The advantages of developing renewable energy are obvious, since the issues of energy, environment, and climate change brought about by the rapid development of the world economy have become prominent global challenges today (Huang et al. 2022; Wu et al. 2022, 2023). Coalbed gas (CBG), mainly composed of methane (30% to more than 95% (Zhang et al. 2016), is a reserve-rich unconventional natural gas resource with buried between coal seams, which is expected to play an important role in the future energy portfolio (Ma et al. 2022; Mastalerz and Drobniak 2020). In recent years, methane from CBG has been utilized or converted into high value-added products through a range of means, all of which include fuel cells (Yang et al. 2022a, b), dry reforming of methane (Yang et al. 2023; Zhang et al. 2004), and partial oxidation (Chang et al. 2023; Sedov et al. 2022), has become a focus of attention. As a result of the high symmetry of the methane structure, the selective activation of its C-H bonds has been regarded as the “holy grail” of catalysis (Meng et al. 2019), which typically requires harsh conditions to efficiently cleave the four strongly localized C-H bonds with a bond energy of 439 kJ/mol. Therefore, it is the focus and challenge of current studies to develop new catalysts capable of selectively and efficiently converting and utilizing methane from CGB.

The oxide MOs of transition group metals M (M = Mo, V, Fe, Co and Cu) have been employed for the selective conversion of CH₄ because of their unique activity and selectivity (Ravi et al. 2017). The Co-based catalysts have demonstrated an excellent activity in catalyzing combustion of methane, partial oxidation of methane to methanol or syngas, as well as oxidative coupling of methane (Taylor et al. 1998; Zhang et al. 2005). In our previous study, a bifunctional material (Co₃O₄/(SiAl@Al₂O₃) coupled with a catalytic component (Co₃O₄) and a phase-change heat-storage component (SiAl@Al₂O₃) was firstly applied to the catalytic combustion of lean methane (Li et al. 2020). Mousavian and Esrafili (2020) found that the Co-modified C₂₄N₂₄ fullerene had excellent catalytic activity towards CH₄ oxidation to CH₃OH by theoretical calculations, and the reactive electron energy barrier of the CH₄ + O_ads → CH₃OH process on Co@C₂₄N₂₄ was only 0.60 eV. Blankenship et al. (2021) achieved high yields of methane aerobic conversion to the antioxidant methyl ester under moderate temperatures and pressures using highly dispersed cobalt-containing solid catalysts. Their work claimed that the cobalt-based catalyst had the most competitive activity (conversion and yield) versus any of the known transition metal aerobic catalytic systems. The reaction of cobalt pre-catalysts with methane and longer alkane congeners has been reported to require the passage of oxygen species (Strassner et al. 2013), while cerium dioxide, an important rare earth oxide, is widely used as a multiphase catalyst, fuel cell and biomedical material due to its excellent oxidation-reduction and oxidation-storage capacity (Cheng et al. 2021; Montini et al. 2016; Wu et al. 2021). Li and co-workers (Li et al. 2019) investigated a mechanism for ethanol steam reforming (ESR) reaction using density functional theory for Co₁₃/CeO_2 − x configuration. Their studies showed that the ESR process depended on the valence state of the Co sites, specifically, maintaining a higher Co⁰/Co²⁺ ratio resulted in a higher proportion of Co⁰ and Co^x+ sites, which helped to improve the ESR activity. The significance of metal-oxide interactions for the activation of methane over powdered cobalt dioxide-cerium dioxide catalysts was emphasized by Zhang et al. who immobilized Co on the cerium surface and used the redox nature of CeO₂ to activate methane (Zhang et al. 2018).

