English

• INTRODUNTION

  As one of the most environmental-friendly oxidants, ozone (O₃) has considerable oxidation potential of 2.07 V^[1] and wide applications in organic synthesis, ^[2-4] sterilization, ^[1] disinfection, ^[5] etc. The electrochemical ozone production (EOP) route was considered to be the promising method for O₃ production, in which process H₂O molecules split and were oxidized on the anode to form the O₃ product. The EOP attracted considerable attention due to its advantages including simple equipment requirement and harmful byproducts reduction.^[6] However, the EOP efficiency was usually limited due to the competitive reaction pathway of oxygen evolution reaction (OER).^[6-11] The OER process was generally considered to be more favorable than the EOP because of the lower anodic potential of O₂ formation. To promote the selectivity of O₃ under electrolysis, effective strategies are required to substantially elevate the OER over-potential, thus reducing the competitive O₂ generation. In-depth understanding for the reaction mechanisms of O₂/O₃ formation is therefore required to reveal the key factors in affecting the over-potential and provide insights in regulating the O₂/O₃ selectivity.

  With an intention to promote the inherent molecular oxygen adsorption, various catalysts including Pt, ^[12] PbO₂, ^[13] SnO₂, ^[14,15] and boron-doped diamond (BDD) were used for the feasible EOP.^[16,17] Within the above mentioned catalysts, PbO₂ was most widely used as the electrode material in electrochemical reactions including OER^[18-20] and EOP^[11,13] due to its good conductivity, stability, and low cost.^[21] Previous work by Zhong and coworkers also reported a novel β-PbO₂ nanorod (NR) exposing (101) and (110) facet as the effective EOP electrocatalyst.^[22]

  The adsorbate evolution mechanism (AEM) was mostly adopted for the OER and EOP mechanisms, which follows the four- and six-proton couple electron-transfer (PCET) mechanisms in OER and EOP processes, respectively. In AEM mechanism, the adsorbed reaction intermediates including OH*, OOH*, O*, O₂*, O₂*+OH*, O₂*+O* and O₃* are suggested to originate from H₂O.^[23-29] In addition to the AEM mechanism, the lattice oxygen oxidation-mediated mechanism (LOM) was proposed in recent years, whereby the O₂ product was considered to originate from the surface lattice oxygen.^[22,30-32] Mefford and coworkers have proved the participation of lattice oxygen by ab initio modeling in the Sr²⁺ doped cobaltite perovskites La_1-xSr_xCoO_3-δ catalyst, in which the Co-O covalent interaction as well as surface oxygen vacancy concentration was modified by Sr²⁺ doping.^[31] Zhong et al. reported the spontaneous LOM reaction pathway on the β-PbO₂ nanorod electrocatalyst exposing (101) and (110) surface.^[22] In situ ¹⁸O isotope-labeling differential electrochemical mass spectrometry (DEMS) experiments in combination with DFT revealed the possibility of LOM reaction mechanism, with a moderate energy barrier for lattice oxygen diffusion predicted on the (101) and (110) surfaces (0.74 and 1.25 eV). Wang and coworkers further investigated the AEM/LOM mechanism thoroughly on the PbO₂ (101) surface, showing that LOM reaction pathway is more favorable than the AEM reactions mainly attributed to the weak Pb-O covalent interactions and facile lattice oxygen diffusion. Theoretical overpotential within the LOM mechanism was calculated to be 0.48 V for the O₃ formation. Although the detailed reaction mechanism has been fully investigated on the PbO₂ (101) surface, the understanding of O₂/O₃ selectivity with the effect of multiple reaction mechanisms still remains insufficient.^[33]

  In this work, the PbO₂ (110) surface was used as the catalyst model for theoretical investigations of the OER/EOP mechanism. DFT calculations were performed to give comprehensive understandings of the reaction mechanism. DFT in combination with the ab initio molecular dynamic (AIMD) simulations revealed that the O₃ formation is dominated by the LOM-2 mechanism, in which two surface lattice oxygens and one oxygen from H₂O participated in the formation of O₃. The PbO₂ (110) surface lattice oxygen is predicted to be readily migrated and desorbed from the surface to form oxygen vacancies due to the weak Pb-O covalent interaction. H₂O adsorption and splitting subsequently occurred on the PbO₂ (110) surface with oxygen vacancies, resulting in the fulfilling of oxygen vacancies. The reaction network involving surface lattice oxygen consuming and refilling via the OER/EOP and H₂O dissociation was proposed.

