameter, the lattice strain leads to destabilization. Conversely, aligning with the RuO₂ lattice parameter results in slight stabilization, consistent with Section 3.1.2. The different stabilization behavior of IrO₂ and TiO₂ substrates is likely due to the different magnitude of lattice mismatch, but also due to the different orientations of strain and stress.

The investigation reveals that RuO₂ layers grown on IrO₂ substrates exhibit enhanced stabilization due to minimal lattice mismatch, while RuO₂ on TiO₂ substrates faces destabilization due to greater overall lattice mismatch, with odd-even oscillations in corrosion potential observed for both substrates in (110) direction. The (100) direction does not display such oscillations, but a significantly higher degree of stabilization due to the lattice mismatch.

3.2 Reaction pathways

In the second part of our investigation into the surface corrosion of the RuO₂(110) surface, we examine the corrosion at the Ru_br site, which exhibits six-fold coordination at typical OER operating potentials. We follow the mechanism proposed by Liu et al.,²⁹ consisting of a stepwise addition of H₂O from the electrolyte, followed by the removal of proton/electron pairs, resulting in the transformation of octahedral RuO₆ into tetrahedral RuO₄, which subsequently detaches from the surface. Here, we investigate how a dopant sublayer, or quasi-random distribution of dopant atoms alter the energetics and reaction steps in the mechanism.

For the removal of Ru_br, we propose the following steps illustrated in Fig. 6, with the free energy profile depicted in Fig. 7:

Fig. 6 The Ru_br corrosion mechanism on the RuO₂(110). Colors: sky blue for Ru_bulk, red for O, yellow for H, black for Ru_diss (dissolution Ruthenium), and lime for O_ads (adsorbed oxygen).

Fig. 7 The free energy profile of the Ru_br corrosion mechanism on the RuO₂(110) surface at an electrode potential U_SHE = 1.23 V. Free energies were calculated at pH = 0.

Reconstruction step (a and b): this pivotal step initiates corrosion by lifting a Ru_br atom, forming two new Ru–O bonds with the neighboring O_ot. This Ru atom, now referred to as Ru_diss, requires +1.180 eV to accomplish this first, energetically uphill step.

First H₂O adsorption (c–g): in this step, an H₂O molecule is initially adsorbed on top of the new undercoordinated Ru site. This step is followed by the desorption of two-electron (e⁻)–proton (H⁺) pairs. The process begins with H₂O adsorption and progresses until only terminal oxygen remains. Consequently, the newly formed RuO₆ species undergoes a second reconstruction, transitioning into a tetrahedral RuO₄ species. During this transformation, one of the O_br atoms detaches from the underlying Ru, becoming another terminal O. Simultaneously, the Ru_diss atom detaches from the underlying O_3f and one of the neighboring O_ot atoms. It is now connected to one O_ot and one O_br, establishing two terminal O atoms in a four-fold coordination (Ru_4f).

Second H₂O adsorption (h and i): mirroring the preceding step, a second H₂O molecule adsorbs. Upon the removal of the first H⁺/e⁻ pair, the Ru_diss atom severs its bond to the neighboring O_br, forming a RuO₃(OH) complex attached only to O_ot. The final removal of H⁺/e⁻ is exergonic and leads to the formation of a RuO₄ species.

Dissolution step (j and k): in the final step, the RuO₄ detaches from the surface, leaving an empty Ru_cus site behind. Subsequently, this site is saturated by the adsorption of the final H₂O molecule and the detachment of two H⁺/e⁻ pairs.

The free energy profile of the Ru_br corrosion mechanism on the RuO₂(110) surface, as illustrated in Fig. 7, shows the free energy at each step. Notably, the initial reconstruction step (step b) presents the highest energetic threshold at 1.180 eV, indicating its unfavorable energetic characteristics. This chemical step is not influenced by the potential and likely represents the actual bottleneck under typical OER operating potentials.

