Bayesian learning-assisted catalyst discovery for efficient iridium utilization in electrochemical water splitting

Abstract

Reducing noble metal dependence in oxygen evolution reaction (OER) catalysts is essential for achieving sustainable and scalable green hydrogen production. Bimetallic oxides, with their potential for high catalytic performance and reduced noble metal content, represent promising alternatives to traditional IrO₂-based OER catalysts. However, optimizing these materials remains challenging due to the complex interplay of elemental selection, composition, and chemical ordering. In this study, we integrate density functional theory (DFT) calculations with Bayesian learning to accelerate the discovery of high-performance, low-Ir bimetallic oxides, identifying surface Ir-doped TiO₂ as an optimal catalyst. Guided by theoretically optimized surface compositions and oxygen vacancies, we synthesized atomically dispersed Ir on TiO₂, achieving a 23-fold increase in Ir mass-specific activity and a 115-millivolt reduction in overpotential compared to commercial IrO₂. This work exemplifies a sustainable, data-driven pathway for electrocatalyst design that minimizes noble metal usage while maximizing efficiency, advancing scalable solutions in renewable energy and hydrogen production.

Data-driven discovery of Ir-doped TiO₂ boosts OER activity for sustainable green hydrogen production.

INTRODUCTION

Green hydrogen produced from renewable energy sources is a promising energy carrier that can address global energy security, mitigate climate change, and reduce environmental pollution (1, 2). Electrochemical water splitting, particularly proton exchange membrane water electrolysis (PEMWE), offers high current density and rapid responsiveness, making it suitable for coupling with intermittent renewable energy sources such as wind and solar (3). A key bottleneck in water electrolysis is the oxygen evolution reaction (OER) at the anode, which involves complex multielectron transfer steps and requires efficient and stable electrocatalysts. Now, Ir-based oxides, particularly IrO₂, are the most effective catalysts for OER in acidic environments due to their optimal balance of activity and stability. Yet, the scarcity and high cost of iridium limit the scalability of these catalysts, posing a major challenge for the commercialization of PEMWE, making it crucial to reduce noble metal content for cost-effective hydrogen production.

Strategies such as catalyst support, doping, and defect engineering have been explored to reduce iridium usage (4). Loading active noble metal species onto a supporting substrate or incorporation of non-noble metals alongside iridium oxides offers effective ways to reduce the consumption of precious metals (5). Intriguingly, it has also been found that the inert non-noble metal oxides, such as Ti and Ce, can be activated by noble element, enabling them to serve as active sites and participate in OER process (6–8). In addition, their tunable structures enable further enhancements in catalytic performance and conductivity through chemical ordering and defect engineering (9, 10). These structural flexibility enables bimetallic oxides to reduce noble metal content while enhancing catalytic activity through synergistic effects between guest and host elements (11). However, despite these advantages, optimizing bimetallic oxides remains challenging due to the complex interplay between elemental composition, chemical ordering, and structural defects, which collectively influence catalytic activity and stability. Experimental trial-and-error and high-throughput computations alone are often insufficient for efficiently navigating the vast configuration space.

Bayesian optimization combined with machine learning surrogate model offers a powerful approach for efficiently identifying high-performance candidate materials from a vast configuration space (12, 13). In this study, we leverage an effective data-driven approach that combines density functional theory (DFT) with Bayesian optimization to efficiently explore and optimize bimetallic oxide catalysts for OER. By calculating the theoretical overpotential for each element in 66 different binary oxides, we identified Ir-doped TiO₂ as a highly promising combination due to its potential for dual active sites. Using a Gaussian process–based Bayesian optimization, we fine-tuned the Ir surface composition, chemical ordering, and oxygen vacancies, finding that an Ir surface ratio of ~12.5% could achieve more than 40-fold increase in calculated Ir mass-specific activity compared to rutile IrO₂. This enhancement is attributed to the introduction of Ir and oxygen vacancies, which enhance Ti site activity while maintaining Ir site performance. Guided by these theoretical insights, we synthesized atomically dispersed Ir on TiO₂ with optimized oxygen vacancies, achieving a 23 times enhancement in Ir mass-specific activity, and lowered the overpotential by 115 mV relative to commercial IrO₂. This work exemplifies a sustainable approach to catalyst discovery, reducing noble metal content and advancing the development of scalable, high-performance electrocatalysts for green hydrogen production.

RESULTS

Initial screening

The search for binary oxide began with the identification of suitable alloying elements (Fig. 1A). Considering rutile-type IrO₂ oxide as the state-of-the-art commercial OER electrocatalyst, the thermodynamically stable (110) surface model for rutile was used as the support substrate. Although some non-rutile–type oxides loaded with noble metals have achieved excellent activity, such as the work by Li et al. (14) on Ir loaded onto $\mathrm{\gamma }$-MnO₂, we selected the classical rutile-type oxide support in this work to verify the effectiveness of Bayesian learning. The doping structures were constructed by replacing a host atom in coordinately unsaturated site (CUS) with a guest atom, as depicted in fig. S1. Six different rutile oxide supports (IrO₂, MoO₂, TiO₂, MnO₂, PdO₂, and SnO₂) were selected and doped with 11 potential guest elements (Au, Ir, Mn, Mo, Nb, Pt, Re, Ru, Sn, Ti, and V). The selected oxide supports all adopt the rutile structure, including IrO₂ and five structurally compatible oxides (PdO₂, RuO₂, TiO₂, SnO₂, and MoO₂) to ensure consistent comparison. Dopants were chosen on the basis of their presence in the selected oxides (Ir, Pd, Ru, Ti, Sn, and Mo) and extended to V, Re, Pt, Nb, Mn, and Au to cover a broader range of chemical properties. Systems with excessive structural distortion upon doping were excluded to ensure reliable screening results. To evaluate OER activity, the theoretical overpotential for doped atoms and their neighboring host atoms were calculated by computational hydrogen electrode method (tables S1 to S4) (15, 16).

Fig. 1. Workflow and bimetallic oxide combination screening.