The synergistic effect between cobalt and cerium is essential for the successful completion of the catalytic process, significantly improving catalytic reactivity and stability (Liu et al. 2019). It has been reported by Zhou et al. (2021) that Co tends to cover the surface of CeO_1.96 with a monolayer structure at very low Co coverage to form a Co-O-Ce structure under room temperature, and the particles grow into a three-dimensional structure as the Co coverage increases. In addition, they found that the cobalt on Co/CeO₂ catalysts exhibited high thermal stability and highly dispersed small particle size due to the strong metal-support interaction of Co with ceria. Cerium dioxide can alter the electronic properties and oxygenophilicity of Co (Martono and Vohs 2012; Vovchok et al. 2018; Zhang et al. 2018). The chemistry of cobalt on cerium dioxide was very different from that of bulk cobalt because cobalt can form on cerium dioxide in metallic and oxidized states, which play different roles in chemical reactions (Zhang et al. 2018). In addition, metal/metal-oxide clusters have received increasing attention for their size-related properties as a key facilitator of heterogeneous catalytic processes (Zheng et al. 2022). Therefore, it is necessary to obtain physical information about Co-Ce catalysts using computational simulations to understand their detailed structures, chemical states and interactions.

Here, a systematic study of the growth pattern of small (x = 1 ~ 6) Co_x clusters on the surface of CeO₂(110) was performed using density functional theory. The focus was placed on the structure, electronic information, and metal-support interactions of the loaded Co_x/CeO₂(110) surface. Furthermore, the mechanism of activating methane on the optimal Co₅/CeO₂(110) configuration is highlighted. This fundamental study of Co growth on the CeO₂(110) surface, which contributed to the understanding of its promising catalytic behavior, provided theoretical guidance for the improved design of optimal Co/CeO₂ catalysts for tailored catalytic reactions.

All spin polarized Density Functional Theory (DFT) calculations in this study were performed using the first-principles calculations as implemented in the DMol³ code (Delley 2000). The generalized gradient approximation (GGA) (Perdew et al. 1996) Perdew-Burke-Ernzerhof potential for solids (PBEsol) (Perdew et al. 2008) functional was used to calculate the exchange and correlation energies. The following electrons were treated as valence electrons: Ce-5s, 5p, 5d, 4f, and 6s; Co-4s, 4p, and 3d; C-2s and 2p; H-1s; O-2s and 2p (Liu et al. 2017; Tian et al. 2018). The adsorption properties were calculated using the spin-unrestricted approach (Delley 1990). Added a dual-numeric basis set (version 4.4) (Delley 2006; Kumari et al. 2015) with orbital polarization for molecular orbitals (Delley 1990). The global orbital cut-off was set to 5.8 Å (Tian et al. 2018). The interactions between ions and electrons were described using the DFT semi-core pseudopotential (DSPP) (Kumari et al. 2015). The convergence criteria for the optimization of all structural configurations were the atomic force threshold of 2.0 × 10^− 3 Hartree/Å, the maximum displacement of 5.0 × 10^− 3 Å, the total energy change of 1.0 × 10^− 5 Hartree, and the self-consistent field (SCF) of 1.0 × 10^− 6 Hartree. Brillouin zone integrations were performed on the CeO₂ bulk and CeO₂(110) surfaces with 6 × 6 × 6 and 2 × 2 × 1 Monkhorst-Pack grids, respectively. The bulk lattice parameters of CeO₂ crystal was calculated to be a = b = c = 5.421 Å, which was well consistent with the previous calculations (a = b = c = 5.423 Å from Ref. (Tian et al. 2017, 2018) and experimental results (a = b = c = 5.410 Å from Ref. (Adachi and Imanaka 1998). This indicates that the calculation methodology used in this work is reliable.

Among the three low Miller index surfaces of CeO₂, the (111) surface is the most stable, the (110) surface is the second most stable, and the (100) surface is the least stable (Tian et al. 2017). The catalytic activity of CeO₂(110) surface is always considered to be higher than that of (111) and (100) surfaces, so it was chosen to investigate the reaction mechanism (Chutia et al. 2018; Tian et al. 2017; Zhou et al. 2022). As recently reported by Qu et al. (2022) that the Ru-loaded CeO₂(110) configuration is extremely competitive for the first C-H bond dissociation of methane compared to CeO₂(111). Therefore, we selected (110) surface to study the growth characteristics of Co_x (x = 1 ~ 6) and investigated the CH₄ activation mechanism on the optimal Co/CeO₂(110) model. The CeO₂(110) surface was a model of an optimized CeO₂ bulk primitive cell cut and expanded to 2 × \(\sqrt{10}\) with four atomic layers, the bottom two being fixed. 15 Å vacuum layer was used to avoid unphysical interactions of the model due to periodic mirroring. For the calculations of the CH₄*, CH₃*, CH₂*, CH*, C*, H₂*, O₂* and Co_x (x = 1 ~ 6) cluster, the (10 × 10 × 10) ų box was used.

