Cerium dioxide (CeO₂) is widely used in many important catalytic processes, such as vehicle emission control, the water-gas-shift reaction and petroleum cracking [1-4]. This material is especially useful in many catalytic oxidation reactions, including the oxidation of CO [5-7]. The unique catalytic performance of CeO₂ in these applications is related to its remarkable ability to store and release oxygen [8]. Accordingly, it is important to understand the formation of oxygen vacancies in ceria and the related structural, energetic and electronic properties, as these may directly affect the activity of CeO₂ in various applications [8]. Many experimental and theoretical studies have revealed some important characteristics of oxygen vacancies on low-index ceria surfaces [9-19], among which CeO₂(111) has been determined to be the most stable, followed by CeO₂(110) and (100) [20-24].

CeO₂(100) is unstable due to the presence of surface dipoles, as it is a Tasker Type 3 oxide surface with an A-B-A-B layered structure, where A is the oxygen anion and B is the cerium cation [25]. In several theoretical studies employing a slab model, CeO₂(100) has been constructed by removing half the O on both the top and bottom layers. In this manner, the entire slab maintains a stoichiometric composition and is also non-polar, both of which allow periodic ab initio calculations [26]. Nevertheless, there have been few detailed studies of the surface structures and compositions of CeO₂(100), and its surface activities during catalytic reactions are not yet clearly understood.

Several experimental studies have already shown that the CeO₂(110) and/or (100) facets are more active than the more common CeO₂(111) facets for catalytic reactions such as CO oxidation[27, 28]. In particular, Zhou et al. [27] used high-resolution transmission electron microscopy to examine CeO₂ nanorods and nanoparticles and found that the exposed (100) and (110) planes on the CeO₂ nanorods were unusually reactive.

In the present work, we employed calculations based on density functional theory corrected by on-site Coulomb interactions (DFT+U) to obtain a better understanding of the atomic compositions, structures and stabilities of CeO₂(100) surfaces. This theoretical approach has previously been successfully applied to the study of the surface and bulk distributions of oxygen vacancies, metal doping and adsorption/reaction of probe molecules on ceria catalysts [29-37]. We also modeled CO oxidation on these same surfaces to further examine the reactivity of CeO₂(100).

The spin-polarized DFT+U calculations were conducted using the Vienna ab initio Simulation Package (VASP) [38, 39]. The projector-augmented wave (PAW) method [40, 41] was employed to describe the interactions between the atomic core and valence electrons. The cerium 5s, 5p, 5d, 4f and 6s electrons and the carbon and oxygen 2s and 2p electrons were included as the valence electrons and a kinetic energy cutoff of 400 eV was applied in conjunction with the plane wave basis set expansion. We selected a U value of 5.0 eV for the Ce 4f states based on previous theoretical studies [42-44]. Slabs were employed to model the CeO₂ surfaces with a vacuum gap of > 0.15 nm. While studying surface compositions, the CeO₂(100) surface was modeled using a slab with 12 atomic CeO₂ double layers in which all the atoms were allowed to relax. In contrast, surface adsorption and reaction analyses employed a slab with 7 CeO₂ double layers, with the bottom two layers being fixed during calculations. A 2 × 2 expansion of the surface unit cell was applied and Brillouin-zone integration was performed with a 2 × 2× 1 Monkhorst-Pack grid [45].

The total oxygen vacancy formation energy (E_vac) was defined as:

where E_slab is the total energy of the CeO₂(100) slab with both the top and bottom layers terminated by a complete layer of oxygen, E_slab/vac is the total energy of the CeO₂(100) slab with the oxygen layer partially removed, E_O2 is the total energy of a gas phase O₂ molecule and n is the total number of oxygen vacancies (or the number of oxygen atoms removed) in the slab. A negative value of E_vac indicates that the formation of oxygen vacancies is an exothermic process. It is important to emphasize that the full-layer-O terminated CeO₂(100) slab considered in the above equation is actually non-stoichiometric and O rich. The vacancy formation energies were calculated only to compare the stabilities of different stoichiometric CeO₂(100) surface slabs built by removing the extra O from this non-stoichiometric slab.

