Recent advances in nanotechnology have provided new opportunities for designing and screening well-defined catalysts ^{[1, 2, 3, 4]}. Catalytic performance has been reported to strongly depend on particle size and shape. Because of their prominent redox properties, reducible metal-oxide nanocrystals have been extensively studied for catalyzing various important reactions such as CO oxidation and alkane oxidation ^{[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]}. Among these oxides, spinel cobalt oxide (Co₃O₄), an important semiconductor material, has been extensively studied ^{[7, 8, 9, 10, 11, 12]} and found to be particularly effective in catalyzing many important reactions such as CO oxidation, N₂O decomposition, and low- temperature methane conversion. The shape and plane structure of Co₃O₄ nano-catalysts have been found to play essential roles in controlling catalytic reactivity and selectivity. For example, Li and coworkers ^[7] effectively synthesized different shapes of Co₃O₄ nanocrystals and found that the nanocrystal (112) and (011) planes were much more reactive than the (001) plane in catalyzing methane decomposition. Later they demonstrated that the nanocrystal (011) planes are more active than (001) planes for CO oxidation ^[8]. The temperature-programmed reduction experiments further showed that the (011) planes had stronger reducing properties than the (001) planes. Similarly, Xie et al. ^[3] reported that oxidation of CO catalyzed Co₃O₄ nanocrystals at temperatures as low as -78 °C. Density functional theory (DFT) calculations have also been carried out to understand the structure sensitivity of Co₃O₄ nanocrystals ^{[16, 17, 18, 19, 20, 21]}. Generally, the high oxidation reactivity of Co₃O₄ planes is attributed to the presence of octahedrally coordinated Co species that can easily convert between Co³⁺ and Co²⁺ via a redox process. However, knowledge about the active sites for catalytic oxidation reactions on Co₃O₄ nanocrystals is still elusive because of their complex surface structure. Taking CO oxidation as an example, Broqvist et al. ^[16] reported that CO could adsorb at Co³⁺ sites on the Co₃O₄(110) surface and then move toward the oxygen ion to form a CO₂ complex. Xu et al. ^[17] and Jiang et al. ^[18] proposed that low-coordinate O sites were responsible for CO oxidation on Co₃O₄ planes. However, Pang et al. ^[19] concluded that both Co³⁺ and O^2f sites controlled the catalytic activity of CO oxidation. These somewhat contradictory results indicate that it is necessary to obtain a clear understanding of the active sites and the nature of high reactivities of Co₃O₄ nanocrystals.

In this work, a DFT investigation has been performed to compare CO oxidation at various possible active sites on Co₃O₄(001) and (011) surfaces. By comparing the energetics of the different reaction pathways for CO oxidation activation, we have demonstrated that the activity of CO oxidation exhibits distinct dependence on the exposed crystal plane and active sites. We propose that the nature of this structural sensitivity originates from the reducibility of the surface sites. This viewpoint provides a potential scheme to design and screen well- defined catalysts. Our results are consistent with previous experimental observations.

All the calculations were performed using DFT methods as implemented in the Dmol3 package developed by Accelrys, Inc. ^{[22, 23, 24]}. The exchange-correlation potential is described by the generalized-gradient approximation (GGA) with the spin- polarized exchange-correlation functional of Perdew- Burke- Ernzerhof (PBE) ^[25]. The localized double-numerical basis sets with polarization functions (DNP) were used to describe the valence orbitals of the atoms, whereas relativistic effective core potentials (ECP) were employed for replacing the core electrons of Co ^{[23, 26]}. A Fermi smearing of 0.2 eV and a real-space cutoff of 4.5 Å were used. All the slabs were periodically repeated with a vacuum spacing of 15 Å between the images in the direction perpendicular to the surface. Two-dimensional Brillouin integration was performed with an 8 × 8 × 8 k-point mesh for the bulk crystal and a 4 × 4 × 1 k-point mesh for the slabs. Larger k-point meshes were also tested and the total energy showed nearly converged behavior. In the geometry relaxation calculations, the spin-polarization Kohn-Sham formalism was used for the self-consistent field (SCF) iterations and molecular symmetry was not enforced. The convergence criteria were set as 1×10^-4 eV, 1×10^-3 eV/Å, and 5×10^-3 Å for energy, energy gradient, and geometry, respectively. In all calculations, stoichiometric supercell models were used. The method is found to correctly reproduce the structural parameters, magnetic moment, and band gap of the bulk Co₃O₄, indicating that the selected exchange-correlation functional is appropriate. See our recent study for details ^[6]. The transition states were obtained using the Complete LST/QST method ^[27] with a force criterion of 0.05 eV/Å. Vibrational analysis was further performed to ensure that each transition state had only one imaginary frequency. The zero point energy (ZPE) was included in all energetics. Surface slab models cleaved from the bulk crystal were used to model the Co₃O₄ (001) and (011) planes, as shown in Fig. 1. Each slab consists of four atomic layers, where the two bottom layers were held fixed during optimization while the top two layers were allowed to relax. We note that there are two types of surface structure for each plane based on different cleavage depths. The one with the lower surface energy was chosen for the (001) and (011) planes. Discussions on the stability of the different slab models can be found in previous theoretical studies ^{[6, 16, 28, 29]}.