To mimic the growth structure of clusters, Co_x (x = 1 ~ 6) were optimized by random placement on CeO₂(110) surfaces. However, the number of possible geometries becomes too numerous to be fully considered as the size of the Co clusters increases. Thus, we acquired Co clusters from the face-centered cubic structure relying on the findings of Datta and Ma et al. (Datta et al. 2007; Ma et al. 2006) to determine their geometry. We maintain that the clusters obtained are unquestionably representative, although this approach may not necessarily yield the most stable Co_x clusters. The initial adsorption model for Co_x (x = 1 ~ 6) clusters was shown in Fig. S1. Co₁ and Co₂ had only one initial structure, while examining Co₃, we focused on the planar triangular (Co_3 − p) model as the initial adsorption configuration rather than the linear model (Co_3 − l) due to the triangular structure of Co₃ being more energetically stable (Datta et al. 2007). There were two kinds of structures in Co₄ without considering linear structure: planar rhombohedral structure, Co_4 − p, and spatial tetrahedral structure, Co_4 − t. Because of the unique structure of Co₄, exploring the optimal adsorption structure of Co₄ is the key to investigating the growth mode of Co_x on the surface of CeO₂(110) (surface tiling or three-dimensional clusters). According to the optimal adsorption structure of Co₄, we investigated the adsorption of stereo-structured Co₅ and Co₆ on CeO₂(110) surface. Nearly all of the possible clustering sites for Co_x(x = 1–6) have been considered on the surface of CeO₂(110) according to the model we have constructed (see Supplementary material).

In this work, the adsorption energy (\({\rm{E}}_{{\rm{C}}{{\rm{o}}_x}}^{{\rm{ads}}}\)) of Co_x(x = 1–6) on CeO₂ (110) surface in the growth study was obtained from the following equation:

where \({\text{E}}_{{\text{Co}}_{{x}}\text{/}{\text{CeO}}_{\text{2}}\text{(110)}}\), \({\text{E}}_{{\text{Co}}_{{x}}}\) and \({\text{E}}_{{\text{CeO}}_{\text{2}}\text{(110)}}\) is represent the energies of the system after adsorption of Co_x clusters on the CeO₂(110) surface, Co_x cluster and CeO₂(110) surface, respectively.

Similarly, the adsorption energy (\({\text{E}}_{{\text{CH}}_{\text{4}}}^{\text{ads}}\)) of CH₄ on Co_x/CeO₂(110) model can be obtained:

where \({\text{E}}_{{{\text{C}\text{H}}_{4}\text{-Co}}_{{x}}\text{/}{\text{CeO}}_{\text{2}}\text{(110)}}\) is the energy of the system after adsorption of CH₄ on the optimal Co_x/CeO₂(110) model, and \({\text{E}}_{{\text{CH}}_{\text{4}}}\) is energy of methane in the gas phase. The adsorption energies of CH₃* and H* species are calculated with reference to \({\text{E}}_{{\text{CH}}_{\text{4}}}^{\text{ads}}\).

The binding energy (E_B) of per Co atom in the Co_x/CeO₂(110) (x = 2 ~ 4) model was defined as

where \({\text{E}}_{\text{Co}}\) represent the energies of a single Co atom. Binding energy was used to characterize the stability of the structure (negative value, exothermic, stable; positive value, endothermic, unstable).

