First-Principles Study of Sn-Doped RuO₂ as Efficient Electrocatalysts for Enhanced Oxygen Evolution

Abstract

Improving the catalytic performance of the oxygen evolution reaction (OER) for water splitting in acidic media is crucial for the production of clean and renewable hydrogen energy. Herein, we study the OER electrocatalytic properties of various active sites on four exposed (110) and ($\overline{1}$10) surfaces of Sn-doped RuO₂ (Sn/RuO₂) with antiferromagnetic arrangements in acidic environments. The Sn/RuO₂ bulk structure with the Cm space group exhibits favorable thermodynamic stability. The coordinatively unsaturated metal (M_cus) sites distributed on the right branch of the volcano plot are generally more active than the bridge-bonded lattice oxygen (O_br) sites located on the left. Different from the conventional knowledge that the most active site is located in the nearest neighbor of the doped atom, it has a lower OER overpotential when the active site is 3.6 Å away from the doped Sn atom. Among the sites studied, the 46-Ru_cus site exhibits the optimal OER catalytic performance. The inherent factors affecting the OER activity of each site on the Sn/RuO₂ surface are further analyzed, including the center of the d/p band at the active sites, the average electrostatic potential of the ions, and the number of transferred electrons. This work provides a reminder for the selection of active sites used to evaluate catalytic performance, which will benefit the development of efficient OER electrocatalysts.

1. Introduction

Since fossil fuel reserves are limited and their excessive use causes environmental pollution, it is urgent to explore alternative energy to replace fossil fuels [1,2,3]. Clean and renewable hydrogen (H₂) energy generated by electrochemical water splitting is considered an ideal substitute and has received widespread attention [4,5,6]. The water splitting process involves two key reactions: the oxygen evolution reaction (OER) and the hydrogen evolution reaction (HER). Compared with HER, the slow kinetic OER greatly reduces the overall efficiency of H₂ preparation [7,8,9]. In this case, researchers have been conducting in-depth studies on various OER catalysts to improve their catalytic performance, such as precious metals, transition metal oxides, single-atom catalysts, etc. [10,11,12,13,14] Especially in an acidic environment, the advantages of higher ionic conductivity, fewer unfavorable reactions, and faster system responses are beneficial to promote OER reaction rates [15,16,17,18]. Therefore, designing highly efficient OER catalysts in acidic conditions is of great significance for the development of sustainable energy.

Rutile-phase RuO₂ with outstanding OER catalytic performance in acidic media has always been a benchmark catalyst [19,20,21]. Given that electrochemical reactions usually occur on the catalyst surface, the introduction of doped atoms is a common effective strategy to improve the efficiency of electrocatalysts, which will affect properties such as the number of exposed active sites, intrinsic activity, and electronic structure [22]. For example, Chen et al. indicated that the doping of Mn atoms can regulate the d-band center of the Ru active site in RuO₂, lower antibonding Ru-O states, and enhance the intrinsic activity of RuO₂ [23]. Hao et al. studied W and Er co-doping RuO₂ lattice, and the results showed that the oxygen vacancies were increased, and the excessive oxidation of Ru was avoided [17]. Meanwhile, some work reported that the introduction of Sn atoms activates adjacent Ru sites and enables synthesized Sn/RuO₂ nanoparticles to achieve high activity and durability [24].

Although great progress has been made regarding the OER catalytic activity of metal-doped RuO₂, there is still room for improvement. Rutile RuO₂ has always been considered a Pauli paramagnetic system, and the majority of studies treat it as a nonmagnetic system [25,26,27,28,29]. However, recent experimental measurements uncovered that its metallic state is linear antiferromagnetic [30,31]. In addition, Miao et al. recently demonstrated that the d-electron correlation of RuO₂ with antiferromagnetic arrangement can tune the adsorption energy of oxygenated species, thereby affecting the OER catalytic performance [32]. Furthermore, the selection of active sites is also crucial to the evaluation of catalytic performance, while most of the previous studies have focused on the Ru atoms near doped atoms [4,15,23,33,34,35], which, to a certain extent, lack the exploration of active sites at other locations.