  COMPUTATIONAL DETAILS

  Periodic DFT calculations were performed by Vienna ab initio simulation package (VASP), ^[34,35] with exchange correlation function of Perdew-Burke-Ernzerhof (PBE)^[36] and the Projected Augmented Wave (PAW) method^[37,38] applied to describe the ion-electron interaction. The cutoff energy for the plane wave basis sets was 400 eV. The convergence criteria of geometry and energy were set to be 0.02 eV/Å and 10^-6 eV, respectively. For O and Pb elements in the PbO₂ (110) surface, O^2s2p and Pb^6s6p5d were treated as the valence state, respectively. The climbing image nudged elastic band (CI-NEB) approach^[39,40] in combination with the dimer method^[41-44] was applied to search the transition states. Harmonic frequencies of the adsorbates in the local minima and transition states were calculated with a much tighter energy convergence of 10^-6 eV, and zero-point energy (ZPE) corrections were included in the calculated energy barriers and reaction energies.

  The PbO₂ (110) surface was constructed upon the optimized β-PbO₂ with space group P4₂/mnm, in which the lattice constant of the bulk phase was calculated to be a = b = 5.08 Å, c = 3.45 Å.^[33] The symmetric and stoichiometric PbO₂ (110) surface was constructed with the supercell of p-(3 × 2) and the thickness of four Pb₁₂O₂₄ atomic layers, and the lattice constant value for the slab model was predicted to be 10.37Å × 14.31Å × 28.48Å. The Brillouin zone of PbO₂ was sampled by Monkhorst-Pack k-points grids of (2 × 2 ×1). The vacuum space is larger than 15 Å to avoid the interactions between adjacent PbO₂ (110) slabs. Owing to the considerable computational cost resulted from the large cell, the bottom half layers of the slab model were kept constrained in their bulk phase throughout the calculations.

  The Gibbs free energies for each elementary step were calculated by: G = E_elect + E_ZPE - TS, where E_elect is the electronic energy (0 K) by DFT calculations, and E_ZPE is the zero-point energy. For surface-adsorbate species, all 3N degrees of freedom of the adsorbates were treated as harmonic vibrations, and the entropy was calculated as a sum of the contributions from these vibrational motions. In the initial stage of H₂O adsorption and splitting, the gaseous H₂O molecule was adsorbed on the surface, and the entropy of H₂O molecule was treated by the standard entropy (S (T, P°)), which was calculated by Shomate equation in the NIST-JANAF thermochemical table. Under basic conditions (pH > 7), hydroxide anions are oxidized and two/three H₂O molecules are produced along with O₂/O₃. To make a connection to experiment, in which the standard hydrogen electrode was applied as the reference, the adsorption energies of intermediates are referenced to the reservoir species of H₂O and H₂ in the model by Man et al.^[25] Free energies for hydroxide ion (OH^-) were treated as G_H2O - 1/2G_H2. Adsorption energies for reaction intermediates are defined as follows:

  $ \begin{aligned} & \Delta {\mathrm{G}}_{{\mathrm{OH}}^*}={\mathrm{G}}_{{\mathrm{OH}}^*}-{\mathrm{G}}*-\left({\mathrm{G}}_{{\mathrm{H}} 2 {\mathrm{O}}}-1 / 2 {\mathrm{G}}_{{\mathrm{H}} 2}\right) \\ & \Delta {\mathrm{G}}_{{\mathrm{O}}^*}={\mathrm{G}}_{{\mathrm{O}}^*}-{\mathrm{G}}*-\left({\mathrm{G}}_{{\mathrm{H}} 2 {\mathrm{O}}}-{\mathrm{G}}_{{\mathrm{H}} 2}\right) \\ & \Delta {\mathrm{G}}_{{\mathrm{OOH}}^*}={\mathrm{G}}_{{\mathrm{OOH}}^*}-{\mathrm{G}}*-\left(2 {\mathrm{G}}_{{\mathrm{H}} 2 {\mathrm{O}}}-3 / 2 {\mathrm{G}}_{{\mathrm{H}} 2}\right) \\ & \Delta {\mathrm{G}}_{\left({\mathrm{O}} 2^*+{\mathrm{OH}}^*\right)}={\mathrm{G}}_{\left({\mathrm{O}} 2^*+{\mathrm{OH}}^*\right)}-{\mathrm{G}}*-\left(3 {\mathrm{G}}_{{\mathrm{H}} 2 {\mathrm{O}}}-5 / 2 {\mathrm{G}}_{{\mathrm{H}} 2}\right) \\ & \left.\Delta {\mathrm{G}}_{\left({\mathrm{O}} 2^*+{\mathrm{O}}^*\right)}={\mathrm{G}}_{\left({\mathrm{O}} 2^*+{\mathrm{O}}^*\right)}\right) {\mathrm{G}}*-\left(3 {\mathrm{G}}_2 {\mathrm{O}}-3 {\mathrm{G}}_{{\mathrm{H}} 2}\right) \end{aligned} $