Furthermore, removing the first H⁺/e⁻ pair following the addition of the second H₂O (step h) is also quite high in free energy at 1.120 eV. This is the electrochemical step in nature, and its free energy can be lowered by increasing the applied potential. This indicates that the initially formed RuO₃(OH)/RuO₄ complexes may have a significant lifetime on the surface and may act as possible active sites in the OER, as proposed by Klyukin et al.³⁰

We examined the influence of various dopants on the reaction pathway toward RuO₄ formation to gauge the potential enhancement in stability against RuO₂(110) surface corrosion due to surface modification. Here, we distinguish between two possible modification strategies: (1) supporting RuO₂ on a substrate of a different oxide, for which we only consider Ir, as it has a similar lattice parameter to RuO₂, thereby avoiding strain effects, and (2) doping, i.e., the quasi-random substitution of Ru ions by other ions, and the respective influence on the reaction steps of the corrosion mechanism. Here, we consider Ti, Ir, and W, as representatives of the three groups favoring different oxidation states as identified in Section 3.1.2.

3.2.1 Influence of substrate sublayer. Initially, we scrutinized the mechanism of Ru_br removal over an IrO₂(110) support substrate, utilizing three layers of IrO₂ with varying thicknesses of RuO₂. Based on our thermodynamic results (Fig. 5 and S7†), we selected a thickness of three layers to represent odd layers. Arguably, one layer shows a more pronounced change in stability due to the direct effect of the sublayer being exposed during the corrosion. This direct effect even changes the reaction mechanism in some cases, complicating the comparison. The direct effect of sublayer dopants will be considered separately in Section 3.2.2. Hence, we chose three layers to gauge the indirect effect of the support on the surface stability. Thermodynamically, we observed in Fig. 5 that odd and even layers lead to destabilization and stabilization compared to pure RuO₂(110), respectively.

In Fig. 8, we illustrate the influence of the layer thickness on the free energy profile for the Ru_br corrosion mechanism on the RuO₂@IrO₂(110) surface with two models (2L, 3L) of RuO₂. We observed a significant correlation between the thermodynamic free energy of corrosion (represented by the free energy difference between the final state k and initial state a in Fig. 8) and reaction mechanisms, represented by the free energy of the highest intermediate (ΔG_max). The reaction steps of corrosion on the supported RuO₂(110) surfaces largely follow the same sequence as on pure RuO₂(110), only the energies are shifted: The corrosion intermediates on odd layers exhibit higher free energies than their even-layer counterparts, indicating increased stability and reduced susceptibility to corrosion, both in terms of thermodynamics and in terms of thermodynamic barriers. However, the highest energetic threshold, i.e., the reconstruction step (step b), remains unchanged for three layers of RuO₂ (green line), standing at 1.197 eV. For two layers of RuO₂ (orange line), the second H₂O adsorption, coupled with the removal of a proton/electron pair (step h) requires a free energy of 1.01 eV, which is not significantly different from the initial reconstruction step (step b), indicating a possible shift in the reaction pathway at this potential (U_SHE = 1.23 V). However, at a potential typically applied during OER (U_SHE > 1.4 V), the initial reconstruction step, being a purely chemical step, remains the highest energetic threshold.

Fig. 8 Free energy profile at U_SHE = 1.23 V for Ru_br corrosion mechanism on RuO₂@IrO₂(110) surface, comparing 2L and 3L RuO₂ models. Free energies were calculated at pH = 0. Colors: sky blue for Ru_bulk, red for O, black for Ru_diss, and brown for Ir.

3.2.2 Influence of randomly distributed dopants. Continuing our investigation into the effects of dopants (Ti, Ir, W) on the reaction mechanisms, we arranged our investigation based on the surface termination preferences of cus sites at U_SHE = 1.23 V. Specifically, we examined the reactions considering Ti, which favors termination without O; Ir, which favors termination with OH; and W, which favors O termination.

We initially focused on examining the Ti_0.67Ru_0.33O₂ mixture, maintaining two fixed layers of RuO₂ at the bottom while allowing three layers of Ti_0.67Ru_0.33O₂ to relax. Fig. 9 focuses on the impact of Ti atom distribution on the free energy profile of the Ru_br corrosion mechanism on the Ti_0.67Ru_0.33O₂(110) surface. We consider two different configurations, each defining a specific neighborhood around the dissolving Ru_cus atom, to elucidate the influence on individual reaction steps. In configuration 1, the bridge atom next to the dissolving atom is replaced by Ti, while the neighboring cus atom participating in the dissolution mechanism remain Ru. In configuration 2, the neighboring bridge atom remains Ru, while the neighboring cus atom is replaced by Ti. We note that, on these doped surfaces, there are many possible realizations of the corrosion mechanism, involving the bridge and cus sites, and in some cases, different cus sites. We tested multiple configurations and bond-breaking sequences to identify the pathways with the lowest free energy. This comparative analysis, illustrated in Fig. S9,† highlights key differences between chosen and non-chosen configurations, revealing how dopants can alter the reaction mechanism compared to pure RuO₂(110). The results shown below reflect the most favorable pathways identified.