In the Co_x/CeO₂(110) model, the E_B is contributed by metal-substrate and metal-metal interactions. The metal-metal cohesive energy (E_Co−Co, in eV per Co atom) and the metal-substrate adhesion energy (E_Co−O(Ce), in eV per Co atom) were derived from the following equations, respectively:

E_Co−O(Ce) = E_B- E_Co−Co=(\({\text{E}}_{{\text{Co}}_{{x}}\text{/}{\text{CeO}}_{\text{2}}\text{(110)}}\)- \({\text{E}}_{{\text{Co}}_{{x}}}\)- \({\text{E}}_{{\text{CeO}}_{\text{2}}\text{(110)}}\))/x (5).

The growth structure of cobalt clusters on the CeO₂(110) surface can be determined by comparing E_Co−Co and E_Co−O(Ce). The former has to be more negative than the latter to form clusters, and vice versa.

The linear synchronous transition/quadratic synchronous transition (LST/QST) method (Halgren and Lipscomb 1977) with conjugate gradient minimization was used to search for the transition states (TS) of each radical reaction during the complete dissociation of methane. The root mean square (RMS) force on the transition state was optimized to be less than 5.25 kJ/mol·Å. The vibrational frequency analysis confirmed that the transition state structure has one and only one imaginary frequency. The activation energy barrier (E_a) and the reaction energy (E_re) of the radical reaction were calculated by the formulas given in the following equations:

E_a=E_TS-E_IS (6).

E_re=E_FS-E_IS (7).

where E_TS, E_IS and E_FS are the total electron energies of the TS, initial state (IS) and final state (FS), respectively.

3.1 Growth pattern of Co_x (x = 1 ~ 6) on CeO₂(110) surface

Six initial adsorption sites for the adsorption of monoatomic Co on the CeO₂(110) surface were considered, which included Ce top site (Ce-top), O top site (O-top), double oxygen bridge site (Double-O-br) and three different oxygen bridge sites (O-br (1), O-br (2), O-br (3), see Fig. S2. Three stable adsorption sites were formed after the relaxation of the Co₁/CeO₂(110) structure, shown in Fig. 1, with respective adsorption energies of -6.10, -4.69, and -7.13 eV. The double-O-br site was the most stable adsorption site for Co₁ on the CeO₂(110) surface, which was consistent with that of Ni₁ (Li et al. 2016). The Co adsorption energy was stronger in CeO₂(110) than in CeO₂(111) (-4.89 eV) (Tian et al. 2018). Table 1 summarized the bond length information of the stable structure of Co_x/CeO₂(110). The Co-O bond lengths in the Co₁/CeO₂(110) structure with Co adsorbed at the double O-br site were 3 × 1.85 Å and 1.84 Å, respectively, which are smaller than the experimentally reported R_Co−O(CoO) = 2.14 Å and R_Co−O(Co/CeO₂) = 1.97 Å by Deng et al. (2020). The distance d_Ce−O= 2.68 Å between surface O and subsurface Ce is greater than the standard value of 2.35 Å indicates that surface O is more active. In addition, the Mulliken charge analysis showed that isolated Co atom was transferred 0.44 e to the support, resulting in the reduction of two Ce⁴⁺ to Ce³⁺.

Adsorption energies a of Co single atoms on the CeO₂(110) surface and the top and front views of the corresponding stabilized adsorption configurations (O-br (1) b O-br (2) c and Double O-br d)