The adsorption energy (E_ads) of CO on the CeO₂(100) surface was defined as:

where E_CO/CeO2 is the total energy of the interacting CO/CeO₂ system and E_CeO2 and E_CO are the energies of the clean CeO₂ surface and of an optimized CO molecule, respectively. Accordingly, a positive E_ads values indicates that the adsorption process is exothermic.

The surface structures of various low index CeO₂ surfaces, especially the most stable CeO₂(111) surface, have been previously described in detail, as have the configurations and stabilities of the corresponding surface oxygen vacancies [10, 11, 13]. However, CeO₂(100) is much less stable than CeO₂(111), primarily because it is a polar surface. In this work, we employed symmetric slab models to perform a precise study of the surface compositions, structures and corresponding stabilities of CeO₂(100) surfaces.

The polar CeO₂(100) surface consists of alternating layers of Ce cations and O ions. As a result of this stoichiometry, the number of O ions in each layer is twice that of Ce ions. Accordingly, one can expect that the O-terminated CeO₂(100) surface would involve a complete layer of exposed O atoms and therefore strong repulsive interatomic O-O interactions that might significantly destabilize the surface. In earlier research, a surface with half the top layer of O removed was typically used to model the CeO₂(100) surface [46]. In the current work, we also used this model as a reference to study the surface compositions and stabilities, employing a slab model with 12 layers of Ce cations, and terminating both the top and bottom surfaces of the slab with O while maintaining just half the original complete O layer. This approach ensured that the entire slab remained symmetric while keeping the CeO₂ stoichiometry (Fig. 1). It should be noted that surface models with added CeO₄ units on the CeO₂(100) surface have also been proposed to explain the surface structures observed in experimental work [47, 48], and the resulting theoretical stabilities have been found to be very similar to that of the reference CeO₂(100) surface. Since we were primarily interested in studying surface compositions (that is, the O coverage effect of the O-terminated CeO₂(100) surface) we did not include these additional CeO₄ in the current work.

To study other possible surface compositions, we built symmetric and stoichiometric slabs by leaving more than half the full layer of O on the top and bottom surfaces while creating the corresponding number of O vacancies (O_v) in the bulk to maintain stoichiometry. Specifically, within a 2 × 2 surface cell, each full-layer surface of the slab consisted of 8 O ions, so the reference surface slab had 4 O on the surface of each side (Fig. 1(b) and 4V+0V in Fig. 2). The other surfaces analyzed had 5-8 O ions maintained on each surface, while the corresponding 1-4 O vacancies were left in the bulk area of each half of the slab. We initially constructed a CeO₂(100) surface with 5 surface O ions and 1 O_v in the bulk of each half of the slab (3V+1V in Fig. 2), and Table 1 summarizes the oxygen vacancy formation energies calculated with respect to the slab having a complete layer of O on both sides. In the case of the reference CeO₂(100) surface with half the full layer of O removed, the calculated total O vacancy formation energy was -12.97 eV. The overall oxygen vacancy formation energies for the surfaces with 5 O ions were determined to be -7.4 to -1.0 eV, indicating that these surface structures were less stable than the reference surface. In addition, by comparing the relative stabilities of slabs with 5 surface O ions and one bulk O_v at different positions, it was clear that the bulk O_v prefers to remain close to the surface within the subsurface area, and that the slab becomes less stable as the O_v moves deeper into the bulk.

We also built and studied CeO₂(100) slabs with 6 and 7 O ions on each surface. Correspondingly, 2 and 3 O_v were distributed in the bulk of each side of the slabs (see 2V+2V and 1V+3V). Again, we considered different locations of these vacancies in the bulk. The data in Table 1 clearly show that, as the number of O ions on the surface increases, the overall stability is reduced. It is also once more evident that the bulk oxygen vacancies are preferentially situated close to the surface.

As an extreme case, we also studied a surface with a complete O layer. Accordingly, a total of 4 oxygen vacancies were distributed in the bulk area of each half of the slab (0V+4V). Again, we considered variations in the O_v distribution. The calculated vacancy formation energies in Table 1 demonstrate that a uniform distribution of the vacancies among the different bulk layers resulted in much lower stability compared with the scenario in which all the vacancies are in the same layer close to the surface. In general, the calculated results show that the surface configuration with half the complete O layer removed is the most energetically stable among all the stoichiometric CeO₂(100) surfaces considered in this work.