In this work, we comprehensively studied the OER catalytic performance of different active sites on Sn-doped antiferromagnetic RuO₂ (Sn/RuO₂)(110) and ($\overline{1}$10) surfaces based on density functional theory (DFT). The stable geometric structure and atomic magnetic distribution of Sn/RuO₂ bulk and surfaces are determined. Based on this, the adsorption energy and linear relationship of reaction intermediates *OH, *O, and *OOH at various active sites were calculated, and then the OER active volcano curve was plotted. It was found that the doping of Sn atoms effectively improved the OER activity of RuO₂, and the OER performance of coordinatively unsaturated metal (M_cus) sites is generally higher than that of the bridge-bonded lattice oxygen (O_br) sites. Moreover, the site nearest to the doped Sn atom does not have the best OER activity. Finally, the effects of the d/p-band center, the average electrostatic potential of the ions and the charge transfer on the OER catalytic performance of Sn/RuO₂ surface were further analyzed, which revealed the conditions for the optimal active site.

2. Results and Discussion

2.1. Stable Models of Sn/RuO₂ Bulk and Surfaces

A reasonable Hubbard U value can accurately describe the electronic correlation in RuO₂. As shown in Figure 1, RuO₂ bulk is a nonmagnetic structure without considering U, while when the U_eff value is about 2 eV, the antiferromagnetic distribution RuO₂ structure is more stable, agreeing with previous studies [30,32]. As U_eff increases to 4 eV, there is a band gap (0.47 eV) near the Fermi level, and RuO₂ is no longer metallic, which is inconsistent with the actual properties of the material. Therefore, subsequent structure and activity studies are based on the U_eff value of 2 eV.

As shown in Figure 2a, a p(2 × 2 × 2) RuO₂ supercell was modeled, in which, when 16 Ru atoms are randomly replaced by 2 Sn atoms, there will be 120 possible configurations. After screening for unequal symmetry, all the doping systems that have only six independent space groups, namely, Cmmm, Cm, P2/m, C2/m, Pmmm, and Fmmm (Figure S1), are found. So, it is necessary to calculate the six doping structures with different space groups and then select the most stable model as the system we focus on. Doped Sn atoms are located at the original Ru position, and their initial spin settings are the same as that of the original Ru atoms. As shown in Table S1, we consider the different spin configurations of each system. When two Sn atoms are in the nearest neighbor and their spin direction is opposite (Figure 2b), the Sn/RuO₂ structure (Cm) with the most negative formation energy is thermodynamically stable.

Based on this, we explored the OER catalytic performance of Sn/RuO₂ along the [110] direction. The schematic diagram of Figure 2c shows that different atomic distributions of Sn/RuO₂ slabs in the [110] and [$\overline{1}$10] directions will result in different exposed surfaces and active sites. Especially for the Sn/RuO₂($\overline{1}$10) surface, exposed surfaces with and without doped Sn atoms appear alternately. These surfaces are composed of the vertically oriented octahedral rows (singly coordinated O atoms at the surface) and the horizontally oriented octahedral rows (doubly coordinated O atoms at the surface). This work focuses on the OER catalytic activity of the M_cus and O_br sites on the Sn/RuO₂ surfaces. Finally, the active sites and atomic distributions on the four unequal exposed surfaces of Sn/RuO₂(110) and ($\overline{1}$10) are shown in Figure 3a–d.

2.2. Reaction Mechanism and Free Energy Diagram

OER in acidic media usually follows a four-electron reaction path (Equations (1)–(4)), and H₂O molecules deprotonate in turn to form *OH, *O, and *OOH intermediates, and then *OOH is further converted into product O₂.

$$*+{\mathrm{H}}_2\mathrm{O} \left(\mathrm{l}\right) \to *\mathrm{O}\mathrm{H}+{\mathrm{H}}^{+}+{\mathrm{e}}^{-} (\Delta G_1=∆G_{*\mathrm{O}\mathrm{H}})$$

(1)

$$*\mathrm{O}\mathrm{H}\to *\mathrm{O}+{\mathrm{H}}^{+}+{\mathrm{e}}^{-} (\Delta G_2=∆G_{\mathrm{*}\mathrm{O}}-∆G_{\mathrm{*}\mathrm{O}\mathrm{H}})$$