Fig. 9 The free energy profile at U_SHE = 1.23 V illustrates the Ru_br corrosion mechanism on the Ti_0.67Ru_0.33O₂(110) surface in two configurations. Free energies were calculated at pH = 0. Colors: sky blue for Ru_bulk, red for O, black for Ru_diss, and green for Ti.

This specific modification of the environment alters the energetics of the reaction steps as follows: configuration 1 (orange line in Fig. 9) exhibits higher free energy and greater stability compared to pure RuO₂ (blue line) and configuration 2 (green line). The free energy reaches its maximum value of 2.075 eV in configuration 1 (orange line in Fig. 9) during the reconstruction step (step b), while configuration 2 reaches a maximum of 1.264 eV during the same step. Notably, in configuration 1, the nearest bridge neighbor to Ru_diss is Ti_br. During the reaction steps, especially in the second H₂O adsorption step (step h), no proton/electron pair is removed, and the H adsorbs onto O_br (which is on Ti_br). Then, in step j, the OH on Ti_br is removed.

In configuration 2, the nearest neighbor is another Ru_br. The transition from step a to step b, due to the unfavorable terminal O at Ti_cus in step a, involves three preparatory sub-steps (from b'′′ to b' shown in detail in Fig. S8†). These sub-steps include the adsorption of H₂O on the Ti_cus atom. Upon the removal of the first H⁺/e⁻ pair, the Ru_diss atom severs its bond to the neighboring OH of Ti_cus. The final removal of H⁺/e⁻ is exergonic, resulting in the formation of the regular step b. Notably, we observed a significant drop in free energies, attributed to changes in the reaction mechanism compared to pure RuO₂(110), starting from step f. Unlike pure RuO₂, where the tetrahedral RuO₄ species is connected to neighboring O_br and O_ot, in configuration 2, the RuO₄ species prefers being connected to two O_ot, resulting in an exergonic reaction step (e → f). This is mainly because it is highly unfavorable for Ti_cus to be capped by terminal oxygen; moving the RuO₄ species to the cus sites avoids this scenario. Similarly, upon the removal of the final H⁺/e⁻ pair in the second H₂O adsorption step, the Ru_diss atom severs its bond with the neighboring O_ot of Ru_cus akin to the Walden inversion proposed by Hess et al.²⁵ This results in the formation of a RuO₄ species attached only to the O_ot of Ti_cus, thereby avoiding the unfavorable terminal O at Ti_cus. In the final step, RuO₄ detaches, leaving an empty Ti_cus site, as Ti_cus prefers termination without O.

Moving on to the Ir_0.67Ru_0.33O₂ mixture, we adopted a similar methodology by fixing two layers of RuO₂ at the substrate while allowing three layers of Ir_0.67Ru_0.33O₂ to relax. The distribution of Ir atoms in configurations 1 and 2 of Ir_0.67Ru_0.33O₂ mirrors that of Ti atoms in Ti_0.67Ru_0.33O₂.

Fig. 10 illustrates how the Ir distribution influences the free energy profile of the Ru_br corrosion mechanism on the Ir_0.67Ru_0.33O₂(110) surface. Like in Fig. 9, we explore two configurations: configuration 1 (orange line) shows a ΔG_max of 2.248 eV during the dissolution step (step j), whereas configuration 2 (green line) peaks at 1.479 eV during the second H₂O adsorption step (step h). Configuration 1 exhibits higher free energy and greater stability compared to pure RuO₂ (blue line) and configuration 2. Notably, in configuration 1, the nearest neighbor to the Ru_diss is Ir_br. Starting from the second H₂O step (step h), upon the removal of the first H⁺/e⁻ pair, the Ru_diss atom severs its bond with the neighboring O_br–Ir_br, resulting in the Ir_br being saturated by terminal OH. The subsequent steps take place exclusively on the cus sites. In configuration 2, the nearest neighbor is another Ru_br, and no changes in reaction mechanisms occur after step f, unlike configuration 2 of Ti_0.67Ru_0.33O₂.

