Accelerating the discovery of new catalysts enabling high activity and cost efficiency is the key to the achievement of many current electrochemical energy conversion technologies toward reducing our dependence on non-renewable resources and mitigating the global warming crisis ^{[1, 2]}. In this regard, water splitting technologies have been the center subject of the spotlight. The oxygen evolution reaction (OER)—an anode reaction in water splitting—is severely encumbered by the sluggish kinetics involving four-proton/electron-coupled reaction process ^[3-6]. Proton exchange membrane (PEM) electrolyzer possesses many advantages compared with the alkaline electrolyzer, such as high loading flexibility, high current densities and voltage efficiency ^{[3-5, 7, 8]}. However, the implementation of these advantages is based on the premise of acid-resistant, highly active oxygen evolution electrocatalysts.

Although some electrocatalysts reported recently are found to be active for OER under harsh acidic operation conditions, the state-of-the-art electrocatalyst is still IrO₂ due to the trade-off between activity and stability. IrO₂ contains high content of expensive, scarce iridium, making it unfeasible for future large-scale commercialization ^{[3-5, 9-14]}. Therefore, it is urgent to develop highly active, stable and low-cost OER electrocatalysts. An effective protocol of reducing the usage of noble metal content is diluting the noble metal with earth-abundant materials, such as perovskites, pyrochlores and fluorite-like compounds ^{[13, 15-18]}. Recently, 6H-perovskite SrIrO₃ is demonstrated by our group to contain 27.1 wt% less iridium than IrO₂, but exhibits higher intrinsic catalytic activity for OER in acid ^[4]. The unique face-sharing IrO₆ octahedral dimers (i.e., Ir₂O₉) are believed to be responsible for the high catalytic activity in this type of perovskites. However, the iridium content is still undesirable in 6H-perovskite SrIrO₃, because besides the Ir₂O₉ dimers, there is another iridium-containing, auxiliary IrO₆ octahedra in this structure. Therefore, it is of great interest to find new 6H-perovskites which contain lower iridium content than SrIrO₃. A further systematical investigation on 6H-perovskites would be conducive to reveal the fundamental relationship of structural motifs and electrocatalytic activity. Such knowledge is also important for the prediction and rational design of efficient electrocatalysts for OER in acid.

In this work, we propose a class of lanthanide-contained, 6H-perovskites with a general formula of Ba₃LnIr₂O₉ (Ln = lanthanides) as OER electrocatalysts, in which the iridium content reduced by 50.11 wt%–51.26 wt% in comparison with IrO₂. We identify Ir₂O₉ octahedral dimers in this class of 6H-perovskites as the active subunits for OER, and their catalytic activities are regulated by the LnO₆ octahedra that directly connects with Ir₂O₉ octahedral dimers. We further find that the catalytic activity is correlated with the difference of adsorption free energy (∆G_O - ∆G_OH) between O* and OH* reaction intermediates, and the calculated O p-band center. Finally, Ba₃LaIr₂O₉ is identified as the most active catalyst among 6H-perovskites we studied, thanks to its optimal O p-band property.

The first-principle calculations are conducted by using plane-wave pseudopotential approach within the framework of density functional theory (DFT) as implemented in the Vienna Ab Initio Simulation Package (VASP) ^{[19, 20]}. The generalized gradient approximation formulated by Perdew, Burke, and Ernzerhof (PBE) is used as the exchange-correlation functional ^[21]. The electron-core interactions are described with the frozen-core projected augmented wave pseudopotentials ^[20]. A 400 eV cut-off energy for plane-wave basis set is used for all calculations. The convergence threshold for energy is set to 10^-4 eV and for force is 0.05 eV/Å. 5×5×5 and 5×5×1 Monkhorst-Pack k-point grid is employed for the geometric optimization of bulk and slab models, respectively ^[22]. An 11×11×1 k-point grid is employed for projected density of states (PDOS) calculations. The correction of the van der Waals (vdW) interactions is considered by introducing DFT-D2 method ^[23]. The dipolar correction is included and the symmetrization is switched off for the calculations of the slab models. The crystal orbital Hamiltonian population (COHP) is calculated to analyze the chemical bonding of adjacent Ir atoms in Ir₂O₉ octahedral dimers, which has been implemented in the LOBSTER program ^[24-26]. Negative -COHP value indicates antibonding states, while the positive -COHP value means bonding states. The Fermi level is set to 0 eV.

O 2p-band center (ε_2p) relative to the Fermi level was obtained by using the below equation ^[27]:

where ε is the energy referring to E - E_Fermi, and n_2p (ε) is the projected density of states (PDOS) for O-2p orbital.

All the theoretical models of Ba₃LnIr₂O₉ are assumed as P63/mmc space group, according to the structure reported by Doi et al. ^[28]. After optimization, by cleaving these optimized structures through the (001) plane, the corresponding slab models were obtained, with a 20 Å vacuum space to prevent the interaction between periodic images. All slab models have the thickness of six octahedral layers, and the upper 1/3 layers in the model are fully relaxed while the remaining kept frozen during the calculations.