(2)

$$*\mathrm{O}+{\mathrm{H}}_2\mathrm{O} \left(\mathrm{l}\right)\to *\mathrm{O}\mathrm{O}\mathrm{H}+{\mathrm{H}}^{+}+{\mathrm{e}}^{-} (\Delta G_3=∆G_{\mathrm{*}\mathrm{O}\mathrm{O}\mathrm{H}}-∆G_{\mathrm{*}\mathrm{O}})$$

(3)

$$*\mathrm{O}\mathrm{O}\mathrm{H}\to \mathrm{*}+{\mathrm{O}}_2\left(\mathrm{g}\right)+{\mathrm{H}}^{+}+{\mathrm{e}}^{-} (\Delta G_4=4.92-∆G_{\mathrm{*}\mathrm{O}\mathrm{O}\mathrm{H}})$$

(4)

where * represents the active site on the catalyst surface; $\Delta G_{1-4}$ represents the reaction free energy of each step; and $\Delta G_{\mathrm{*}\mathrm{O}\mathrm{H}}$, $\Delta G_{\mathrm{*}\mathrm{O}}$, and $\Delta G_{\mathrm{*}\mathrm{O}\mathrm{O}\mathrm{H}}$ represent the adsorption free energy of *OH, *O, and *OOH intermediates, respectively, which can be obtained through Equations (5)–(7). The zero-point energy and entropy of the related gaseous molecules are displayed in Table S2.

$$∆G_{*\mathrm{O}\mathrm{H}}=G_{*\mathrm{O}\mathrm{H}}+1/2G_{\mathrm{H}2}-G_{\mathrm{H}2\mathrm{O}}-E_{*}$$

(5)

$$∆G_{*\mathrm{O}}=G_{*\mathrm{O}\mathrm{H}}+G_{\mathrm{H}2}-G_{\mathrm{H}2\mathrm{O}}-E_{*}$$

(6)

$$∆G_{*\mathrm{O}\mathrm{O}\mathrm{H}}=G_{*\mathrm{O}\mathrm{O}\mathrm{H}}+3/2G_{\mathrm{H}2}-2G_{\mathrm{H}2\mathrm{O}}-E_{*}$$

(7)

Following the above reaction steps, the adsorption of *OH, *O, and *OOH intermediates (Figure S2) was calculated. The OER reaction free energy diagram at equilibrium potential (1.23 V) and relaxed structures at the M_cus and O_br sites of Sn/RuO₂ are shown in Figure 4, and the adsorption configuration of the remaining sites is similar. The Sabatier principle indicates that the activity of the catalyst is related to the adsorption intensity of the reaction intermediate [36,37]. Too strong an adsorption will hinder the desorption of the intermediate, resulting in the occupation of active sites; while too weak an adsorption will be unfavorable for site activation. Therefore, an ideal catalyst has a moderate binding strength with the intermediate. Generally, the elementary reaction step with the maximum reaction free energy is the rate-determining step (RDS), which significantly affects catalytic activity. The RDS of each site on the Sn/RuO₂(110) and ($\overline{1}$10) surfaces is mainly the process of *O formation and the conversion of *O into *OOH.

In Figure 4a, some sites bind too strongly to *OH, such as the 26-O_br site bridging Ru-Sn atoms (26-O_{br_Ru-Sn}), the 27-O_{br_Ru-Ru} site, the 12-Ru_cus site, and the 14-Ru_cus site, making the subsequent transformation of *O to *OOH difficult; whereas the adsorption of *O at the 11-Sn_cus site is so weak that there is a large RDS (*OH → *O). In contrast, the $\Delta G$ of *OH → *O at the 25-Ru_cus site is smaller and exhibits excellent OER catalytic activity on the Sn/RuO₂(110) surface. Figure 4b shows the free energy diagrams of OER on the surface of Sn/RuO₂($\overline{1}$10). Similarly, a higher $\Delta G_{\mathrm{*}\mathrm{O}}$ at the 31-Sn_cus site is unfavorable to OER progression. When lattice oxygen participates in the reaction, the adsorption of *OH and *O at the 33-O_br, 35-O_br, and 47-O_br sites is too strong, which, to some extent, hinders the formation of *OOH and its deprotonation process. However, the adsorption of oxygenated species at the 34-Ru_cus and 44-Ru_cus sites is moderate, displaying outstanding OER catalytic activity. The results are consistent with the previous study [24], where the Sn_cus sites exhibit the RDS at *OH → *O, while the Ru_cus sites show the RDS at *O → *OOH due to the strong *O binding strength.