(A) Workflow of the Bayesian optimization accelerating the design of OER electrocatalyst. (B) DFT-calculated heatmap of oxygen evolution reaction activity for various dopant-support combinations. The OER overpotential is represented by the color-coding double ring, with red indicating low overpotential and blue indicating high overpotential. The inner circles denote the overpotential when dopant atoms act as reaction sites, while the outer rings indicate the overpotential for metal sites in the oxide serving as reaction sites. (C) Free energy profiles of oxygen evolution reaction on Ti site in pure TiO₂ (orange) and Ir-doped TiO₂ (green)_. (D) Free energy profiles of oxygen evolution reaction on Ir site in pure IrO₂ (orange) and Ir-doped TiO₂ (green).

Figure 1B illustrates OER activity of 66 kinds of binary oxides. As expected, Ir sites in IrO₂ exhibit outstanding activity. It is well known that RuO₂ exhibits higher OER activity than IrO₂, but its activity calculated by DFT is lower than IrO₂ in Fig. 1B. This underestimation has also been widely reported in previous studies and is generally attributed to systematic errors inherent in DFT or to the possibility that RuO₂ follows a different reaction pathway or involves alternative active sites (17, 18). For oxides such as RuO₂, PdO₂, MnO₂, and IrO₂, doping has a relatively minor effect on the activity of the host elements. In contrast, the activity of Sn and Ti sites in SnO₂ and TiO₂, respectively, is notably influenced by the choice of doped elements. Notably, substantial enhancements in OER activity are observed at the Ti site when noble metals such as Ir and Ru are doped into TiO₂. Considering both the activity of guest and host element sites, as well as the cost-effectiveness of the TiO₂ support, we selected Ir-doped TiO₂ as the optimal binary oxide combination. Previous work by Nørskov and coworkers (19) has demonstrated the potential of Ir-doped TiO₂ as an effective OER catalyst. Moreover, several experimental studies have reported Ir-supported titanium oxides, lending further credibility to our screening approach (20, 21). Building on our screening results and the foundation laid by previous studies focused on compositional aspects, this work further deepens the understanding of IrTi-mixed oxides by systematically tuning both the Ir content and oxygen vacancies.

Figure 1 (C and D) presents the DFT-calculated OER-free energy profiles for Ti and Ir sites in Ir-TiO₂ with respect to pure TiO₂. Pure TiO₂ shows poor OER activity due to its weak adsorption affinity for oxygenated intermediates. Upon doping with Ir, the adsorption strength at the Ti site notably improves, reducing the free energy change for the potential-determining step (PDS), i.e., the oxidation of OH* to O*, from 2.82 eV in pure TiO₂ to 1.76 eV in Ir-TiO₂. For the Ir site, the free energy change of the PDS in Ir-TiO₂ (1.67 eV) is comparable to that of IrO₂ (1.73 eV). Consequently, both Ti and Ir sites in IrTiO₂ demonstrate high OER activity, benefiting from the synergistic effects of Ir doping.

Bayesian optimization of surface composition

Bayesian optimization was used to identify the optimal surface composition and chemical ordering for Ir-TiO₂. A machine learning model capable of predicting activity across different Ir surface ratios and chemical arrangements was developed. Information about the environment of the adsorption site—such as atomic count, coordination numer, and other related features—was extracted as inputs for the machine learning model (figs. S2 and S3). The difference in adsorption free energies between oxygen and hydroxyl, ΔG_O − ΔG_OH, was calculated and used as the output for the machine learning model. Through Nørskov’s microkinetic model, the reaction site’s current density was inferred from ΔG_O − ΔG_OH (15). The overall activity was considered as the average of the current densities of all CUS in the structure. Gaussian process regression (GPR) was selected for its ability to quantify uncertainty, allowing Bayesian optimization to balance exploration (high-uncertainty regions) and exploitation (high-activity regions) using the expected improvement (EI) acquisition function.

Eight iterations of Bayesian optimization were conducted to identify the most active Ir-TiO₂ configuration (figs. S4 and S5). This process generated a dataset of 139 DFT-calculated ΔG_O − ΔG_OH values, enabling a machine learning model with a prediction accuracy of 0.06 eV for ΔG_O − ΔG_OH (Fig. 2A). As shown in Fig. 2A, most ΔG_O − ΔG_OH values are concentrated in the high-activity region (optimal ΔG_O − ΔG_OH ≈ 1.53 eV), confirming that Bayesian optimization effectively prioritizes high-activity regions and avoids the sampling biases typical of random sampling. Separate surrogate models were trained for predicting the adsorption free energy difference ΔG_O − ΔG_OH and the thermodynamic stability of the structures. Bayesian optimization was also used to identify the most stable Ir-TiO₂ configuration (fig. S6), resulting in a model with a prediction accuracy of 0.004 eV/atom for formation energy (Fig. 2B).

Fig. 2. Bayesian optimization of IrTiO_2.

(A) Parity plot of the machine learning model predicting $\mathrm{\Delta }{G}_{\mathrm{O}}-\mathrm{\Delta }{G}_{\text{OH}}$ for IrTiO₂. (B) Parity plot of the machine learning model predicting formation energy for IrTiO₂. The reported mean absolute error of the surrogate model (in eV/atom) is normalized to the total number of atoms in the slab, including all elements. The train-to-test set ratio is 8:2, and the reported mean absolute error is the average of 10 random cross-validation runs. (C) Machine learning predicted mass activity (relative to IrO₂) at 1.53 V as a function of Ir loading for the most active and the most stable IrTiO₂ configuration. (D) Most active IrTiO₂ oxide configuration at Ir surface ratio of 18.75%. (E) Most stable IrTiO₂ oxide configuration at Ir surface ratio of 18.75%.

Figure 2C and fig. S7 present the machine learning–predicted relative mass activity and relative current density of the most active and most thermodynamic stable structures as a function of Ir loading and Ir surface ratio. The mass activity in this work refers to the Ir mass-specific activity, defined as the catalytic current normalized by the mass of Ir atoms in the system, thereby reflecting the intrinsic utilization efficiency of the precious metal. The relative mass activity and relative current density are both referenced to that of a four layer 2 × 4 rutile IrO₂ model. Even at low doping levels, the addition of Ir notably boosts mass activity by activating nearby Ti sites, with optimal activity achieved when nearly all CUS Ti sites are engaged. Beyond this optimal Ir ratio, however, further increases in Ir content provide marginal activity enhancement, leading instead to a decay in mass activity due to the excessive Ir loading.