  where G*, G_OH*, G_O*, G_OOH*, G_{(O2* + OH*)} and G _{(O2* + O*)} are the free energies of *, OH*, O*, OOH*, O₂*+OH* and O₂*+O*, respectively; G_H2O and G_H2 are those of H₂O and H₂ molecules separately. In this work, the applied potential was considered by the computational hydrogen electrode method (CHE), with ΔG_U = -neU term added to the reaction free energy, where U is the electrode applied potential, e is the transferred charge, and n is the number of proton-electron transferred pairs. pH corrections (ΔG_pH) were calculated by k_BT×ln10×pH, where k_B is the Boltzmann constant and T is the temperature. Reaction free energies were calculated to qualitatively describe the possible reaction pathway for O₂/O₃ formation. Adding the k_BT×ln10×pH term in each elementary step would not affect the main conclusion in this work, and thus the pH effect was not included here.

  AIMD simulations were also carried out at the Γ point implemented in the VASP code, with the time step length to be 1 fs and the system temperature maintained at 298 K by using the Nose-Hoover thermostat in the NVT ensemble.^[45,46] The solvent condition was also considered by adding water molecules to the vacuum gap. Within the constructed PbO₂ (110) surface model, the vacuum gap was predicted to be 10.37Å × 14.31Å × 14.17Å. 20 water molecules were added in the vacuum gap with the density calculated to be 0.28 g/cm³, which was lower than that of the standard value (1.0 g/cm³) due to the large vacuum gap in the constructed slab model. Depending on the slab model mentioned above, more H₂O molecules (~70) should be inserted in the vacuum to reach the target density of 1.0 g/cm³. However, the calculations were limited due to the significant computational cost by introducing such large amount of H₂O molecules. In this work, the AIMD simulation was applied to only provide qualitative discussions of the AEM/LOM reaction pathway. Thus, the slab containing 20 H₂O molecules was used throughout AIMD simulations. For the relative distributions of H₂O molecules, van-der Walls interaction was considered when constructing the initial structure for AIMD calculation, with the COMPASS force field used in this process.^[47] The structure was first pre-equilibrated using the classical MD calculation before AIMD simulation.

  RESULTS AND DISCUSSION

  Structure and Stability of Surface Lattice Oxygen Site on Pristine PbO₂(110). For the pristine PbO₂ (110) surface, two types of lattice oxygen atoms were exposed: the first is the surface lattice oxygen atoms (O_latt-1) with the coordination number of 2, which distribute with the zigzag configuration; and the other type coordinates with 3 oxygen atoms on the exposed surface, as shown in Figure 1(a). Previous work by Wang and coworkers has fully explored the stability or the surface lattice oxygens by calculating the oxygen vacancy formation energies, ^[33] showing that the oxygen vacancy formation energies were calculated to be -1.23 and -0.59 eV, respectively by removing the O_latt-1 and O_latt-2 from the (110) surface.^[33] Despite the over-binding of gaseous O₂ molecule and underestimation of O₂ energy, ^[48-54] the surface oxygen vacancy formation still remains thermodynamically favorable by adding the correction values of ~0.80 eV at the PBE level. As a result, the O_latt-1/O_latt-2 site on the (110) surface is likely to encounter the facile diffusion and coupling to generate gaseous O₂/O₃, leaving behind the O_vac1 and O_vac2 sites on the surface, which would promote the subsequent H₂O adsorption and refilling process.