Fig. 10 The free energy profile at U_SHE = 1.23 V illustrates the Ru_br corrosion mechanism on the Ir_0.67Ru_0.33O₂(110) surface for two configurations. Free energies were calculated at pH = 0. Colors: sky blue for Ru_bulk, red for O, yellow for H, black for Ru_diss, and brown for Ir.

Lastly, we investigated the W_0.21Ru_0.79O₂ mixture, employing the same layer arrangement as in the previous mixtures. Similar to the previous examinations, we chose two configurations: configuration 1, where the neighboring bridge and cus atoms are W and Ru, respectively, and vice versa, in configuration 2. We selected a lower doping content in this case because W is the least similar to Ru, and addition of too much dopant may alter the properties in unpredictable ways; nevertheless, significant effects are observed here, because the specific doped sites have a larger effect on the corrosion behavior than the overall doping content, as shown in Section 3.1.2.

Fig. 11 depicts how the W distribution influences the free energy profile of the Ru_br corrosion mechanism on the W_0.21Ru_0.79O₂(110) surface. It explores two configurations relative to pure RuO₂. Notably, configuration 2 (green line) shows the highest free energy step at 1.144 eV during the final dissolution step (step j), while configuration 1 (orange line) peaks at 1.182 eV during the first reconstruction (step b).

Fig. 11 The free energy profile at U_SHE = 1.23 V illustrates the Ru_br corrosion mechanism on the W_0.21Ru_0.79O₂(110) surface for two configurations. Free energies were calculated at pH = 0. Colors: sky blue for Ru_bulk, red for O, black for Ru_diss, and violet for W. Note: step j consists of three steps represented by the highest free energy among them; please refer to Fig. S10† for details. *.

The dramatic change in configuration 2 can be explained by the strong preference of W_cus to remain terminated by O at the given potential: upon the removal of the final H⁺/e⁻ pair in the second H₂O step, the Ru_diss atom severs its bond with the neighboring O_br of Ru, forming a RuO₄ species attached only to the O_ot of W. While in the regular mechanism considered for all other cases, RuO₄ desorbs, along with the O_ot, W_cus requires to remain saturated. Therefore, before the dissolution step (step j), to lower this high free energy, a third H₂O molecule adsorbs, detaining two H⁺/e⁻ pairs, as shown in Fig. S10.† This alteration in the mechanism akin to the Walden inversion proposed by Hess et al.²⁵ reduces the highest free energy step from 1.305 eV to 1.144 eV.

From the different behavior of the three dopants and their different termination preferences we learn that the choice of dopant can alter not only the free energies of the reaction steps, but also the nature of these steps. To avoid states that are too high in free energy due to unfavorable terminations of the metal sites next to Ru_diss, additional H₂O molecules may partake in the reaction toward RuO₄. On Ti-doped RuO₂, we observe that the initial reconstruction is complicated by the lack of terminal O at Ti_cus; however, the final states involving the removal of RuO₄ are simplified as they allow the Ti_cus to recover its vacant state. On the other hand, in W-doped RuO₂, W_cus has such a strong preference to be capped with O_cus that additional steps are required late in the mechanism to detach RuO₄ from the surface.

Close inspection of the data presented in Fig. 7–11 suggests that the thermodynamics of corrosion are highly correlated across a large variety of surface modifications. Based on all the data presented in this section, we quantitatively examined the correlation between the thermodynamic corrosion potential and the ΔG_max of the full reaction energy profiles to assess the suitability of ΔG_tot as a descriptor for screening studies. As depicted in Fig. 12, our correlation analysis reveals a robust positive relationship (R² = 0.96) between the total free energy (0 ≤ ΔG_tot ≤ 1.5 eV) and the maximum free energy (1.0 eV ≤ ΔG_max ≤ 2.2 eV). This finding provides compelling evidence of the inherent connection between these parameters, highlighting a fundamental relationship governing material stability across diverse surface configurations across a large range of free energies. The maximum free energy (ΔG_max) is particularly significant for kinetic studies as it often represents the potential-determining step of a reaction, thus influencing the overall reaction rate and, in the case of corrosion, stability. Since ΔG_tot is a highly accessible quantity, requiring only the computation of initial and final state of the surface, we propose it as a descriptor suitable for screening the efficacy of different surface modifications via computation. Furthermore, this suggests that the stepwise corrosion mechanism does not need to be known in order to predict relative stabilities between similar surfaces.