The most active configuration of IrTiO₂ at Ir surface ratio of 18% (Fig. 2D) displays an ordered arrangement of Ir and Ti atoms, where all Ir atoms are isolated by Ti atoms. This ordered configuration effectively maximizes synergistic interactions between Ir and Ti, resulting in enhanced OER activity due to optimized electronic effects that promote oxygen adsorption and reaction kinetics at Ti sites (fig. S8).

Interestingly, the stability Bayesian optimization reveals a different trend. Configurations with aggregated Ir atoms are thermodynamically more stable (Fig. 2E and fig. S6). This trend may be attributed to the collective bonding preferences in different local environments: Phase-separated structures feature Ir-O-Ir and Ti-O-Ti linkages, which could be energetically more favorable than the mixed Ir-O-Ti motifs in ordered configurations. In these segregated configurations, fewer Ti sites neighbor Ir atoms, reducing the electron transfer and catalytic synergy necessary for optimal OER performance (fig. S9). As a result, these segregated structures exhibit lower mass activity than the ordered configurations and require a higher Ir surface ratio to achieve optimal mass activity (~50%), as shown in Fig. 2C.

The divergence between the most active and most stable configurations outlines the upper and lower bounds of the activity trend under real conditions and highlights the trade-off between maximizing catalytic activity and achieving thermodynamic stability, underscoring the importance of atomic-level design in balancing these properties in Ir-TiO₂ catalysts.

Effects of oxygen vacancy on IrTiO₂

Building on the balance between catalytic activity and thermodynamic stability, we explored strategies to enhance Ti site activation in segregated structures by introducing oxygen vacancies into IrTiO₂. To achieve this, a machine learning model was developed to predict OER activity for IrTiO_2-x, supported by an OER activity database generated by randomly removing oxygen atoms from existing IrTiO₂ structures. Approximately 285 DFT-calculated ΔG_O - ΔG_OH values for IrTiO_2−x were accumulated, with the ΔG_O − ΔG_OH distributions for Ti and Ir sites, both with and without oxygen vacancies, shown in Fig. 3 (A and B). The introduction of Ir broadens the ΔG_O − ΔG_OH distribution for Ti sites, spanning the range between pure TiO₂ and pure IrO₂, while the addition of oxygen vacancies further shifts the ΔG_O − ΔG_OH values of Ti toward those of IrO₂. In contrast, the ΔG_O − ΔG_OH distribution for Ir sites remains concentrated within a narrow range, indicating that Ir loading and oxygen vacancies have a relatively minor impact on Ir sites.

Fig. 3. Effect of oxygen vacancies on the OER activity of IrTiO_2.

(A) Frequency distribution histogram of $\mathrm{\Delta }{G}_{\mathrm{O}}-\mathrm{\Delta }{G}_{\text{OH}}$ on Ti sites without and with oxygen vacancies. (B) Frequency distribution histogram of $\mathrm{\Delta }{G}_{\mathrm{O}}-\mathrm{\Delta }{G}_{\text{OH}}$ on Ir sites without and with oxygen vacancies. The vertical dashed lines in blue and red, respectively, depict the $\mathrm{\Delta }{G}_{\mathrm{O}}-\mathrm{\Delta }{G}_{\text{OH}}$ values of pure TiO₂ and pure IrO₂. (C) Machine learning predicted mass activity at 1.53 V relative to IrO₂ of IrTiO₂ and IrTiO_2−x as a function of Ir loading. (D) Charge density differences calculations of O adsorbed on Ti site in pure TiO₂, IrTiO₂, and IrTiO_2−x; yellow signifies charge accumulation, and cyan indicates charge depletion. (E) Charge density differences calculations of O adsorbed on Ir site in pure IrO₂, IrTiO₂, and IrTiO_2−x. (F) DFT-calculated projected density of states (PDOS) of TiO₂, IrTiO₂, and IrTiO_2−x, and IrO₂. The 2p states of O atoms, 3d states of Ti atoms, and 5d states of Ir atoms in the surface are colored by red, green, and orange, respectively. The energies are all referenced to the vacuum level, and the Fermi level for each system was denoted by the vertical black dashed line. a.u., arbitrary unit.

Using this dataset, we developed a machine learning model for IrTiO_2−x with acceptable prediction accuracy of 0.10 eV for ΔG_O − ΔG_OH (fig. S10). The model was subsequently used to optimize oxygen vacancy configurations in IrTiO₂ (fig. S11). Figure 3C shows the relative mass activity of the most stable IrTiO₂ structures and the maximum activity achieved after introducing a single oxygen vacancy. The results reveal that with 12.5% Ir surface doping and the incorporation of oxygen vacancies, a mass activity exceeding 40 times that of IrO₂ can be achieved. While the surrogate model may not resolve this enhancement with quantitative precision, it effectively captures the qualitative trends and identifies promising configurations for further validation (22, 23). To address stability concerns, we additionally calculated the oxygen vacancy formation energies and identified the most stable IrTiO_2−x structure (fig. S12), whose predicted mass activity is shown in fig. S13. Despite slightly lower activity compared to the most active IrTiO_2−x variant, it still demonstrates a more than 40-fold enhancement over IrO₂, confirming the effectiveness of vacancy engineering in activating Ti sites while retaining structural stability.