Fig. 1. Surface models for Co3O4(001) and (011). The ions of the top layers are shown in a ball and stick model. Blue, Co atom; red, O atom. On each slab, there are two types of oxygen ions (Ot and O°), which differ in the way they are bonded in the lattice structure. Ot is bonded to one Co2+ ion and 1-3 Co3+ ions, while all atoms near O° are Co3+ ions. Both the Ot and O° ions on the (001) surface are threefold coordinated, while on the (011) surface the Ot ions are twofold coordinated and the O° ions are threefold coordinated.

We first consider CO adsorption on the Co₃O₄ surfaces. The optimized adsorption configurations and the corresponding distances are shown in Fig. 2. Three possible sites denoted as Co, Co-O°, and Co-O^t on each surface are considered for CO oxidation. Only CO molecules with C-coordination are considered to interact with each surface, which is propitious to approach the surface and subtract the lattice oxygen to form CO₂. At Co sites, the CO is found to adsorb perpendicularly to the Co-O bond. The distances between the C and the Co atom range from 1.826 to 1.920 Å. At the Co-O pair site, CO adsorption leads to the formation of a nonlinear O-C-O species at each surface, where the C atom binds to both the lattice Co ion and the oxygen ion. The C-Co and C-O distances are 1.88-1.96 and 1.27-1.35 Å, respectively. In all cases, both C-O bond and Co-O bonds are lengthened, relative to the clean surface and the gas molecule. This can be attributed to the highest occupied molecular orbital (HOMO) 5σ of the CO transferring additional charge to the surface Co ion, thus weakening both C-O and Co-O bonds ^{[16, 17]}. Mulliken population analysis confirms that the surface Co ions become less positively charged by ~0.3e on both surfaces.

Fig. 2. Possible adsorbed configurations of CO molecule on Co3O4 surfaces.

The CO adsorption energy is further considered to elucidate the interaction between CO and the substrate. It is calculated according to the formula E_ads = E_CO@slab - E_slab - E_CO, where E_slab is the energy of the surface slab, E_CO@slab is the energy of the surface slab with CO adsorbed, and E_CO is the energy of the isolated CO molecule. The calculated adsorption energies for each configuration are summarized in Table 1. On the (001) surface, CO can strongly adsorb at Co sites with a high adsorption energy of -1.10 eV, but only weakly adsorbs at Co-O pair sites with lower adsorption energies at Co-O pair sites. On the (011) surface, the adsorption energies at Co, Co-O^t, and Co-O° sites are -1.14, -1.15, and -0.72 eV, respectively, which indicates competitive adsorption at different sites.

Table 1 The adsorption energies (Eads) at Co, Co-Oo, and Co-Ot sites. Surface Eads/eV Co Co-Oo Co-Ot (001) -1.10 -0.01 -0.29 (011) -1.14 -0.72 -1.15

Table 1 The adsorption energies (Eads) at Co, Co-Oo, and Co-Ot sites.

CO oxidation on a Co₃O₄ substrate or other transition metal oxides is generally reported to follow the Mars-van Krevelen (MvK) mechanism, where CO molecules react with the lattice oxygen ions and gaseous O₂ molecules replenish the oxygen defects ^{[3, 30, 31, 32, 33]}. Both experimental and theoretical studies have suggested that lattice oxygen abstraction by CO is crucial for CO oxidation ^{[3, 18, 19, 20, 21, 30, 31]}. Especially, Jiang et al. ^[20] also proposed that the CO reaction with lattice oxygen ions was the rate limiting step, and that the O₂ molecule could easily dissociate without a barrier between two neighboring oxygen vacancies. Therefore, in the present study we focus on the oxidation of CO with the lattice oxygen ion and aim to elucidate the structure sensitivity and crystal plane effect.

On the basis of the adsorption energies, CO is highly energetically favorable to adsorb at the Co site. To achieve oxidation of CO with the lattice oxygen ion, a configuration change of CO moving from the Co site to the Co-O site is necessary. The diffusion barriers are calculated and are listed in Table 2. It is found that all the barriers for the configuration change are relatively high (more than 0.8 eV), indicating that the process has a room temperature reactivity based on the estimation of transition state theory. These results also imply that at very low temperatures such as -78 °C ^[3], adsorbed CO species at Co sites do not substantially contribute to the formation of CO₂ and thus have no direct relation to the reported crystal plane effect. In contrast, adsorption at the Co site could hinder further adsorption of CO at the Co-O site because the Co site is already occupied.