Fig. 12 Correlation between ΔG_tot and ΔG_max illustrates material stability interconnections across surfaces. Free energies were calculated at pH = 0 and U_SHE = 1.23 V.

Overall, our investigation into Ti_0.67Ru_0.33O₂, Ir_0.67Ru_0.33O₂, and W_0.21Ru_0.79O₂ mixtures unveils nuanced variations in reaction mechanisms and surface atom distributions. These findings underscore the critical role of dopant selection in optimizing RuO₂ surface stability against corrosion. By elucidating the intricate interplay between dopants, surface terminations, and reaction pathways, our study provides valuable insights for the design and engineering of advanced materials exhibiting long-term stability for applications ranging from catalysis to energy storage.

4 Discussion

To begin our discussion, we contextualize our investigation into the thermodynamic stability of the RuO₂(110) surface within the broader scope of existing experimental and theoretical studies. Our investigation corroborates those of Over et al.,³¹ who identified the RuO₂(110) surface as the most stable among various facets. Additionally, our results are consistent with Hess et al.^25,32 on RuO₂(100) and its c(2 × 2) reconstructed facets as detailed in Fig. 3. Stoerzinger et al.³³ also examined the oxygen evolution reaction (OER) activity across different facets (100), (110), (101), and (111), confirming that the (110) facet is the most stable, while the (100) facet is the most active. Our study specifically targets the stability of the RuO₂(110) surface against corrosion and aims to enhance this stability.

Several studies have explored the incorporation of dopants into RuO₂ to improve stability. Kasian et al.¹⁰ focused on the stabilization effect of Ir in RuO₂, demonstrating that incorporating 25% Ir significantly enhances stability. Similarly, Escalera-López et al.³⁴ investigated the electrochemical activity–stability relationship of Ir–Ru mixed oxides (Ir_xRu_1−xO₂), finding that 20% Ir improves stability while maintaining high activity. Both studies indicated a significant positive effect on surface stability with a slight decrease in activity, which informed our chosen Ir concentration in Fig. 4c. Our results are consistent with these findings, showing a significant improvement in the stability of the RuO₂(110) surface. In studies exploring OER activity and electrocatalyst stability, Ir_xRu_1−xO_y catalysts with Ir concentrations up to 70% were developed, achieving 3 A cm⁻² at 1.8 V with strong stability in PEM electrolysis, though high turnover frequency altered Lewis acidity, impacting water oxidation.³⁵ Additionally, tuning the near-surface composition of Ru and Ir via surface segregation resulted in a Ru_0.5Ir_0.5 alloy exhibiting four times higher stability than the best Ru–Ir OER materials, without compromising catalytic activity.⁹ This is consistent with our investigation of the Ir_0.67Ru_0.33O₂ mechanism, where the high Ir concentration contributes to one of the most stable surfaces, as shown in Fig. 10. We note that doping RuO₂ with Ir poses an economic challenge, as the high cost of Ir may limit practical application. Our findings indicate that substituting specific Ru sites by Ir may result in significant enhancement, an insight that could be exploited to reduce the Ir content of mixed (Ru,Ir)O₂ for OER applications.

Our study investigates the influence of lower cost doping elements, such as Ti and W, which have been proposed in the literature as potential dopants for RuO₂. Hao et al.¹² investigated the stability and activity of RuO₂ with W and Er (W_0.2Er_0.1Ru_0.7O_2−δ). They found that adding W and Er significantly increases the catalyst's oxygen vacancy formation energy, improving durability and activity. This finding informed our chosen W concentration in Fig. 4c and 11 of the reaction mechanism investigation. Our predictions in Fig. 4c allow us to identify optimal dopant sites that enhance the durability and stability of the M_0.21Ru_0.79O₂(110) surface.

For Ti_xRu_1−xO₂, Godínez-Salomón et al.¹¹ demonstrated that incorporating Ti (12.5–50%) enhances catalyst stability and reduces Ru dissolution, with low Ti concentrations (12.5–20 at%) significantly improving stability compared to pure RuO₂. Regarding IrO₂ substrates, most studies focus on RuO₂ substrates enhancing the surface activity of IrO₂. Our study uniquely examines the effect of RuO₂ thickness on an IrO₂ substrate, identifying the optimal thickness for maximal stability. Fig. 5 reveals a distinct odd-even layer behavior that suggests that uneven layers, such as 1 or 3, exhibit the highest stability.