To shed light on the activity enhancement mechanism of Ti site by Ir dopant and oxygen vacancy, we analyzed the electronic structure of TiO₂, IrTiO₂, IrTiO_2−x, and IrO₂ through charge density difference and projected density of states (PDOS) calculations. As illustrated in Fig. 3D and fig. S14, Ir doping enhances the adsorption affinity of oxygen on Ti site through charge redistribution from Ir to Ti, while the introduction of oxygen vacancies further strengthens the charge transfer. The enhanced charge transfer is quantitatively demonstrated by the Bader charge calculations results, which show that the charge transfer amounts of the oxygen atom adsorbed on Ti site to the catalyst surface in TiO₂, IrTiO₂, and IrTiO_2−x are −0.61|e|, −0.67|e| and − 0.69|e|, respectively, and the charge transfer amounts of the iridium atom neighboring to Ti site to the catalyst surface in IrTiO₂ and IrTiO_2−x are +1.80|e| and + 1.63|e|, respectively. PDOS results reveal that Ir doping introduces new electronic states between the conduction band and valence band of Ti (Fig. 3F). Our previous work has shown that Ir doping states raise the highest occupied states (HOS) of the system, which activates otherwise inert Ti sites by increasing energy gain of electrons transferred during O adsorption (24). Introducing oxygen vacancies further elevates the HOS, enhancing Ti site activation and improving the conductivity of IrTiO₂, which collectively boosts catalytic activity.

Synthesis and characterization of IrTiO_2−x

Theoretical predictions suggest that doping with a small amount of Ir and introducing oxygen vacancies can notably enhance the OER catalytic activity of the IrTi bimetallic oxide material. Following the above theoretical prediction, atomically dispersed Ir on TiO_2−x nanorods (IrTiO_2−x) was synthesized by a simple and scalable impregnation-calcination method. First, TiO₂ nanorod array was grown on carbon cloth (fig. S15) by a hydrothermal method, and then, the TiO_2−x nanorods with oxygen vacancy was successfully obtained via the calcination of TiO₂ nanorod array at 700°C for 4 hours in H₂/Ar flowing gas, which is confirmed by the electron paramagnetic resonance (EPR) signal assigned to oxygen vacancy (fig. S16) (25, 26). The x-ray diffraction (XRD) pattern of the TiO_2−x nanorods displays a typical rutile structure (JCPD #21-1276) mixed with a small amount of anatase phase (JCPD #21-1272) (fig. S17) (27). The scanning electron microscopy (SEM) images show that TiO_2−x nanorods have diameters ranging from 50 to 100 nm and a length of around 2 μm (fig. S18). Subsequently, Ir atom was dopped on TiO_2−x nanorods by impregnation and calcination process (see Materials and Methods for more details), the XRD pattern of IrTiO_2−x is consistent with TiO_2−x support (fig. S17), and no characteristic diffraction peak related to Ir can be detected, implying the high dispersion of Ir in the catalyst, and the element content of Ir in the catalyst was measured to be 14.2 μg·cm⁻² by inductively coupled plasma optical emission spectroscopy (ICP-OES; table S5). The morphology of TiO_2−x nanorods keeps unchanged after the introduction of Ir (fig. S18). High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images of IrTiO_2−x present that the well-ordered lattice fringe (0.321 nm) corresponds to the (110) plane of rutile TiO₂, and isolated bright dots (Ir atoms) are randomly scattered on the TiO_2−x support (Fig. 4A and fig. S19). While our thermodynamic modeling suggests that Ir atoms tend to aggregate in the most stable configurations, this appears to differ from the dispersed Ir distribution observed experimentally. This discrepancy may arise from the kinetic constraints during synthesis, which can lead to metastable states being trapped. EPR spectra of IrTiO_2−x further suggests the prominent existence of oxygen vacancy after overgrowth of Ir (Fig. 4B).

Fig. 4. Characterization and electrocatalytic OER performance of catalysts.

(A) HAADF-STEM images of IrTiO_2−x. (B) EPR spectra of IrTiO₂ and IrTiO_2−x. (C) Ir L₃ edge XANES spectra of IrTiO_2−x, commercial IrO₂, and Ir foil. (D) Fourier transforms of k³-weight Ir L₃ edge EXAFS spectra for IrTiO_2−x, commercial IrO₂, and Ir foil. (E) LSV curves of TiO₂, IrTiO₂, IrTiO_2−x, commercial IrO₂, and 20% Ir/C. (F) Overpotential of IrTiO₂, IrTiO_2−x, commercial IrO₂, and 20% Ir/C at 10 mA·cm⁻². (G) Mass activity of IrTiO₂, IrTiO_2−x, commercial IrO₂, and 20% Ir/C at 1.53 V versus RHE. (H) Tafel slopes derived from (E). (I) EIS plots of IrTiO₂, IrTiO_2−x, commercial IrO₂, and 20% Ir/C. MA, mass activity.

The chemical state and local coordination environment of Ir species were investigated by x-ray photoelectron spectroscopy (XPS) and x-ray absorption spectroscopy (XAS). Figure S20 shows the XPS spectra of Ir 4f for IrTiO_2−x and IrTiO₂ catalyst. The binding energy peaks at 62.25 and 65.14 eV belong to Ir 4f_7/2 and Ir 4f_5/2, respectively, indicating that the oxidation state of Ir is 4+ (28, 29). The x-ray absorption near-edge structure (XANES) spectroscopy of Ir L₃-edge for IrTiO_2−x together with Ir foil and IrO₂ as references is presented in Fig. 4C. The white line intensity of Ir L₃ edge represents the transition from occupied 2p electron to empty 5d orbital. A more empty Ir 5d orbital state in the catalyst corresponds to the higher intensity of the white line, implying the higher oxidation state of Ir (30). Obviously, the white line intensity of IrTiO_2−x almost coincides with the commercial IrO₂, demonstrating that the valence state of Ir mainly exists in 4+. Moreover, the coordination configurations were analyzed by extended x-ray absorption fine structure (EXAFS). Figure 4D displays the Fourier transform EXAFS spectra of Ir species in the R-space. For IrTiO_2−x, there is no obvious peak at 2.51 Å (for Ir-Ir scattering in metallic Ir), but the dominant peak around 1.63 Å ascribed to the Ir─O bond can be observed, indicating the atomic dispersion of the Ir species in the sample (fig. S21) (31, 32).