The Gibbs free energy of each step for OER is computed according to the equation ΔG = ΔE + ΔZPE - TΔS. The ΔE is the energy differences obtained by DFT calculations. The values of ΔZPE are determined by the vibrational frequencies calculations and the values of TΔS are obtained from the standard tables for the gas phase molecules. The entropy for the adsorbate at the surface active site is assumed to be zero and the influence of temperature on the enthalpy is neglected in our calculations. Moreover, an external bias U is imposed on each step by introducing – eU in the calculation of free energy. Then, the reaction free energy of each elementary step can be expressed as following Eqs. (1-4) ^{[19-21, 23]}:

(1)

(2)

(3)

(4)

where E_H2O and E_H2 are the computed total energies for H₂O and H₂ molecules, respectively. The free energy of O₂ is obtained from the reaction H₂O → 1/2O₂ + H₂ by using the experimental free energy change of 2.46 eV per water molecule. E(^*), E(HO^*), E(O^*) and E(HOO*) represent energies of the clean surface and oxygen-containing intermediate species adsorbed on the surface, respectively.

The crystal structure of Ba₃LnIr₂O₉ 6H-perovskite adopts space group P63/mmc. As shown in Fig. 1(a), there are face-shared Ir₂O₉ octahedral dimers, which are alternatively connected with LnO₆ octahedra in a corner-shared mode along the c-axis. Electron location function (ELF) was calculated to analyze the bonding characteristic of Ir-Ir bonds in the Ir₂O₉ octahedral dimers of Ba₃LaIr₂O₉. Fig. 1(b) reveals that there is metallic feature between the Ir–Ir bonds in the Ir₂O₉ octahedral dimers. Additionally, we further investigate the Ir–Ir bonds of Ba₃LnIr₂O₉ by calculating the crystal orbital Hamiltonian population (COHP). As shown in Fig. 1(c), there are two sharp peaks in the bonding state area below the Fermi level, indicating the strong interaction of Ir–Ir bonding in Ir₂O₉ octahedral dimers. The density of states (DOS) (Fig. 1(d)) shows a wide overlap between Ir 5d and O 2p orbitals, suggesting the strong orbital hybridization of Ir 5d and O 2p orbital in Ba₃LaIr₂O₉. The DOS is cross the Fermi level, indicating the metallic behavior of Ba₃LaIr₂O₉.

We investigate oxygen evolution activities of this class of 6H-perovskites according to adsorbate evolution mechanism (Fig. 2), which is a four-electron transfer pathway for OER proposed by Rossmeisl et al. ^{[29, 30]}. The four-electron transfer pathway for OER in acid can be expressed as below Eqs. of (5)–(8):

(5)

(6)

(7)

(8)

where^* represents surface active site. The HO^*, O^* and HOO^* are the adsorbed intermediates on the surface active site. ∆G_OH, ∆G_O and ∆G_OOH are the Gibbs adsorption energies of these intermediates, respectively. The most thermodynamically unfavorable reaction step for OER is defined as potential-determining step (PDS) (i.e., max{∆G_(1–4)}/e). The theoretical overpotential is then expressed as the difference between the potential required by PDS and the equilibrium potential, 1.23 V.

We construct the theoretical models by cleaving the (001) plane of Ba₃LnIr₂O₉ bulk structure to obtain the corresponding surface slabs with three possible atom-exposed surfaces (Fig. 3(a)), including the surface with exposed Ln atoms (labelled as surface Ln), the surface with exposed Ir-I atoms (labelled as surface Ir-I) and the surface with exposed Ir-II atoms (labelled as surface Ir-II). Ir-I and Ir-II represent the iridium atoms in IrO₆ octahedra that indirectly and directly connect to the LnO₆ octahedra, respectively. We calculate surface energies of the three possible surfaces (Fig. 3(b)), and find that the surface energies of the surface Ir-I and surface Ir-II are similar and smaller than that of surface Ln. This result indicates that the two iridium-containing surfaces are more favorable to be exposed, compared with the surface Ln. In addition, the surface Ln is found to be unable to adsorb oxygen-involved intermediates, indicating that the surface Ln cannot serve as the catalytic active surface for OER. Thus, we next discuss the catalytic activities of the surface Ir-I and surface Ir-II in a detailed way.