  Figure 1

  

  Figure 1.  The optimized structure of (a) pristine PbO₂ (110), (b) PbO₂ (110) with O_vac1 and (c) PbO₂ (110) with O_vac2. The upper and lower figures in each sub-figure are side and top views, respectively. (d) Projected density states (PDOS) for the 2p orbital of the O_latt-1 and O_latt-2 sites on the pristine PbO₂ (110) surface. (e) Crystal orbital Hamilton population analysis (COHP) of the Pb-O_latt-1 and Pb-O_latt-2 bonds. Copyright 2022, American Chemical Society.

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  Furthermore, the PbO₂(110)-O_vac2 surface would reconstruct during the structural optimization, as shown in Figure 1(c). The above results demonstrated higher stability of the O_latt-2 site ascribed to the different Pb-O covalency.^[33] Therefore, the projected density of states was used to qualitatively describe the Pb-O_latt-1/O_latt-2 covalency, with corresponding results depicted in Figure 1(d). For pristine PbO₂ (110) surface, the valence state for Pb was generally predicted to be +4, indicating that four electrons were transferred from Pb to neighboring O sites with the valence electron distribution of 6s⁰5d¹⁰6p⁰. The 5d orbital was still fulfilled, resulting in Pb-6s/6p participating in the covalent interactions with O-2p orbital. Crystal orbital Hamilton population analysis (COHP) also demonstrated that the covalent interaction between Pb and the O_{latt-1/latt-2} site was dominated by the Pb-6s/6p interaction with the O-2p orbital.

  Mechanistic Study of Competitive AEM/LOM Reaction Pathway. Under basic conditions (pH > 7), hydroxide anions (OH^-) are oxidized to produce O₂/O₃ in the OER and EOP reaction on the anode, while H⁺ protons are reduced to H₂ on the cathode. It was worth mentioning that only the half-reaction was investigated to reveal the electrocatalytic mechanism of O₂/O₃ formation, in which the reaction was initiated by OH^- adsorption on the surface to form OH* adsorbate. Detailed reaction intermediates for proposed pathways are shown in Scheme 1. For AEM reaction pathway, the O₃ formation consists of six PCET elementary steps and one O₂-O coupling step, ^[55,56] as shown in the following equations:

  $ \begin{aligned} & {\mathrm{OH}}^{-} \rightarrow {\mathrm{OH}}^*+{\mathrm{e}}^{-} \end{aligned} $

  (1)

  $ {\mathrm{OH}}^*+{\mathrm{OH}}^{-} \rightarrow {\mathrm{O}}^*+{\mathrm{H}}_2 {\mathrm{O}}({\mathrm{I}})+{\mathrm{e}}^{-} $

  (2)

  $ {\mathrm{O}}^*+{\mathrm{OH}}^{-} \rightarrow {\mathrm{OOH}}^*+{\mathrm{e}}^{-} $

  (3)

  $ {\mathrm{OOH}}^*+{\mathrm{OH}}^{-} \rightarrow {\mathrm{O}}_2{ }^*+{\mathrm{H}}_2 {\mathrm{O}}({\mathrm{I}})+{\mathrm{e}}^{-} $

  (4)

  $ {\mathrm{O}}_2{ }^*+{\mathrm{OH}}^{-} \rightarrow {\mathrm{O}}_2{ }^*+{\mathrm{OH}}^*+{\mathrm{e}}^{-} $

  (5)

  $ {\mathrm{O}}_2{ }^*+{\mathrm{OH}}^*+{\mathrm{OH}}^{-} \rightarrow {\mathrm{O}}_2{ }^*+{\mathrm{O}}^*+{\mathrm{H}}_2 {\mathrm{O}}({\mathrm{I}})+{\mathrm{e}}^{-} $

  (6)

  $ {\mathrm{O}}_2{ }^*+{\mathrm{O}}^* \rightarrow {\mathrm{O}}_3{ }^*+^* $

  (7)

  Scheme 1

  

  Scheme 1.  Schematic diagram of the proposed reaction network of (a) AEM pathway and (b) LOM pathway. Adsorbate species originated from H₂O are shown in blue font.