Electrocatalytic OER performance

The electrocatalytic performance for OER of IrTiO_2−x and TiO₂ was investigated in 0.1 M HClO₄ solution at room temperature (experimental details are provided in the Supplementary Materials). For comparison, the catalytic activities of TiO₂, commercial IrO₂, and 20% Ir/C were also tested under the same conditions. The linear sweep voltammetry (LSV) curves with iR compensation for these catalysts are shown in Fig. 4E. Pure TiO₂ exhibits negligible activity, whereas IrTiO₂ achieves a lower overpotential (ƞ) of 330 mV to reach a current density of 10 mA·cm⁻². To enhance the OER activity further, oxygen vacancies were introduced into the catalyst, creating IrTiO_2−x, which displays high OER activity with an overpotential of only 295 mV at 10 mA·cm⁻² (Fig. 4F), outperforming TiO₂, commercial IrO₂ (410 mV), and 20% Ir/C (382 mV).

In addition, mass activities were calculated to assess the cost-effectiveness of the atomically dispersed structure. Notably, the mass activity of IrTiO_2−x reached 807 A·g_Ir⁻¹ at 1.53 V [reversible hydrogen electrode (RHE)] (Fig. 4G and fig. S22), which is nine times higher than that of commercial IrO₂ (83 A·g_Ir⁻¹) and 23 times higher than 20% Ir/C (34 A·g_Ir⁻¹). Electrochemically active surface areas (ECSAs) were estimated by double-layer capacitance (Cdl) measurements from cyclic voltammetry with variable scan rates (fig. S23 and table S6), showing that IrTiO_2−x has a higher ECSA than IrTiO₂. These results demonstrate the excellent OER activity of IrTiO_2−x, which can be attributed to the maximized atom efficiency of Ir atoms and the synergistic effect of Ir doping and oxygen vacancies that activate inert Ti sites, validating the theoretical prediction. Furthermore, EPR spectra confirm that the oxygen vacancies in IrTiO_2−x remain stable after the OER test (fig. S24). Because the EPR spectra were not collected on the same sample before and after OER testing, they cannot conclusively quantify changes in vacancy concentration. Nevertheless, the presence of EPR signals after the OER indicates that oxygen vacancies are retained to a notable extent during the reaction, supporting their structural stability under operating conditions.

In addition, the Tafel slope of IrTiO_2−x (68 mV·dec⁻¹) is considerably lower than that of IrTiO₂ (79 mV·dec⁻¹), commercial IrO₂ (113 mV·dec⁻¹), and 20% Ir/C (88 mV·dec⁻¹) (Fig. 4H), indicating faster OER kinetics for IrTiO_2−x. The lower charge transfer resistance (R_ct) of IrTiO_2−x, obtained from electrochemical impedance spectroscopy (EIS) analysis, further demonstrates more efficient charge transfer at the IrTiO_2−x catalyst-electrolyte interface, implying a faster reaction rate (Fig. 4I and table S7). Furthermore, the performance of IrTiO_2−x in terms of mass activity and overpotential surpasses that of most reported Ir-based catalysts for acidic OER (fig. S25 and table S8). In addition, the chronopotentiometry measurement was carried out to evaluate the stability of the catalyst. As shown in fig. S26, the overpotential of IrTiO_2−x was increased by 60 mV after a continuous operation of more than 10 hours at 10 mA cm⁻². Compared with the commercial IrO₂ and commercial Ir/C, the IrTiO_2−x exhibit a relatively stability.

The operando differential electrochemical mass spectrometry (DEMS) experiments with ¹⁸O isotope labeling were performed to investigate OER mechanism of IrTiO_2−x. The different molecular mass involving ³²O₂, ³⁴O₂, and ³⁶O₂ during the OER process were collected and analyzed. First, the OER was conducted in 0.1 M HClO₄ electrolyte that prepared using ¹⁸O-labeled water. As presented in fig. S27A, the reaction predominantly yielded ³⁶O₂ as the main product, with trace amounts of ³⁴O₂ detected. This minor ³⁴O₂ originated from ¹⁶O impurities derived from H₂¹⁶O in the 70% HClO₄ electrolyte system or possibly from the lattice oxygen of the catalyst. Subsequently, the second OER test of the catalyst that used in the first step was conducted in 0.1 M HClO₄ electrolyte that prepared using ¹⁶O-labeled water. As shown in fig. S27B, ³²O₂ was the dominant product, with no detectable ³⁴O₂ or ³⁶O₂ signals. This result conflicts with the lattice oxygen-mediated (LOM) mechanism, as the expected exchange of ¹⁸O with lattice oxygen in IrTiO_2−x during the first OER step would have produced ³⁴O₂ or ³⁶O₂ species (33). Thus, the DEMS experiments results demonstrated the conventional adsorbate evolution mechanism (AEM), which in agreement with the DFT results. As shown in the LSV curves in fig. S28, we further evaluated the OER catalytic activity of pristine TiO₂ and oxygen-deficient TiO_2−x. The results indicate that the introduction of oxygen vacancies leads to negligible changes in catalytic performance, suggesting that oxygen vacancies in TiO₂ do not serve as active sites for the OER. These experimental results confirm that the introduction of oxygen vacancies does not alter the OER mechanism or the active site in for IrTiO_2-x.

DISCUSSION

In summary, we developed a Bayesian learning-assisted strategy to design efficient, low-Ir OER catalysts by combining theory and experiment. The resulting Ir-TiO_2−x electrocatalyst exhibited notably improved activity and reduced noble metal usage. Guided by the theory prediction, the successful synthesis and experimental validation of atomically dispersed Ir on TiO₂ nanorods with oxygen vacancies have shown a remarkable enhancement in OER activity. While there are still gaps between theoretical models and specific experimental conditions, they helped narrow the experimental design space by highlighting the importance of balancing Ir content and oxygen vacancy concentration for optimal performance. By leveraging advanced computational techniques and machine learning, this work demonstrates the potential of data-driven catalyst design in advancing renewable energy technologies, aligning with global sustainability goals. The methodologies presented here are not only applicable to OER but could also be extended to other material system, such as supports like $\mathrm{\gamma }$-MnO₂ (14), and other catalytic reactions such as oxygen reduction and carbon dioxide reduction, ultimately contributing to a more sustainable energy future.