2.3. Active Volcano Plot of OER Theory Overpotential

Theoretical overpotential (${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}$) is an important parameter in evaluating the OER activity of a catalyst. A lower ${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}$ value generally means better OER catalytic performance.

$${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}} =\max \{\Delta G_1, \Delta G_2, \Delta G_3, \Delta G_4\}/\mathrm{e}-\mathrm{1.23\; V}$$

(8)

From the definition of the ${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}$, it can be seen that in order to achieve a lower ${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}$, the $\Delta G_i$ of each step should be close to 1.23 eV; that is, ${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}$ tends to 0 V, thereby balancing the binding strength of the reaction intermediates so that they are not too strong or too weak. Since OER activity is mainly determined by the $\Delta G_{\mathrm{*}\mathrm{O}\mathrm{O}\mathrm{H}}$, $\Delta G_{\mathrm{*}\mathrm{O}}$, and $\Delta G_{\mathrm{*}\mathrm{O}\mathrm{H}}$, and they have a linear relationship with each other (Figure 5a), this simplifies the description of OER activity in the system.

As shown in Figure 5b, ${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}$ and $\Delta G_{\mathrm{*}\mathrm{O}}-\Delta G_{\mathrm{*}\mathrm{O}\mathrm{H}}$ exhibit an approximate activity volcano plot, which is widely used for screening and developing efficient electrocatalysts. The O_br sites in the four exposed surfaces studied are concentrated on the left branch of the volcano curve, while the M_cus sites are mainly located on the right branch of the volcano plot, which can be attributed to the relatively weak binding of the M_cus site to *O than the O_br sites. Figure 5b displays that more unsaturated Ru_cus sites occupy the upper part of the volcano plot, where the 46-Ru_cus site (0.51 V) located at the top has the best OER catalytic activity. Then, the activity is followed by the 34- (0.58 V), 48- (0.80 V), 25- (0.82 V), and 14- (0.89 V) Ru_cus sites. The binding strength of *O and *OH at these sites is moderate, in line with the Sabatier principle.

In addition, we also calculated the OER catalytic performance of the pure RuO₂(110) surface at the Ru_cus active sites before and after considering Hubbard U, and the corresponding reaction free energy diagram is shown in Figure S3. Before considering U_eff, the ${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}$ of RuO₂(110) is 0.87 V, consistent with the previous results [38]. After considering U_eff, the ${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}$ of the Ru_cus site on the RuO₂(110) surface is reduced by 0.14 eV, and its OER catalytic activity is enhanced. Compared with the ${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}$ of 46-Ru_cus site on the Sn/RuO₂($\overline{1}$10) surface, we can conclude that Sn doping activates the Ru-O bond and further improves the catalytic performance of OER.