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  Whereas for LOM mechanism, three possible reaction pathways were proposed (LOM-1, LOM-2, and LOM-3), as shown in blue, red and yellow reaction pathways in Scheme 1 (b), respectively. Within the proposed LOM-1 reaction pathway, the O₂* was initially generated from the four-step PCET mechanism. Instead of direct desorption, the O₂* intermediate further coupled with the exposed surface lattice oxygen to form O₃. In proposed LOM-2 pathway, the adsorbed O* intermediate originated from H₂O further coupled with two surface lattice oxygen atoms to form O₃, leaving behind two oxygen vacancy sites which are further fulfilled by OH^- in the solvent condition. In LOM-3 pathway, the O₂* was firstly generated via the surface lattice oxygen diffusion and coupling, which further reacted with the adsorbed OH* to form O₃ product. Detailed reaction energies as well as the theoretical over-potential are shown in free energy diagrams in Figure 2.

  Figure 2

  

  Figure 2.  DFT calculated free energy diagrams of (a) AEM pathway, (b) LOM-1 pathway, (c) LOM-2 pathway and (d) LOM-3 pathway.

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  For the AEM reaction pathway, we suppose that the reaction occurred in the alkali solvent condition, initiating with OH^- adsorption on the Pb site form OH*. The free energy change was calculated to be 2.15 eV at 298 K and U = 0.00 V. Upon the adsorbed OH* intermediate, the reaction was then followed by two-step electron elementary steps, with O* and OOH* intermediates formed on the surface. Reaction energies were calculated to be 2.08 and -1.94 eV, respectively. Note that we are unable to locate the local-minimum structure of OOH* adsorbate, since the fragment would easily dissociate to form Pb-O₂*/O_latt-H* intermediate and the O_latt acted as the Brønsted basic site in this process. In step 4, the OOH* intermediate further reacted with OH^- to get the O₂* intermediate. Based on calculation, the reaction was also highly endothermic (2.24 eV) under the applied potential of 0.00 V. After forming the O₂* intermediate, two competitive reaction pathways accompanied with the O₂/O₃ formation were proposed. The first is the O₂* direct desorption to form gaseous O₂, with the reaction energy calculated to be slightly exothermic of -0.31 eV. Alternatively, the O₂* was also likely to further react with OH^- to form O₃* via two elementary reaction steps, with the reaction energies calculated to be 2.25 and 2.03 eV, respectively for the formation of O₂*+OH* and O₂*+O*. The adsorbed separated O₂*+O* intermediates further coupled to generate the target product (O₃*), and the calculated reaction energy was -0.67 eV. In the proposed AEM mechanism, the reaction energies of O₂* and O₂*+OH* were calculated to be comparable to each other. Despite the dissociation of OOH* intermediate and the raised O₂* formation energy, O₂*+OH* was treated as the potential-determining step (PDS) with the theoretical over-potential predicted (η) to be 0.73 V under the applied potential of 1.51 V.

  In LOM-1 pathway, the reaction was initiated by OH^- adsorbing on O_latt to form the O_lattOH* intermediate. The reaction energy and O_latt-OH* bond length were calculated to be 0.96 eV and 1.42 Å, respectively. The deprotonation step was then followed to generate O_lattO* with the reaction energy of -0.05 eV. After forming O_lattO* adsorbate, the reaction was then followed by two PCET steps to form the O_lattO*+OH* and O_lattO*+O* intermediates, with the reaction energies calculated to be 1.90 and 2.63 eV, respectively. The O₃* was subsequently generated via O_lattO*, O* coupling. It is worth noting that in the LOM-1 pathway, the exposed O_latt and Pb sites play different roles for O₃ selective formation: The O_latt attracts the adsorption of OH^- and stabilizes the O_lattO* intermediate, while the Pb provides additional adsorption and evolution site of OH^-. The O₂*+O* formation step was predicted to be the PDS and the η^EOP was calculated to be 1.12 V. It should be noted that after forming O_lattO* intermediate, the exposed surface lattice oxygen was also likely to diffuse and couple with O_lattO* to form O_lattOO_latt* (O₃*). The reaction energy was calculated to be slightly endothermic of 0.54 eV (LOM-2 in Figure 2(b)). Different from LOM-1 and LOM-2, the oxygen atoms in O₂* intermediate were originated from O_latt in LOM-3 reaction pathway. The corresponding free energy diagram is shown in Figure 2(d). The reaction energy of O_latt diffusion and coupling was calculated to be only 0.49 eV, and those following the oxygen evolution to O₂*+OH*/O₂*+O* to be 1.28 and 0.94 eV, respectively. The O₃* was generated via the O₂*-O* coupling with a moderate reaction energy of 0.46 eV.