MATERIALS AND METHODS

DFT calculation

All DFT calculations were performed using the Vienna ab initio simulation package (version 6.3.2) (34). The Perdew-Burke-Ernzerhof functional was used to describe the exchange-correlation interactions (35). Projector-augmented wave method was used to treat the interaction between the core and valence electrons, the pseudopotentials used treat Ti (3p, 3d, 4s), Ir (5d, 6s), and O (2s, 2p) electrons as valence states. A plane wave basis set with a kinetic energy cutoff of 400 eV was used (36). The unit cells of rutile oxides in P4₂/mnm space group were download from Material Project database and reoptimized by DFT. For OER activity calculations for single atom-doped oxide, a 2 × 1 (110) surface model for rutile oxide was constructed with a four-layer-thick slab with 48 atoms. For optimal ratio and configuration calculations for IrTiO₂, a larger 4 × 2 (110) surface model with four-layer-thick slab with 192 atoms was used. On the basis of the IrTiO₂ model, one to four oxygen vacancies were randomly removed to model IrTiO_2−x. Considering that oxygen vacancies on the surface of the bimetallic oxides tend be oxidized and refilled under working conditions, oxygen vacancies were generated in the interior of the slab model rather than on the surface. We also calculated the oxygen vacancy formation energies for both the surface and subsurface layers, and the results show that the formation energy is lower in the subsurface layer than on the surface. Furthermore, oxygen vacancies were not introduced directly at the nearest neighbors of reaction site to avoid creating an overly unsaturated coordination state, which could result in structural reformation during optimization and excessively strong adsorption energies. A vacuum layer of 7.5 Å was added above and below the slab to avoid the periodic interactions. For the slab models, the bottom two atomic layers were fixed during geometry optimization to mimic bulk-like behavior, while the top two layers were fully relaxed. The Monkhorst-Pack k-point mesh for bulk, 2 $\times$ 1 slab and 4 $\times$ 2 slab optimization tasks were 10 $\times$ 10 $\times$ 10, 5  $\times$ 5 $\times$  1, and 3  $\times$ 3 $\times$  1, respectively (37). In accordance with Vegard’s law, the lattice parameters for the IrTiO₂ bimetallic oxide model was determined as the weighted average of the lattice parameters of pure TiO₂ and pure IrO₂ based on the stoichiometric ratio of Ti and Ir (38). The optimization was stopped when the energy changes and forces drop below $5\times {10}^{-5}$ eV and 0.03 eV/Å. DFT + U methods were used to address the excessive delocalized of d electrons, and Hubbard U values were set at 3.3 V for Ti element, 3.75 V for Mn element, and 3.25 V for V element. Other U values are adapted from (39).

The adsorption energies of *O and *OH were calculated by the following equations

$$∆E_{\mathrm{O}}=E_{\mathrm{O}\ast }-E_{\ast }-(E_{{\mathrm{H}}_2\mathrm{O}}-E_{{\mathrm{H}}_2})$$ (1)

$$∆E_{\text{OH}}=E_{\text{OH}\ast }-E_{\ast }-(E_{{\mathrm{H}}_2\mathrm{O}}-1/2E_{{\mathrm{H}}_2})$$ (2)

where the $E_{\ast }$ , $E_{\mathrm{O}\ast }$ and $E_{\text{OH}\ast }$ are DFT-calculated energies for clean surface, surface with O, and surface with OH, respectively. The $E_{{\mathrm{H}}_2\mathrm{O}}$ and $E_{{\mathrm{H}}_2}$ are energies of H₂O (−6.76 eV) and H₂ (−14.22 eV), respectively, which are calculated by DFT using a H₂O and H₂ molecule placed on a 10 $\times$ 10 $\times$ 10–Å cubic cell model. The free energy of each adsorbate can be obtained from the following equation

$$∆G=∆E+∆\text{ZPE}-T∆S$$ (3)

Here, the $∆E$ is the DFT-calculated energy, $∆\text{ZPE}$ and $T∆S$ are the zero-point energy correction and entropy correction, respectively. In this work, the $∆\text{ZPE}-T∆S$ values from literature for *OH (0.35 eV) and *O (0.05 eV) were used (15). The adsorbate evolution mechanism consisting of four-step electron-coupled proton transfer steps was used. We also calculated the free energy profile of the LOM pathway on Ir-doped TiO₂ (fig. S29). The results show that the free energy increase of the PDS for LOM is notably higher than that for AEM, confirming AEM as the more favorable reaction pathway.

The adsorption energies of *O and *OH were computed, and adsorption energies of OOH were obtained using the linear relationship between $\mathrm{\Delta }{G}_{\text{OOH}}$ and $\mathrm{\Delta }{G}_{\text{OH}}$$(\mathrm{\Delta }{G}_{\text{OOH}}=\mathrm{\Delta }{G}_{\text{OH}}+3.2\text{eV})$ (15). The reaction free energies of four OER elementary step can be obtained by

$$∆G_1=∆G_{\text{OH}}$$ (4)

$$∆G_2=∆G_{\mathrm{O}}-∆G_{\text{OH}}$$ (5)

$$∆G_3=∆G_{\text{OOH}}-∆G_{\mathrm{O}}$$ (6)

$$∆G_4=4.92-∆G_{\text{OOH}}$$ (7)

The overpotential is calculated by the following equation

$$\mathrm{\eta }=\text{max}\left(\mathrm{\Delta }{G}_{\mathrm{i}}\right)/e-1.23\mathrm{V}$$ (8)

Here, $\text{max}\left(\mathrm{\Delta }{G}_{\mathrm{i}}\right)$ is the maximum reaction free energy of four elementary steps.