2.4. Analysis of Electronic Properties on Sn/RuO₂(110) and (110) Surfaces

The possible factors underlying the differences in the activity exhibited by various sites on the Sn/RuO₂(110) and ($\overline{1}$10) surfaces are further explored. The distance of M_cus or O_br active sites from the nearest doped Sn atom (d_M/O-Sn) on the Sn/RuO₂ surfaces is counted. For example, the distance between the 32-Ru_cus and 31-Sn_cus site is measured in Figure 3c, while the 34-Ru_cus site is counted as its distance from the nearest neighbor Sn atom instead of the 31-Sn_cus site. As shown in Figure 6a, Sn doping effectively enhanced the OER catalytic activity of RuO₂, such as 46-Ru_cus, 32-Ru_cus, and 48-Ru_cus sites. However, in the case of either M_cus or O_br sites (Figure S4), it is not commonly assumed that the site closest to the doped atom is most active. When the value of d_M/O-Sn at the active sites is approximately 3.6 Å, they exhibit outstanding OER catalytic performance. For transition metal oxide catalysts, the band center (ε) of the active atom is closely related to the binding strength of the adsorbed oxygenated species and the catalyst surface. Usually, a lower band center allows for the occupation of a high-energy anti-bonding state, resulting in a weak adsorption [39]. The active sites involved include Ru, Sn, and O atoms, so we explored the relationship between the Ru-d, Sn-p, and O-p band centers (${\epsilon }_{\mathrm{p}/\mathrm{d}}$) and the ${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}$.

As shown in Figure 6b, the ${\epsilon }_{\mathrm{p}/\mathrm{d}}$ of the active site of the Sn/RuO₂(110) and ($\overline{1}$10) surfaces has a clear linear relationship with ${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}$, and the closer the ${\epsilon }_{\mathrm{p}/\mathrm{d}}$ is to the Fermi level, the better the OER catalytic activity at this site. However, it can also be observed from Figure 6b that the ${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}$ vs. ${\epsilon }_{\mathrm{p}}$ of the Sn_cus sites deviates from the trend line, which may be due to the intrinsic properties of the Sn atom located in the main group and the transition metal Ru atom located in the subgroup being quite different. To confirm this hypothesis, we calculated the ${\epsilon }_{\mathrm{p}}$ of the antimony (Sb) atom near the Sn atom, the ${\epsilon }_{\mathrm{d}}$ of the rhodium (Rh) atom around the Ru atom on the periodic table, and the OER catalytic activity of either Sb or Rh doped with RuO₂(110), respectively (Figure S5). The data point of the 11-Sb_cus site in Figure 6 is around the Sn site, which is also far away from the trend line; while Rh/RuO₂ (purple data point) is located around the RuO₂ system, which conforms to the trend line. Similar to Sn/RuO₂, the 14-Ru_cus site (d_Ru-Sb/Rh = 3.6 Å) on the Sb (Rh)/RuO₂(110) surface also displays optimal OER performance (Figure 6c). Slightly different from the Sn and Sb atoms, the Rh site exhibits OER activity comparable to that of the 14-Ru_cus site, mainly due to the similar valence electron distribution of Rh and Ru atoms. The electron density of states (DOS) for Sb/RuO₂ and Rh/RuO₂ is further compared (Figure 6d). In the Sb/RuO₂(110) surface, the electronic states near the Fermi level are predominantly contributed by the 12-Ru_cus and 14-Ru_cus sites. As for the Rh/RuO₂, the 11-Rh site exhibits a higher electron occupancy state near the Fermi level, which accounts for the superior activity of the 11-Rh_cus site compared to the 11-Sb_cus site.

Moreover, we analyzed the contributions of Bader charge (red data points) and average electrostatic potential at the core (blue data points) of metal atoms at each active site to their catalytic activity. Figure 7a–d shows the Bader charge distribution of each atom on the Sn/RuO₂(110) and ($\overline{1}$10) surfaces, where the Sn and Ru atoms donate electrons to the O atoms. The doping of Sn atoms increases the electron transfer of neighboring Ru atoms compared to the distant Ru sites, thereby affecting the adsorption intensity and catalytic activity of the Ru_cus sites. The quantitative analysis is displayed in Figure 7e,f. It is noted that the U_eff correction significantly affects the electronic properties of RuO₂ system. In Figure 7e, the RuO₂(110) surface with U_eff loses more electrons and exhibits a lower average electrostatic potential than the RuO₂(110) surface without U_eff. Usually Ru-based catalysts are easily over-oxidized into unstable high valence state Ru in acidic electrolytes, resulting in the gradual dissolution of the materials [17]. However, the less charge is transferred from 46-Ru_cus and 34-Ru_cus sites than the original undoped RuO₂. This indicates that Sn doping not only enhances the OER activity but also reduces the oxidation state of partial Ru sites and increases their antioxidant properties. Du et al. also indicated that electron enrichment on Ru ions can decreases oxidation and maintain the stability of RuO₂ in the hybrid catalyst [40]. The 12-Ru_cus and 32-Ru_cus sites closest to the Sn atom transfer more electrons than the other Ru_cus sites and possess a high overpotential. Overall, lower OER activity at the Ru_cus site correlates with more negative electrostatic potential and higher charge transfer.