  Upon the above results, the O_lattOH* formation was predicted to be PDS in the LOM-2 pathway, with the reaction energy calculated to be 0.96 eV, whereas for LOM-3, PDS was predicted to be the O_lattO_latt*+OH* formation step, and the calculated reaction energy for this OH^- adsorption step was 1.28 eV. However, both the two values are lower than 1.51 eV (the equilibrium potential of EOP). Hence, the theoretical over-potential could not be determined in LOM-2 and LOM-3, also indicating the reaction could occur spontaneously under the condition of 1.51 V.

  The selective formation of O₂/O₃ was mainly ascribed to competitive reaction pathways after the O₂* intermediate formation: O₂* is directly desorbed to form gaseous O₂, and O₂* further reacts and couples with OH^- or surface lattice oxygen (O_latt) to form O₃*. For all reaction pathways involved in O₂/O₃ formation, the O₂ formation was predicted to be thermodynamically more favorable with the condition of U = 0.0 and 1.51 V. However, for elementary steps coupled with proton and electron transfer, the applied external potential has significant impact on the reaction free energy due to the ΔG_U term introduced. For AEM reaction path, the energy difference of OH^- adsorption on O₂* pre-occupied surface to OH*+O₂* and O₂* direct desorption was decreased from 2.56 to 1.05 eV with the U value of 0.00 and 1.51 V, respectively; whereas for LOM-1 pathway, the energy difference of the above processes drops from 2.20 to 0.69 eV with the increase of U value. Therefore, the crossover point for O₂/O₃ selectivity inversion was predictable when increasing the applied potential. Furthermore, the above results show that the reaction free energies from PCET steps are more sensitive toward the U value upon the CHE method, which would result in the LOM reaction pathways more favorable at the low potential range, while the AEM reaction mechanism is likely to dominate the OER/EOP reaction at the high potential range. In addition to the applied potential effect on the reaction energies and product selectivity in OER/EOP process, the adsorption configurations for each reaction intermediate would also be affected by the applied potential. Previous work by Wang and coworkers has fully investigated the potential-dependent CO₂ reduction reaction over the single atom catalysts, with the results showing that CO₂ chemisorption structure is significantly affected by the applied potential: CO₂ molecule charged to form the linear CO₂^-, with transition states and final states also polarized and stabilized due to charge redistribution under the potential-dependent solvation condition.^[57] The ΔG~U linear relationships were also obtained, which can be further used to determine the onset potential of CO₂RR, the potential at the maximal CO Faraday efficiency (FE), and the potential at FE_CO = FE_H2 (U_cross).^[57] This work gives a comprehensive understanding of O₂/O₃ selective formation via multiple reaction mechanisms, and further investigations are required for the explicit understanding for applied potential effect on adsorption configurations and reaction energies.

  H₂O Adsorption and Dissociation on PbO₂ (110) Surface with the Effect of Oxygen Vacancy. Depending on the above results, the proposed LOM-2/LOM-3 pathway was more favorable than the AEM reaction, indicating that the surface lattice oxygen would easily diffuse and desorb from the surface. Hence, it is possible to result in the PbO₂ (110) surface structure collapsion. However, experimental results revealed the considerable stability of PbO₂ nanorod catalyst exposing (110) and (101) surface.^[22] This is most likely attributed to the underlying H₂O adsorption/dissociation process, which fulfills the produced oxygen vacancy site under real reaction conditions. Therefore, H₂O splitting on pristine and oxygen vacancy-rich PbO₂ (110) surface was studied to reveal the surface oxygen vacancy refilling mechanism, with corresponding results depicted in Figure 3.

  Figure 3

  

  Figure 3.  Free energy diagram (eV) for H₂O splitting on (a) pristine PbO₂ (110) surface and (b) PbO₂ (110) surface with O_vac1.

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  For pristine PbO₂ (110) surface, the H₂O splitting follows the acid-base interaction mechanism: The OH^-/H⁺ yielded from H₂O dissociation binds to the Lewis acid (Pb) and Brønsted base (O_latt‑1/O_latt‑2) sites, respectively. The reactivity of different Brønsted base sites including O_latt‑1 and O_latt‑2 was systematically investigated. Within Pb-OH/H-O_latt‑1 configuration, the reaction energy of H₂O splitting was calculated to be -0.41 eV, much lower than that of the Pb-OH/H-O_latt‑2 intermediate (0.41 eV). The free energy barrier of H₂O splitting on the O_latt‑1 site was also calculated to be 0.32 eV lower than that on O_latt‑2. The above results revealed that the exposed O_latt‑1 site exhibited a higher reactivity than the O_latt‑2 one. For the calculated transition states, only one imaginary frequency was predicted.