Table 2 Barriers for adsorbed CO configuration change from Co to Co-O sites. Surface Ea/eV CoàCo-Oo CoàCo-Ot (001) 1.17 0.84 (011) 1.08 1.00

Table 2 Barriers for adsorbed CO configuration change from Co to Co-O sites.

We further consider the formation of CO₂ directly from adsorbed CO at Co-O sites. The reaction pathways and transition states are shown in Fig. 3. The processes can be outlined in three steps: (1) the gas CO molecule adsorbs at a Co-O pair site; (2) the adsorbed CO species interacts with the lattice oxygen ion, forming an adsorbed CO₂ species; (3) a CO₂ molecule desorbs into the gas phase. On the (001) surface, the adsorbed CO species only need to overcome small barriers to form CO₂, with 0.24 eV at the Co-O° ion-pair site and 0.70 eV at Co-O^t pair site. This is in contrast with the scant reactivity of the (001) surface reported by the experimental results. Further, the adsorption energies on the (001) surfaces are very small (<0.3 eV) at Co-O sites, which implies that at realistic conditions, CO desorption will strongly affect CO coverage on the surface and thus significantly decrease the rate of CO₂ formation.

Fig. 3. The pathways and energies for CO oxidation with the lattice oxygenion.

This scenario changes when we consider the (011) surface. The CO molecule can easily bind to a Co-O° or Co-O^t pair site with a high adsorption energy. At the Co-O^t site, adsorbed CO can easily abstract a lattice oxygen to form CO₂ after overcoming a small barrier of 0.26 eV. CO oxidation is expected to be difficult at the Co-O° pair site as the barrier for CO₂ formation is very high (0.95 eV), especially when considering the low reaction temperature in the experiments ^[3].

According to the calculated energy pathways, all the adsorbed CO₂ species can easily desorb into the gas phase because of the small desorption energy (<0.3 eV), which indicates that the observed crystal plane effect is mainly determined by CO adsorption and oxygen subtracting steps. The adsorption steps determine the coverage of CO at the ion-pair active site on the surface, and the subtracting step controls the degree of difficulty for the formation of CO₂ species. In conclusion, the lower adsorption energy (more negative) and the smaller barrier for subtracting the lattice oxygen ion lead to a high reactive surface for CO oxidation.

Assuming that the number of Co-O pair sites on each surface is identical, the relative coverage of CO can be determined by a Boltzmann distribution via the formula exp(-E_ads/RT). Since the adsorption energies at the Co³⁺ site on (001) and (011) surfaces are very close (-1.10 vs -1.14 eV), the relative coverage at the Co-O site has a similar reference value, i.e. exp(-E_ads(Co)/RT), and will not largely be affected by the selective occupancy of CO at the Co site. Based on the transition state theory, the rate for the oxygen subtracting step can be expressed by Aexp(-E_a/RT). As a result, the relative reactivity at different reactive sites can be expressed by Aexp(-(E_ads+E_a)/RT). The pre-exponential factor A for each surface is estimated by (k_BT/h)exp(ΔS^≠/k_B), where ΔS^≠ is the change of entropy between the reactant and the transition state, and the temperature T is set to 200 K according to the experimental temperature ^[3]. The calculated pre-exponential factors for (001)-Co-O°, (001)-Co-O^t, (011)-Co-O°, and (011)-Co-O^t are 4.9x10¹⁴, 1.8x10¹⁴, 5.9x10¹⁴, and 9.8x10¹⁴ s^-1, respectively; because these values are all quite similar to each other, this indicates that there is a negligible entropy effect on the rate constant. It was also previously reported that the entropy contribution had little effect on the reaction rate of C-H bond activation over the Co₃O₄ surface ^[6].

Therefore, we chose the energy level of the transition state (E_TS = E_ads + E_a) for the CO₂ formation as an indicator of the reactivity of CO oxidatio_­n, which can be approximately considered as the apparent activation energy relative to the initial state of gas-phase CO. By comparing E_TS at different sites, we can easily obtain the reactivity order: (011)-Co-O^t >> (001)-Co-O° > (011)-Co-O° > (001)-O^t. This indicates that the exposed Co-O^t site on the (011) surface exhibits the highest activity for CO oxidation.