CeO₂-based materials are currently used as active component in three-way catalysts for vehicle emission control. Therefore, in this work, we also examined CO oxidation over CeO₂(100) to illustrate the potential catalytic activity of this material. We initially selected the most stable CeO₂(100) surface, terminated with a half layer of O. The adsorption of CO was modeled at two different sites; at a surface lattice O with two-fold coordination (O_2c) and at a surface O vacancy (Fig. 3(a) and (b)). The calculated adsorption energies and structural parameters at these two sites are provided in Table 2, from which one can see that the CO adsorption at both sites is relatively weak, although adsorption at an O_v site is slightly more favorable. This result is largely consistent with the data reported for experimental assessments of CO adsorption on CeO₂ by Wu et al. [49].

We subsequently predicted the results for a reaction between CO and a single surface O_2c on CeO₂(100), using the CO adsorption state on an O_v as the initial state (ISA, Fig. 4) of the reaction.

According to the results of our calculations, a bent CO₂ species (IMA, Fig. 4) is adsorbed on the surface following the direct reaction between CO and a surface lattice O_2c, with a O-C-O bond angle of 128°. The barrier for the formation of this bent CO₂ at the surface was determined to be 0.67 eV, and the OC-O_2c distance in the transition state (TSA1, Fig. 4) was found to be 0.1673 nm. From the energy profile in Fig. 4, one can also see that the CO₂ adsorption is an exothermic process with an energy change of approximately 0.5 eV. The bent CO₂ adsorbed on the CeO₂(100) surface may move into the gas phase (FSA-1), and we also performed a series of constrained calculations to determine whether there is a transition state for this desorption process. No significant energy barrier was identified for this highly exothermic step (energy change of approximately 2.3 eV).

In addition to CO₂ desorption, we also found that bent CO₂ molecules on the surface can react with other surface lattice O_2c to form two different types of carbonate species. The reaction between the adsorbed CO₂ and a nearby surface O_2c was examined and it was found that an upright carbonate species (FSA-2, Fig. 4) is formed initially with an associated energy barrier of 0.49 eV (TSA-2, Fig. 4). This carbonate formation process is significantly exothermic by 2.15 eV. Subsequently, this upright carbonate can transition to a flat carbonate species on the surface, with a small barrier of 0.20 eV. This flat carbonate is in fact even more stable than the upright species, by 0.84 eV.

This study systematically examined the surface structures of CeO₂(100) and their corresponding stabilities. In addition to the most stable termination state, we also determined several metastable CeO₂(100) surfaces, having higher coverages of surface O. To obtain a comprehensive understanding of the catalytic activity of CeO₂(100), we also modeled CO oxidation over a metastable CeO₂(100) surface having one extra surface lattice O in addition to half a full O layer. The adsorption of CO on four different sites on this surface was considered: at an extra surface lattice O_2c (O_d), a standard surface O_2c (O_s), an O_v site and a surface Ce atom. The calculated adsorption energies and structural parameters at the four different sites are provided in Table 3. These data show that, similar to the results obtained with the most stable CeO₂(100) surface, CO adsorptions were very weak at these sites. Thus, it is very likely that the CO can again react with surface O through an MvK mechanism on this metastable CeO₂(100) surface. We subsequently adopted the adsorption states of CO at the O_s and O_d sites as the initial states (ISB and ISC, respectively, Fig. 5) for its reaction with a typical surface O_s and an additional O_d. It is evident from the calculated energy profiles in Fig. 5 that the barriers were determined to be 0.60 and 0.41 eV, respectively, both of which are lower than the value obtained using the most stable CeO₂(100) surface. These results suggest that the extra surface lattice O is relatively more reactive than the ordinary surface O. Interestingly, we identified no intermediate state involving the adsorbed CO₂ species after the transition states (TSB and TSC) for the CO reaction with these two surface O, and found that a linear CO₂ species forms immediately above the surface.

Additional information regarding the reactivities of surface O and reaction intermediates within the CO oxidation process over CeO₂(100) was obtained by electronic structure analyses of the various key reaction states on the most stable and metastable CeO₂(100) surfaces.