Consistent with recent findings by Chaudhary et al.,³⁶ our study shows that tensile strain (as seen in RuO₂ on IrO₂) enhances corrosion resistance, while compressive strain (as observed in RuO₂ on TiO₂) leads to destabilization of the surface, highlighting the critical role of strain in influencing the corrosion behavior of RuO₂.

In terms of reaction mechanism, while many studies have concentrated on the oxygen evolution reaction (OER) mechanism at RuO₂(110), fewer have delved into the specifics of RuO₂ corrosion mechanisms. Klyukin et al.³⁰ proposed a concept wherein a defect-free surface undergoes transitions leading to RuO₄ formation and subsequent corrosion. Similarly, Liu et al.²⁹ introduced four potential initial reconstruction steps (chemical steps), focusing on one to elucidate a mechanism that results in RuO₄ formation and surface corrosion. We adopted and expanded upon this mechanism in our investigation.

Our study extends beyond merely detailing the corrosion mechanisms of the RuO₂ surface to examine the impact of doping on these mechanisms, as shown in Fig. 8–11. Our findings highlight how the termination of the cus atoms in dopants affects the reaction mechanism and the associated free energies. In contrast to Gong et al.,³⁷ who use metal–oxygen bond strength from MD simulations to predict dissolution rates of complex glasses, our study focuses on thermodynamic descriptors, specifically ΔG_max and ΔG_tot, to assess corrosion resistance in RuO₂. While Gong et al.³⁷ report R² values of 0.80–0.92 for bond strength and dissolution rates, our study finds a strong correlation (R² = 0.96) between ΔG_max and ΔG_tot, demonstrating their effectiveness in predicting material stability. Similarly, Schwöebel et al.³⁸ use hydrogen bond acceptor strength as a descriptor for organic and inorganic compounds, demonstrating a high correlation (R² = 0.97) with experimental data, while our study employs thermodynamic parameters to predict corrosion stability, highlighting the broad applicability of descriptor-based methods across different material types. The concept of 'maximum free energy (ΔG_max)' as a descriptor for stability was first introduced by Exner and Over,³⁹ and our findings further support its utility in understanding reaction rates and mechanisms the trends of reaction rates and mechanisms upon altering the properties of the surface. Further work is required to understand the details of the kinetic processes governing the competition between the OER and the parasitic corrosion leading toward electrode dissolution. Kinetic studies are crucial for offering insights into activation energies, rate constants, and the effects of temperature and other reaction conditions.^40–51 Additionally, we plan to investigate the OER activity of various doped surfaces to compare their performance and stability relative to pure RuO₂.

5 Conclusion

Through comprehensive DFT analyses, we elucidate the stability and reaction mechanisms of RuO₂ catalysts in water electrolysis. Our investigation reveals the intricate interplay between surface orientations, dopants, and corrosion mechanisms, shedding light on key factors influencing RuO₂ stability against corrosion.

Our findings emphasize the critical role of understanding the intricate interplay between surface composition, dopants, and reaction mechanisms to optimize the stability of RuO₂ surfaces. Dopants such as Ir, Ti, and W exhibit diverse effects on stability, with Ir demonstrating superior stabilization compared to other elements. Specifically, Ti favors termination without O, Ir favors OH termination, and W favors O termination, each influencing distinct free energy profiles and reaction pathways, particularly evident in configuration 2 across all mixtures. Based on the correlation between the total change in Gibbs free energy (ΔG_tot) and the maximum Gibbs free energy (ΔG_max) we propose ΔG_tot as an accessible descriptor to predict the effect of different surface modifications on the stability of surface sites.

Overall, our study not only deepens our understanding of the complex behavior of RuO₂ surfaces but also offers valuable insights into designing tailored materials with enhanced stability for various applications, including catalysis and energy storage. These findings lay a solid foundation for future research aimed at optimizing the performance of RuO₂-based materials in real-world applications, thereby advancing the field of materials science and engineering.

Data availability

The Vienna Ab initio Simulation Package (VASP) code used in this study includes versions 5.4.4 and 6.4.2. Detailed information about VASP, including the latest updates and releases, can be found on the official VASP website: https://www.vasp.at/.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors thank the Deutsche Forschungsgemeinschaft and the DFG priority program SPP 2080 (DynaKat) for funding this project (Grant No. 493681475).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5ta00218d

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