Various studies attributed the high oxidation capacity of the Co₃O₄ surface to the presence of octahedrally coordinated Co³⁺ ions ^{[7, 8, 34]}. While it is demonstrated in our present study that both (001) and (011) surfaces contain exposed Co³⁺ ions, they have significantly different reactivity for CO oxidation. This implies that simply attributing reactivity to the presence of exposed octahedral Co³⁺ is not always correct because the exposed surface Co³⁺ ions have different lattice environments. The real active site for CO oxidation is not the Co site, but instead is the Co-O pair site, which is consistent with our recent study on C-H activation on Co₃O₄ nanocrystals ^[6]. In light of these results, one can speculate that low-coordination surface ions contribute to the high activity for CO oxidation. For example, four-coordinate Co³⁺ ions and two-coordinate O^t ions on the (011) surface are more active than the five-coordinate Co³⁺ ions and three-coordinate O^t ions on the (001) surface. As CO oxidation with the lattice oxygen ion abstraction leads to oxygen vacancy formation, and both CO adsorption and oxygen vacancy formation cause reduction of the surface, correlation between the vacancy formation energy and reactivity is expected. The vacancy formation energy is defined as E_vf = E_v + 1/2E_O2 - E_slab, where E_v, E_O2, and E_slab are the energies of the oxygen-defect surface, O₂ molecule, and stoichiometric surface, respectively. Based on this definition, the vacancy formation energy represents the strength of O ion binding to the environmental lattice. The energy levels of the transition states and the oxygen vacancy formation energies are listed in Table 3. One can conclude that there is a positive correlation between the two values. That is, the easier the oxygen ions are to remove, the more reactive the surface. For example, the Co-O^t ion in the Co₃O₄(011) surface that has the lowest vacancy formation energy is found to be the most reactive site for CO oxidation. This accords with previous theoretical research on the importance of low-coordinate oxygen ions in catalytic CO oxidation ^[20]. Our results indicate that exposed Co³⁺ ions are not the direct factor that affects the reactivity; instead, the bonding scheme of surface Co and O ions in the lattice structure that affect the reducibility of Co ions might determine the reactivity. Our results show that lowering the vacancy formation energy via popular methods such as controllable synthesis of specific planes or metal doping in the lattice is promising for higher CO oxidation reactivity.

Table 3 Comparison between the transition state energies and the vacancy formation energy of lattice oxygen. Co-O site ETS/eV Evf/eV (001)-Co-Ot 0.41 3.51 (011)-Co-Oo 0.25 3.32 (001)-Co-Oo 0.21 3.07 (011)-Co-Ot -0.89 2.46

Table 3 Comparison between the transition state energies and the vacancy formation energy of lattice oxygen.

We have performed a theoretical study of CO oxidation with the lattice oxygen ions on Co₃O₄(001) and Co₃O₄(011) surfaces by using density functional theory. It is found that CO oxidation exhibits significant dependence on the crystal plane and active sites, consistent with previous experimental findings. Surface Co-O ion pairs are found to be the active sites for CO oxidation. Co-O^t pairs with O^t bonded to one Co²⁺ ion on the (011) surface are the most active site for CO, with a small barrier of 0.26 eV. The reactivity of Co₃O₄ surfaces is correlated with the vacancy formation energy. The nature of the high reactivity of low-coordination oxygen ions is attributed to their weak binding to the substrate lattice. As a result, low-coordination surface ions have high activity for CO oxidation.

Generally speaking, the ultimate goal of catalysis design is to understand the nature of the catalytic active site and tailor the catalyst from the atomic level, achieving high reactivity and optimizing economization of the catalysts ^[35]. Singly dispersed atoms anchored on metal-oxide surfaces have recently been reported to exhibit robust stability and significant catalytic activity ^{[33, 36, 37]}. This type of catalyst is referred to as a single atom catalyst (SAC) and has become a potential solution to reduce usage of expensive noble metals in catalytic industries. The current study furthers our understanding of this class of catalysts by revealing that the ion-pair active center (IPAC) that naturally exists on the cobalt oxide surface provides a synergistic effect in catalyzing CO oxidation, where the cation contributes to the CO adsorption and the anion facilitates CO₂ formation. Recent theoretical work ^{[6, 38]} also demonstrates that Pd-O pairs on the Pd surface and Co-O pairs on the Co₃O₄ surface can effectively activate C-H bonds synergistically. These results imply that effective creation of dispersed ion-pair active centers on the support (metal or metal oxide) might be vital for screening and designing nanocrystal catalysts with high activity and selectivity.

We are grateful to Professor Yadong Li for helpful discussion. The calculations were performed by using supercomputers at the Computer Network Information Center, Chinese Academy of Sciences, Tsinghua National Laboratory for Information Science and Technology, and the Shanghai Supercomputing Center.