  Considering the higher reactivity of O_latt‑1 site and lower O_vac1 formation energy, O_vac1 formation was predicted to be more thermodynamically favorable than the O_vac1 formation process. Reactivity of H₂O dissociation on the PbO₂ (110) surface was subsequently investigated. The results show that H₂O adsorption and dissociation on the Pb site were also calculated to be more favorable with the adsorption and dissociation energy calculated to be -0.29 and -0.20 eV, respectively. The free energy barrier of this step was calculated to be only 0.18 eV. When considering the reaction pathway of H₂O fulfilling the O_vac1 site, the adsorption and dissociation energies were calculated to be -0.15 and -0.72 eV, respectively. The calculated activation energy was slightly lower than that in the reaction pathway of dissociation on the Pb site, which was calculated to be 0.15 eV. Although the potential energy surface of H₂O splitting via the acid-base interaction was lower than that of the direct H₂O fulfilling pathway, the energy barrier for the direct H₂O fulfilling pathway was slightly lower (0.03 eV). Additionally, the OH fragment in the Pb-OH/H-O_latt‑1 intermediate also likely migrated from the Pb site to O_vac1 due to the energy difference of 0.38 eV.

  Considering the facile splitting of H₂O on the PbO₂ (110) surface with and without oxygen vacancy sites, reaction equilibrium of H₂O dissociation to OH^- and H⁺ was also likely to be promoted, which further enhanced the evolution of OH^- to OH*, as shown in equation 1. Additionally, basic hydroxyl adsorption on Pb site (OH*) over the pristine PbO₂ (110) surface was unlikely to reach the equilibrium coverage since the OH* fragment is also possible to diffuse on the surfaces via the active proton exchange with the undissociated adsorption water (H₂O∗). Previous work by Xia et al also revealed the OH* migration on the monoclinic ZrO₂($ \overline 1 $11) surface by AIMD simulations, and the equilibrium coverage of OH* and H₂O* under different calcination temperatures was predicted.^[58]

  AIMD Simulation of Water on the PbO₂ (110) Surface. AIMD simulations were further carried out to qualitatively reveal the oxygen refilling process on PbO₂ (110) with oxygen vacancies, which aims to explain the durability of β-PbO₂ NRs catalyst under real reaction conditions.^[22] The AIMD simulations were employed at 298 K to illustrate how the oxygen vacancy affects the H₂O splitting on PbO₂ (110). The effects of O_vac1 and O_vac2 on the H₂O splitting have also been investigated, with corresponding results presented in Figure 4 (a) and (b). Over the pristine PbO₂ (110) surface without oxygen vacancies, H₂O molecules were observed to dissociate and adsorb on the surface with the two-fold surface lattice oxygen site (O_latt-1) protonated to HO_latt-1*, and the basic hydroxyls (OH*) chemisorbed on the Pb sites. The corresponding structure is shown in Figure 4 (c).

  Figure 4

  

  Figure 4.  Ab initio molecular dynamics (AIMD) modelling for the dissociation of H₂O on PbO₂ (110) surface. (a) Bond distance plots of Pb-O_w and O_w-H_w on PbO₂ (110) surface with O_vac1, (b) bond distance plots of Pb-O_w and O_latt-1-Pb on PbO₂ (110) surface with O_vac2. Selected snapshots of the AIMD trajectory for water dissociation at 298 K on (c) PbO₂ (110)-DF surface, (d) PbO₂ (110)-O_vac1 surface and (e) PbO₂ (110)-O_vac2 surface.

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  For PbO₂ (110) surface pre-occupied by the O_vac1 site, comparable results were yielded in the initial stage for H₂O adsorption and dissociation, and oxygen vacancy refilling process was also found. Bond distance plots between oxygen atom from H₂O (O_w) and surface Pb sites show that covalent Pb-O_w bond was generated at the time scale of 1.7-4.5 ps, and the Pb-O_w bond length was predicted to be -2.30 Å. For PbO₂ (110) surface pre-occupied by the O_vac2 site, the exposed O_latt-1 site was easy to diffuse under aqueous condition at 298 K, with the O_vac2 site fulfilled, leaving behind the O_vac1 site on the surface at the time scale of 1.0-1.3 ps. The OH* refilling the O_vac1 site was also observed at the time scale of 0.7-1.5 ps. The above results qualitatively demonstrated the H₂O dissociation and diffusion on the PbO₂ (110) surface with and without oxygen vacancies, which also explained the experimental durability of β-PbO₂ NR catalyst exposing the (110) and (101) surfaces: surface oxygen vacancy sites generated by LOM mechanism are possible to be refilled by OH* from H₂O.