In the case of the CeO₂(100) surface with an adsorbed CO₂ complex (IMA, Fig. 4) or with various carbonate species (FSA-2 and FSA-3, Fig. 4), we analyzed the electronic structures by calculating the corresponding density of states (DOS). We also calculated the distribution of localized spin electrons in these systems. The adsorbed CO₂ complex was determined to have two spin-unpaired electrons (Fig. 6(a) and (b)), in keeping with the two isolated gap states in the DOS plot (Fig. 6(c)). The spin-down gap state corresponds to a single localized electron in the 4f orbital of one neighboring Ce, while the localized electron at the surface CO₂ contributes to the spin-up gap state. We also calculated the Bader charges for the surface species in this system, and determined that the surface CO₂ species had approximately 0.88 e, indicating that these species should more properly be considered as CO₂^-. Since the CO molecule is neutral, and the calculated Bader charge of the original surface lattice O was approximately 1.12 e, these results show that the surface adsorption of CO₂ on CeO₂(100) is a redox process, and that overall this process results in a partial electron transfer to surface Ce cations.

We also calculated the DOS and the spin electron densities for the CeO₂(100) surface with adsorbed carbonate species in the FSA-2 and FSA-3 configurations (Fig. 7), and determined multiple gap states from the DOS plots. In the case of the surface with the carbonate in the FSA-2 configuration, three spin-up gap states were identified, one of which is paired with a spin-down state. In contrast, the system with the FSA-3 configuration showed only spin paired electrons in the gap states. Specifically, for the FSA-2 scenario, two surface Ce exhibit two spin-up states, suggesting that the original Ce⁴⁺ ions have been reduced to Ce³⁺. Moreover, the spin-paired gap state in the FSA-2 configuration results from the 2p electrons of the carbonate species. In the case of the FSA-3 configuration, the spin paired gap states are associated with two localized electrons in the 4f orbitals of two surface Ce.

We also analyzed the electronic structures of the FSB and FSC states during the CO reaction with O_s and O_d on the metastable CeO₂(100) surface. The resulting DOS diagram demonstrates the existence of two gap states for these two structures, again as a result of localized Ce³⁺electrons (Fig. 8). It is evident from the calculated distribution of the localized electrons that the two Ce³⁺ in the FSB system remain in the subsurface area while, for the FSC system, one Ce³⁺ is in the subsurface area and the other is in the third layer (Fig. 9). It is important to note that the Ce³⁺ is located in the surface area following the formation of gas phase CO₂ in conjunction with the FSA-1 state during the reaction on the most stable CeO₂(001) (Fig. 9).

In this work, the compositions of CeO₂(100) surfaces were systematically studied using the DFT+U method. From the calculated surface structures and corresponding energetics, we can conclude that the surface having half the full O layer being removed is the most energetically stable. In addition, as the O remaining on the surface increases, the surfaces become less stable. To better understand the electronic origin of the stabilities and reactivities of these surfaces during CO oxidation, we examined the electronic structures of the most stable and metastable surfaces determined in this work.

No gap states or localized spin electrons were identified for the most stable CeO₂(100) surface (Fig. 1(b)). The calculated spin charge density distributions of the several metastable CeO₂(100) structures are shown in Fig. 10. Interestingly, it is evident that, even if these surface slabs are overall stoichiometric, spin electrons still occur at various surfaces and bulk atoms, suggesting electron transfer between O and Ce ions. As an example, if the most stable CeO₂(100) surface is modified by moving one O from the bulk to the surface (Fig. 10(a)), the surface O as well as some surface and bulk Ce cations appear to possess partial spin electrons, indicating charge transfer from the surface O (O^2-) to Ce cations (Ce⁴⁺), such that these O^2- ions are actually oxidized. Moreover, one can also see that, as the oxygen vacancies moves further into the bulk (Fig. 10(b)), oxidized O ions and reduced Ce cations can also occur at the surface and around the vacancies in the bulk. These results can possibly be attributed to the increased local coverage of O ions when extra O are present at the surface, promoting the transfer of electrons from these surface O ions to surface or bulk Ce cations to reduce electrostatic repulsion. Moreover, these oxidized O ions (O^-) can also be expected to be highly active for reactions, due to their radical character.