We calculate the theoretical overpotentials of Ba₃LnIr₂O₉ series for OER for the surface Ir-I and surface Ir-II. Note that several Ba₃LnIr₂O₉ perovskites (Ln = Pm, Eu, Yb) fail to adsorb the oxygen-containing intermediates, and thereby they are not included in our following discussion. We find that: (1) the PDS is the second step (i.e., ∆G_O - ∆G_OH) and third step (i.e., ∆G_OOH - ∆G_O) for the surface Ir-II and the surface Ir-I, respectively; (2) The overpotentials of Ba₃LnIr₂O₉ series at surface Ir-II are significantly lower than those of the surface Ir-I (Fig. S1, Table S1 and Table S2 in the Supporting Information). The surface Ir-II of Ba₃LnIr₂O₉ 6H-perovskites exhibits excellent catalytic activity due to their small theoretical overpotential (ƞ) of < 0.5 V, which is smaller than that of IrO₂ (ƞ = 0.59 V) ^[31]. For example, for Ba₃LaIr₂O₉, the overpotential of the surface Ir-II for OER is 0.35 V, while the overpotential of the surface Ir-I for OER is 0.62 V (Fig. 3(c)). The superior activity of the surface Ir-II is due to the optimized adsorption free energy of O^* intermediates, which results in a good balance between the second and the third steps involved in the OER. By contrast, the adsorption free energy of O^* intermediates for the surface Ir-I is too strong compared with the surface Ir-II, leading to a higher potential needed for the third step for OER.

Considering the similar properties of lanthanides, Ba₃LnIr₂O₉ is an ideal material system to reveal the underlying effects on the activity regularity. We correlate the overpotentials of surface Ir-II and surface Ir-I of Ba₃LnIr₂O₉ with ∆G_O - ∆G_OH, a catalytic activity descriptor for OER. For the surface Ir-I, there is not a volcano plot relationship between ∆G_O - ∆G_OH and catalytic activity (Fig. S2 in the Supporting Information), suggesting that lanthanides do not have a regular influence on the surface Ir-I active sites. In contrast, for the surface Ir-II, a volcano plot is well constructed on the basis of theoretical overpotentials and activity descriptor, ∆G_O - ∆G_OH. As shown in Fig. 4, the Ba₃LnIr₂O₉ all locate at the right side of the volcano plot, which suggests that the PDS is the second step—the deprotonation of OH^* immediate to form O^* immediate. The left side of the volcano plot suggests the PDS is the third step (i.e., the formation of OOH^* intermedicate). It can be seen that the Ba₃LaIr₂O₉ locates at the top peak of this volcano plots, suggesting the optimal catalytic activity for OER is realized by Ba₃LnIr₂O₉. This result further demonstrates that the catalytic activity of the surface Ir-II can be regulated by varying lanthanides in the LnO₆ octahedra to achieve the optimized ∆G_O - ∆G_OH. Among the series of Ba₃LnIr₂O₉, it is believed that the most promising candidate catalyst for OER is Ba₃LaIr₂O₉.

In order to reveal the influence of electronic properties of Ba₃LnIr₂O₉ on ∆G_O - ∆G_OH, we calculate the O p-bands of Ba₃LnIr₂O₉. As shown in Fig. 5, a volcano curve trend is presented by the calculated O p-band center relative to Fermi level versus negative ∆G_O - ∆G_OH. The ∆G_O - ∆G_OH decreases with the O p-band center closer to Fermi level in the left side of the volcano curve, while the ∆G_O - ∆G_OH increases in the right side of the volcano curve when the O p-band center closer to the Fermi level. The above results indicate that a good electrocatalyst in Ba₃LnIr₂O₉ requires an O p-band center neither too far nor too close to the Fermi level, which gives an optimized ∆G_O - ∆G_OH, and thereby a good electrocatalytic activity. It is worth noting that Ba₃LaIr₂O₉ locates at the top peak of the volcano curves. This material has a moderate O p-band center and the minimum ∆G_O - ∆G_OH value, which refers to the optimal activity for OER.

Apart from the activity of Ba₃LnIr₂O₉, the thermodynamic stability is another important prerequisite factor for consideration. Therefore, we calculate the decomposition enthalpy of Ba₃LaIr₂O₉ into the corresponding binary compounds. The decomposition enthalpy is defined as the energy difference between the decomposed products and the Ba₃LaIr₂O₉ perovskite. The positive value of decomposition entropy means the endothermic reaction and thus difficult decomposition of Ba₃LaIr₂O₉. Ba₃LaIr₂O₉ has good thermodynamic stability with fairly large positive value of 3.79 eV. This result suggests that the Ba₃LaIr₂O₉ is screened to be a promising candidate for OER, and its catalytic performance is worth exploring experimentally.

We have presented a new family of lanthanide-contained, 6H-perovskites with largely reduced iridium content as electrocatalysts for OER in acid. The face-shared Ir₂O₉ octahedral dimers in this class of 6H-perovskites are the active subunits for OER, and their catalytic activities can be regulated by the LnO₆ octahedra. Among 6H-perovskites we studied, Ba₃LaIr₂O₉ is identified as the most promising candidate toward OER, with small theoretical overpotentials. Experimental efforts should be encouraged to synthesize this prospective, highly active oxygen evolution electrocatalyst.