As for the O_br sites, given that lattice O binds with OH to release O₂, the reaction intermediates adsorb at the O_br site and the oxygen vacancy (O_v). Thus, the electrostatic potential and Bader charge of two metal atoms near the O_v are taken into account, and the connection between their geometric mean and ${\eta }^{\mathrm{O}\mathrm{E}\mathrm{R}}$ is established (Figure 7f). Similar to the trend of the Ru_cus sites, the OER performance at the O_br sites declines with increasingly negative electrostatic potentials or enhanced electron transfer on adjacent metal atoms. However, an opposite trend is observed at the doped Sn_cus and the O_{br_Ru-Sn} sites. In Figure S6, more electrons are lost at the sites closer to the Sn atom, and their atomic electrostatic potential is significantly lower than that of the Ru_cus and the O_{br_Ru-Ru} sites. As the atomic electrostatic potential and Bader charge gradually decrease, it seems to be more favorable for the OER reaction at the site containing the Sn atom.

To better clarify the role of Sn doping, in the case of Sn/RuO₂($\overline{1}$10) surface, the Crystal Orbital Hamilton Population (COHP) [41,42] is calculated to analyze the bonding interactions between active sites and *O intermediate, including undoped RuO₂ with U_eff, 31-Sn_cus, 32-Ru_cus, and 34-Ru_cus sites. The ICOHP value obtained from the COHP integration indicates the bond strength between atomic pairs; i.e., the more negative the ICOHP, the stronger binding strength. As shown in Figure 8, the order of the ICOHP at various sites is RuO₂ < 34-Sn_cus < 32-Ru_cus < 31-Ru_cus. The adsorption of *O on the undoped RuO₂ is too strong, hindering the conversion of *O to *OOH. The weak adsorption of *O at the 31-Sn_cus site results in a RDS of *OOH → *O. However, the ICOHP at the 34-Ru_cus site is in the middle, and the adsorption strength of *O is moderate. The introduced Sn atoms adjust the original adsorption strength of the oxygenated species, thereby enhancing the electrocatalytic performance of RuO₂. In addition, the differential charge density of O₂ on the RuO₂(110) and Sn/RuO₂(110) surfaces also proves the role of Sn (Figure S7). The Ru atoms donate electrons to O₂ for the formation of Ru-O bonds. For undoped RuO₂, the electrons transferred by the Ru atoms connected to O atom are 1.74 e, whereas for the Sn/RuO₂ surface, this value decreases to 1.69 e. It is clear that Sn doping modulates the electron distribution of neighboring Ru atoms, weakening the binding of Ru_cus sites to O₂, favoring O₂ desorption, and thereby accelerating the OER process.

3. Computational Details

All spin polarization DFT calculations in this work were implemented by the Vienna Ab-initio Simulation Package (VASP) [43,44]. The projector augmented wave (PAW) pseudopotential [45] was used to model the interaction between the ions and electrons, and a 520 eV cutoff energy of the plane-wave was set. The Perdew–Burke–Ernzerhof (PBE) functional in the GGA approximation framework was adopted to describe the exchange correlation of electrons [46]. The Hubbard U method was used to deal with strongly correlated d-electronic systems [47], and an effective U_eff value of 2 eV was used for the 3d electrons in Ru atoms [30,32]. Structural relaxation is performed until the force on each atom is below 0.02 eV/Å, and the energy is converged within 10⁻⁵ eV. A p(2 × 2 × 2) rutile Ru₁₆O₃₂ and a Sn₂Ru₁₄O₃₂ bulk structure with two Ru atoms replaced by Sn (referred to as Sn/RuO₂) were studied, in which a 3 × 3 × 5 Gamma-centered k-point grid was applied. A stoichiometric RuO₂(110) (including 64 Ru atoms and 128 O atoms), Sn/RuO₂(110), and Sn/RuO₂($\overline{1}$10) slab models (composed of 56 Ru atoms, 8 Sn atoms, and 128 O atoms) were constructed to explore the effects of Sn doping. A vacuum layer with 15 Å thickness was used to avoid the interaction between periodic slabs in the direction perpendicular to the surface, and a 2 × 2 × 1 k-point grid was used for these surfaces. During the calculation process, the bottom four atomic layers of slab were fixed while the other atomic layers were sufficiently relaxed. The initial magnetic moment distribution of metal atoms in RuO₂(110), Sn/RuO₂(110), and Sn/RuO₂($\overline{1}$10) slabs was consistent with the antiferromagnetic arrangement in their bulk structures before surface cleaving.