A microkinetic modeling correlating the $\mathrm{\Delta }{G}_{\mathrm{O}}-\mathrm{\Delta }{G}_{\text{OH}}$ with current density was applied to evaluate the OER activity of each reaction site at an applied potential of 1.53 V (40). The logarithm of the current density (log i) was approximated as a piecewise linear function as following

$$\begin{array}{c}\text{log}i=\{\begin{array}{c}8.06\times ∆G-12.98,∆G<1.53\text{eV}\hfill \\ -8.74\times ∆G+12.73,∆G\ge 1.53\text{eV}\end{array}\hfill \end{array}$$ (9)

where $∆G$ is the free energy difference of the reaction from *OH to *O. The activity of a given configuration was evaluated as the average current density over all its CUS sites. The theoretical mass activity was computed by divide the mass activity of IrTiO₂ by that of IrO₂ using a four-layer slab model. The formation energy was used to reflect the thermodynamic stability, which is defined by the following equation

$$E_{\mathrm{f}}=E\left(\mathrm{I}{\mathrm{r}}_x\mathrm{T}{\mathrm{i}}_{1-x}{\mathrm{O}}_2\right)-[\mathit{xE}\left(\text{Ir}{\mathrm{O}}_2\right)+(1-x)E\left(\text{Ti}{\mathrm{O}}_2\right)]$$ (10)

where E(*) is the DFT-calculated energy of ${\text{Ir}}_x{\text{Ti}}_{1-x}{\mathrm{O}}_2$ model, $x$ is the stoichiometric surface ratio of Ir in ${\text{Ir}}_x{\text{Ti}}_{1-x}{\mathrm{O}}_2$ , and $E\left({\text{TiO}}_2\right)$ and $E\left({\text{IrO}}_2\right)$ depict the DFT-calculated energies when the surface ratio of Ir are 0 and 1, respectively.

Feature engineering

To develop a machine learning model capable of predicting intermediate adsorption energies on oxide CUS, we digitally encode the atomic neighboring environment of CUS as input for the machine learning model, as depicted in fig. S3. The metal atoms closest to the CUS site in the oxide were divided into four atomic layers. Starting from the nearest to the farthest layer from the CUS, there are 1, 2, 2, 4, and 2 atoms in each of the five layers, respectively. To enhance the fidelity of feature, the second neighboring layer is subdivided into its own second and fourth neighboring layers, and the fourth neighboring layer is also subdivided into its own second and fourth neighboring layers. Consequently, the neighboring environment of the adsorption site is subdivided into nine atomic layers. The number of Ti atoms, number of Ir atoms, mean coordination number of Ti atoms, and mean coordination number of Ir atoms were used to quantify all nine atomic layers, which made up the 36-dimensional feature. When there are two Ir atoms and two Ti atoms in the fourth neighbor atomic shell of the CUS site, there are three different environments resulting from the atomic occupations. We included angles as part of the features to describe these environments. In addition, we used the overall Ir doping ratio in alloy oxide as an additional dimensional feature. When introducing oxygen vacancies, the oxygen vacancies reduce the coordination number of metal atoms, which is subsequently reflected in the feature. Normalization was used to eliminate bases caused by varying feature values across different dimensions. Principal components analysis (PCA) dimensionality reduction was used to delete redundant features. The DFT calculated $\mathrm{\Delta }{G}_{\mathrm{O}}-\mathrm{\Delta }{G}_{\text{OH}}$ values of CUS site were used as the output for the machine learning model.

The machine learning model capable of predicting stability for given doped IrTiO₂ configuration was also developed. The features for the model were extracted by counting the numbers of different coordination pairs in for five-coordinated CUS, six-coordinated bridge site. The DFT-calculated energy of IrTiO₂ with the reference energies of pure TiO₂ and IrO₂ phases was used as the output target.

Machine learning and Bayesian optimization

We choose the GPR model for its capacity to estimate uncertainties. The radial-basis function (RBF) was used to determine the term in covariance matrix. The RBF function was defined as

$$k(x,x^{\prime })=a^2\text{exp}\left[-\frac{{(x-x^{\prime })}^2}{2b^2}\right]$$ (11)

where $x$ and $x^{\prime }$ were two variables, $a$ and $b$ were scale factor and length factor, and these two factors were optimized in machine learning model training. The scikit-learn package was used for constructing GPR model (41). The predicted $\mathrm{\Delta }{G}_O-\mathrm{\Delta }{G}_{\text{OH}}$ and corresponding uncertainty of each CUS site in IrTiO₂ model were further translated to OER activity $\mathrm{A}$ and corresponding uncertainty ${\mathrm{\sigma }}_{\mathrm{A}}$ . The hypothesis is put forward that the OER activity $\mathrm{A}$ of each site behaves as an independent random variable drawn from a population that follows a normal distribution $N(\mathrm{A},{\mathrm{\sigma }}_{\mathrm{A}}^2)$ . Then, the mean activity $\overline{\mathrm{A}}$ of all eight CUS sites in IrTiO₂ model can be regarded as a random variable satisfying Gaussian distribution in the following form

$$\overline{\mathrm{A}}=N({\displaystyle \sum _{i=1}^8}{\mathrm{A}}_i,1/8{\displaystyle \sum _{i=1}^8}{\mathrm{\sigma }}_{{\mathrm{A}}_i}^2)$$ (12)

The EI was used as the acquisition function to determine the selection of the next IrTiO₂ configuration. EI is defined as followed

$$\text{EI}\left(x\right)=[f\left(x\right)-f\left(x^{+}\right)-\mathrm{\zeta }]\mathrm{\Phi }\left(Z\right)+\mathrm{\sigma }\left(x\right)\mathrm{\varphi }\left(Z\right)$$ (13)

where $Z=[f\left(x\right)-f\left(x^{+}\right)]/\mathrm{\sigma }\left(x\right)$ , $f\left(x^{+}\right)$ is the maximum value in existing dataset, and $\mathrm{\Phi }$ and $\mathrm{\varphi }$ are the cumulative density and probability density function of standard normal distribution, respectively. $\mathrm{\zeta }$ is a hyperparameter in EI function; in this work, a constant value of 0.01 was used for $\mathrm{\zeta }$ . $f\left(x\right)$ and $\mathrm{\sigma }\left(x\right)$ are the predicted mean activity and uncertainty for a given IrTiO₂ structure as described in equation (15).