This work also investigated CO oxidation over CeO₂(100) under various surface conditions. From the calculation results, we determined that the direct interaction between CO and the CeO₂(100) surfaces is rather weak, similar to the case of CO adsorptions on CeO₂(110) and (111) surfaces [50, 51]. These results therefore indicate that CO oxidation by lattice O at CeO₂ catalysts may follow the MvK mechanism in general.

From the calculated results illustrated in Fig. 4, one can see that, on the most stable CeO₂(100), the direct reaction between CO and one surface O_2c leads to the formation of a negatively charged, bent CO₂ species adsorbed at the surface. The desorption of this species as molecular CO₂ can subsequently occur, as well as its further reaction with another surface O_2c, to give rise to various carbonate species on the surface. The latter is much more likely to occur than the generation of gas phase CO₂. As a result, although the CO₂ desorption has no energy barrier, carbonate formation is still highly competitive from the thermodynamic point of view.

We also examined CO oxidation on metastable CeO₂(100) to obtain a comprehensive understanding of the behavior of this surface under practical conditions. Surprisingly, it was determined that, during the reaction of CO with an extra O_2c and the nearby original half layer O_2c, a gas phase CO₂ molecule is directly generated without the formation of negatively charged CO₂ on the surface. This is clearly due to the relatively high activities of these surface O as well as the fact that the presence of too many surface O ions in close proximity to the reaction site inhibits the formation of negatively charged CO₂. This result is similar to the case of CO oxidation on a 2 × 1 reconstructed CeO₂(110) surface. In this scenario, a reconstructed area containing numerous negatively charged surface O ions favors the direct formation of neutral CO₂ without producing any negative intermediates [52]. Our results therefore indicate that the distribution pattern of the surface lattice O on CeO₂ catalysts may greatly affect the reactivity of the material.

The reactivities (or stabilities) of CeO₂(100) surfaces can also be identified based on the results of electronic analyses. Fig. 10 demonstrates that the charge distribution in bulk metastable CeO₂(100) is significantly different from that in the most stable variant. As we have explained, the obvious electrostatic repulsion between overly close surface lattice O tends to destabilize these species, meaning that these surface O then lose some electron density so as to become less negatively charged. The resulting less negatively charged surface O can be more reactive in surface reactions compared with the original O^2- ions. Most importantly, the Ce⁴⁺ cations in the slab can readily accept these electrons as a result of their unique, empty localized 4f orbitals, which facilitate the charge transfer. Thus, as noted above, surface O with locally high coverages, which may occur when the surface oxygen vacancies are healed by the dissociative adsorption of O₂ molecules, can exhibit relatively high activity during CO oxidation, especially in the case of direct CO₂ formation.

We performed DFT+U calculations to study the structures of CeO₂(100) polar surfaces and the reactions between CO molecules and various types of surface O. From the calculated results, we can conclude that, in the case of an O-terminated surface, the full O layer results in significant electrostatic repulsion between the exposed O ions, and the surface is stabilized when the O coverage is reduced. Our symmetric slab model demonstrated that removing half the full layer of O from the top and bottom surfaces produced the most stable stoichiometric surface. Electronic analyses further showed partial electron transfer from the surface O to the Ce⁴⁺ cations (primarily localized in the Ce 4f orbitals) when employing a symmetric, stoichiometric slab with more than half the full O layer maintained on the surface and a corresponding number of O_v in the bulk. This charge transfer process renders the surface O less negative and reduces the electrostatic repulsion among these ions on metastable CeO₂(100) surfaces. CO adsorptions at various CeO₂(100) surfaces are rather weak, and the reaction of CO with surface O follows the MvK mechanism. We further determined that adsorbed bent CO₂ molecules can be formed on the most stable CeO₂(100) surface, and can very readily desorb to the gas phase or react with nearby O_2c to generate carbonate species that are more stable than the gas phase CO₂. In contrast, in the case of the metastable CeO₂(100), there is no adsorption of CO₂ species on the surface, and the direct formation of gas phase CO₂ appears to dominate the reaction. High coverage of O, which makes the surface less stable due to the associated electrostatic repulsion, was also found to be the main factor that prevents the occurrence of negatively charged, bent CO₂.

Acknowledgments

The authors thank the National Super Computing Center in Jinan for computing time.