A negative formation energy (E_f) usually means that the system is thermodynamically stable. Thus, the $E_{\mathrm{f}}^{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}$ was calculated using Equation (9) to determine the stability of Sn/RuO₂ bulk structures.

$$E_{\mathrm{f}}^{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}=E_{\mathrm{S}\mathrm{n}/\mathrm{R}\mathrm{u}{\mathrm{O}}_2}^{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}+2E_{\mathrm{R}\mathrm{u}}^{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}-(E_{{\mathrm{R}\mathrm{u}\mathrm{O}}_2}^{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}+2E_{\mathrm{S}\mathrm{n}}^{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}})$$

(9)

where $E_{{\mathrm{R}\mathrm{u}\mathrm{O}}_2}^{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}$ and $E_{\mathrm{S}\mathrm{n}/\mathrm{R}\mathrm{u}{\mathrm{O}}_2}^{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}$ are the total energy of the systems before (Ru₁₆O₃₂) and after (Sn₂Ru₁₄O₃₂) Sn doping, respectively. $E_{\mathrm{R}\mathrm{u}}^{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}$ and $E_{\mathrm{S}\mathrm{n}}^{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}$ denote the energy of the individual Ru and Sn atom in their metal bulk crystal. In addition, the Gibbs free energy (G) of the system is defined as follows:

$$G=E_{\mathrm{D}\mathrm{F}\mathrm{T}}+E_{\mathrm{Z}\mathrm{P}\mathrm{E}}-TS$$

(10)

in which $E_{\mathrm{D}\mathrm{F}\mathrm{T}}$ is the total energy of the systems calculated by the VASP; and T is the room temperature 273.15 K. $E_{\mathrm{Z}\mathrm{P}\mathrm{E}}$ and S are the zero-point energy and entropy, which can be obtained from the vibration frequency of the adsorbed species.

4. Conclusions

In summary, we systematically investigated the OER electrocatalytic activity of M_cus and O_br sites on different exposed surfaces of Sn/RuO₂(110) and ($\overline{1}$10) based on the DFT+U method. The results demonstrate that the magnetic properties of the RuO₂ structure corrected by Hubbard U change from the original paramagnetic to antiferromagnetic, and the OER overpotential of the RuO₂(110) surface is reduced by 0.14 V. According to the linear relationship between the reaction intermediates *OOH, *O, and *OH, the OER active volcano plot of the Sn/RuO₂(110) and ($\overline{1}$10) surfaces are constructed. The activity of the M_cus sites is generally higher than that of the O_br sites, where the 46-Ru_cus site possesses the optimal OER catalytic performance, followed by the 34-Ru_cus < 48-Ru_cus < 25-Ru_cus < 14-Ru_cus sites. Moreover, contrary to conventional knowledge, the active sites with a distance of about 3.6 Å from the doped Sn atom exhibit a lower OER overpotential rather than the nearest neighbor sites. By studying the electronic properties of various active sites on the Sn/RuO₂ surface, the intrinsic factors affecting activity are further uncovered, such as the center of the d/p band, the electrostatic potential of the atomic core, and the number of electrons transferred. The evaluation of catalytic performance is highly dependent on the correct selection of the active site. This study plays an important role in the simulation and design of high-performance electrocatalysts for energy conversion and storage.