  CONCLUSIONS

  The EOP reactivity on PbO₂ (110) surface was extensively investigated, with the detailed reaction network proposed (AEM, LOM-1, LOM-2, and LOM-3). The results show that for O₃ formation, the LOM-2 reaction pathway was the most thermodynamically favorable, and the first OH* formation step was predicted to be the potential-determining step. Considering the facile diffusion of surface lattice oxygen atoms and formation of oxygen vacancies of the PbO₂ (110) surface, the catalyst was considered to be regenerated by H₂O adsorption and splitting, resulting in surface oxygen vacancy refilling, which also ensured the stability of the PbO₂ (110) surface structure. DFT calculations proved that the H₂O dissociation was dominated by the acid-base interaction mechanism for the PbO₂ (110) surface with and without oxygen vacancy. Pb-OH fragment on the PbO₂ (110)-O_vac1 surface was also likely to migrate to fulfill the O_vac1 due to the energy difference of 0.38 eV. By comparing the reaction energy and energy barrier for H₂O adsorption/dissociation between pristine PbO₂ (110) and PbO₂ (110)-O_vac1, it is also possible to conclude that the introduction of surface oxygen vacancy (O_vac1) could promote the H₂O splitting, which was further verified by AIMD simulations. The above results provided in-depth understanding of the O₂/O₃ selective formation on the PbO₂ (110) electrode surface.

  
  ACKNOWLEDGEMENTS: This work was financially supported by the National Key R & D Program of China (2021YFA1500900) and National Natural Science Foundation of China (21625604, 21878272, 22141001). W. W. Li contributed in writing the manuscript and performing the DFT calculation. S. B. Wang and J. G. Wang designed the research and wrote the paper. All authors commented on and revised the manuscript.
  AUTHOR CONTRIBUTION
  COMPETING INTERESTS
  The authors declare no competing interests.
  Supplementary information is available for this paper at http://manu30.magtech.com.cn/jghx/EN/10.14102/j.cnki.0254-5861.2022-0153
  For submission: https://www.editorialmanager.com/cjschem
  ADDITIONAL INFORMATION
  
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• 

  Figure 1  The optimized structure of (a) pristine PbO₂ (110), (b) PbO₂ (110) with O_vac1 and (c) PbO₂ (110) with O_vac2. The upper and lower figures in each sub-figure are side and top views, respectively. (d) Projected density states (PDOS) for the 2p orbital of the O_latt-1 and O_latt-2 sites on the pristine PbO₂ (110) surface. (e) Crystal orbital Hamilton population analysis (COHP) of the Pb-O_latt-1 and Pb-O_latt-2 bonds. Copyright 2022, American Chemical Society.

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  Scheme 1  Schematic diagram of the proposed reaction network of (a) AEM pathway and (b) LOM pathway. Adsorbate species originated from H₂O are shown in blue font.

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  Figure 2  DFT calculated free energy diagrams of (a) AEM pathway, (b) LOM-1 pathway, (c) LOM-2 pathway and (d) LOM-3 pathway.

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  Figure 3  Free energy diagram (eV) for H₂O splitting on (a) pristine PbO₂ (110) surface and (b) PbO₂ (110) surface with O_vac1.

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  Figure 4  Ab initio molecular dynamics (AIMD) modelling for the dissociation of H₂O on PbO₂ (110) surface. (a) Bond distance plots of Pb-O_w and O_w-H_w on PbO₂ (110) surface with O_vac1, (b) bond distance plots of Pb-O_w and O_latt-1-Pb on PbO₂ (110) surface with O_vac2. Selected snapshots of the AIMD trajectory for water dissociation at 298 K on (c) PbO₂ (110)-DF surface, (d) PbO₂ (110)-O_vac1 surface and (e) PbO₂ (110)-O_vac2 surface.

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