Because binary oxide structures are intractable to be completely enumerate, we conducted Monte Carlo simulation to find the configurations with the highest EI values at various Ir ratio and oxygen vacancy locations. Totally, eight oxide structures were chosen in each iteration (seven structures with equal ratio from 12.5 to 87.5% and one structure with the highest EI), and the $\mathrm{\Delta }{G}_{\mathrm{O}}-\mathrm{\Delta }{G}_{\text{OH}}$ of these searched structures were calculated by DFT calculation and added to the training database to refine the machine learning surrogate model.

Materials

Tetrabutyl orthotitanate (≥99%) and isopropanol were purchased from Aladdin. Chloroiridic acid (H₂IrCl₆, 35% Ir) was purchased from Macklin. Perchloric acid (HClO₄, 70%) was purchased from Sigma-Aldrich. Ethanol and hydrochloric acid (HCl) were purchased from Beijing Tong Guang Fine Chemical Company. Commercial IrO₂ was purchased from Henan Bauhinia Chemical Technology Co. Ltd. Carbon cloth (WOS 1011) was purchased from Taiwan CeTech Co. Ltd. and further treated with nitric acid (HNO₃). Carbon paper (TGP-H-060) was purchased from TORAY.

Synthesis of TiO₂ nanorod array

The TiO₂ nanorod array supported on carbon cloth was firstly prepared by a seed-assisted hydrothermal process (27). Typically, a piece of carbon cloth (1 by 1 cm²) was soaked in isopropanol containing 75 mM titanium butoxide for 3 min. The precursor was dried at 60°C and then annealed at 400°C with heating rate of 2°C/min for 2 hours in air to form a thin layer of TiO₂ seeds. The carbon cloth with TiO₂ seeds was transferred in Teflon-lined stainless-steel autoclave and immersed in a solution containing 5 ml of 6 M HCl and 100 μl of titanium butoxide. Subsequently, the autoclave was heated at 150°C for 8 hours. After that, the hydrothermally treated carbon cloth was calcined at 400°C with a heating rate of 10°C/min for 2 hours in air.

Synthesis of TiO_2−x nanorod array

The TiO₂ nanorod array was annealed at 700°C for 4 hours in H₂/Ar flowing gas to prepare the defective TiO₂ (named as TiO_2−x) nanorod array. Although surface vacancies are preferentially generated during H₂ treatment, their instability under oxidative conditions suggests that only subsurface or near-surface vacancies remain active during OER. This supports the relevance of our computational model, which emphasizes the role of stable subsurface oxygen vacancies in enhancing catalytic activity.

Synthesis of Ir single atoms on TiO_2−x nanorod (IrTiO_2−x)

The IrTiO_2−x catalyst was synthesized by an impregnation-thermal decomposition process. In detail, the piece of carbon cloth loaded with TiO_2−x nanorod array was immersed in H₂IrCl₆ solution (0.5 mg/ml) for 4 hours. the IrTiO_2−x was obtained by calcining the precursor sample at 300°C with heating rate of 5°C/min for 2 hours under argon atmosphere.

Synthesis of Ir single atoms on TiO₂ nanorod (IrTiO₂)

The IrTiO₂ catalyst was prepared by the same method with IrTiO_2−x, except that using TiO₂ nanorod array instead of TiO_2−x.

Characterizations

Field-emission SEM was collected on a HITACHI SU-8010 microscope. High-resolution transmission electron microscopy (HRTEM) was performed on a JEOL JEM-2100F microscope operated at 200 kV. HAADF-STEM images of the catalysts were obtained on Thermo Scientific Themis Z microscope working at 300 kV. Powder XRD patterns were performed on a PANalytical X’Pert PRO diffractometer with Cu-Kα radiation (λ = 1.5418 Å, 40 kV, 40 mA). XPS was collected on Thermo Scientific K-Alpha, and all data were corrected with C 1s peak at 284.6 eV. ICP-OES was carried out by using Agilent 5110. EPR measurements were run on a Bruker EMX PLUS spectrometer. The XAS data were collected at the 1W1B station in Beijing Synchrotron Radiation Facility, and the XANES and at Ir L₃ edge of catalysts were obtained with fluorescence mode. The XAS data at Ir L₃ edge were calibrated to Ir foil, and IrO₂ was used as reference materials. The data analysis was performed using Artemis and Athena in the Demeter software suite by FEFF software.

Electrochemical measurements

The OER performance of the catalysts was studied on a CHI 760E workstation with a standard three-electrode cell. The carbon cloth substrate supported with IrTiO_2−x nanorod array was used as a working electrode. An Ag/AgCl electrode (saturated KCl) and platinum plate (1 cm by 1 cm) were served as the reference electrode and counter electrode, respectively. All measurements were performed in 0.1 M HClO4 electrolyte at room temperature. All potentials in this work were converted into the RHE by the equation of E (versus RHE) = E (versus Ag/AgCl) + 0.27 V.

The LSV was recorded in the potential range of 1 to 2 V versus RHE with a scan rate of 5 mV s⁻¹ after being calibrated with iR compensation. The EIS was conducted at an overpotential of 0.3 V from 0.1 to 10⁵ Hz. The load amount of commercial IrO₂ and 20% Ir/C on the carbon paper are 30 and 15 μg_Ir·cm⁻². The mass activity of catalysts was obtained by the equation of j_geo/m_Ir, where j_geo is the geometric current density (mA·cm⁻²) and m_Ir is the loading of Ir on the carbon cloth (μg_Ir·cm⁻²), which is obtained from ICP-OES results. The ECSA was estimated by electrochemical double-layer capacitance (C_dl) according to the equation of C_dl/C_s, where C_dl was tested in the non-Faradic potential of 1.1 to 1.2 V versus. RHE with a scan rate from 10 to 50 mV·s⁻¹. The C_s is the specific capacitance, and the value is chosen as 35 μF·cm⁻² to estimate the ECSA.

Supplementary Materials

This PDF file includes:

Supplementary Text

Figs. S1 to S30

Tables S1 to S8