Thirteen initial adsorption configurations (Fig. S3) of Co₂ on the surface of CeO₂(110) resulted in six stable Co₂/CeO₂(110) configurations (Fig. 2) after surface relaxation. The adsorption models for Co₂-(a, c, d, f, g) sites and Co₂-(b, e, l, m) sites were geometrically optimized to form the stable adsorption configurations of Co₂-a (Fig. 2b) and Co₂-b (Fig. 2c), respectively. Co₂-h, Co₂-i, Co₂-j and Co₂-k (Figs. 2d-g) form independent adsorption configurations, where Co₂-h and Co₂-k were not reasonable adsorption structures for Co₂/CeO₂(110) because the Co-Co distance was too far here (3.99 and 5.50 Å). The most stable adsorption configuration of Co₂ had the same adsorption site as Co₁, i.e., Co₂-a (Fig. 2b), with an adsorption energy of -10.55 eV, and it formed bonds with four neighboring O atoms with bond lengths of 3 × 1.71 Å and 1.72 Å (Table 1). Comparison of the Co-Co bond lengths in the gas-phase structure reveals that Co-Co increased significantly after Co₂ adsorption (2.13 vs. 2.27 Å). The adsorption energy of Co₂ is 3.42 eV larger than Co₁, and the Co-O bond length was shortened by about 0.14 Å, which was attributed to the enhanced interaction between Co atoms and surface oxygen after the adsorption of Co₂. Here, we considered the initial adsorption geometry of Co₂ with the second Co atom sitting directly on top of the first Co atom without bonding to any surface atom (Fig. S3 Co₂-c), but after structural optimization, we found that Co₂ prefers to grow along the plane of CeO₂(110) (Fig. 2b). It is worth mentioning that some of the models appeared large surface deformations after relaxation of the Co₂/CeO₂(110) surface, which is attributed to the reactivity of the O ions on the CeO₂(110) surface. For CeO₂(110), oxygen vacancy formation energy is calculated to be 1.69 eV, which is much lower than 2.57 eV for CeO₂(111) (Riley et al. 2018).

Adsorption energies a of Co₂ cluster on the CeO₂(110) surface and the top and front views of the corresponding stabilized adsorption configurations. b-g Correspond to the models of Co₂-a, b, h, i, j, k, respectively

In the initial adsorption structure of Co₃, we considered the initial adsorption sites of ten Co₃ triangle structures and explored the two most likely adsorption sites of Co₃ linear structure (Fig.S4), six stable adsorption models were obtained after structural optimization (Fig. 3). The initial adsorption models of Co₃-(b, c, g, i) and Co₃-(d, j, k, l) formed two final adsorption configurations, Co₃-b (Fig. 3c) and Co₃-d (Fig. 3d), respectively, after surface relaxation, while Co₃-a, e, f, h (Figs. 3b, e-g) formed independent adsorption configurations. The third Co atom in the initially adsorbed Co₃-b (Fig. 3c) and Co₃-h (Fig. 3g) grew along near and distant CeO₂(110) surfaces, respectively, which was found to be preferred by the third Co atom to grow along away from the CeO₂(110) surface after surface relaxation. Two typical linear Co₃/CeO₂(110) models exhibited the largest adsorption energies after structural relaxation, -14.98 (Fig. 3e) and -13.43 eV (Fig. 3f), respectively. However, the optimized Co₃ was no longer a cluster structure, with Co-Co interstitial distances of 2.81 and 3.51 Å, respectively, hence they were not applicable to the discussion with the present work. The adsorption model of Co₃-d (Fig. 3d) was confirmed to be the most stable in the present work as it had the largest adsorption energy other than Co₃-e and Co₃-f with − 12.31 eV. In the Co_3 − d model, two cobalt atoms were stably deposited on the Double-O bridge site, while a third cobalt atom was laterally adsorbed along the O-br (2) site, forming five Co-O bonds averaging 1.75 Å in length (Table 1). By the action of the third Co atom, one O ion on the surface of CeO₂(110) protrudes from the surface (2.55/3.00 Å), which was attributed to the asymmetry of the interaction of the third Co atom with the surface O (Nolan 2012). When the cobalt ion undergoes electron transfer with the surface oxygen, the symmetry of the structure is broken, causing a Ce ion to be reduced, increasing the Ce-O distance of that particular cerium atom (Nolan 2012). This phenomenon was similar to the previously reported overflow of O from the CeO₂ surface, and this metal-oxide interaction explained the extraordinary structure-activity dependence of cerium oxide-based catalysts (Song and Hensen 2013; Vayssilov et al. 2011).

Adsorption energies a of Co₃ cluster on the CeO₂(110) surface and the top and front views of the corresponding stabilized adsorption configurations. b-g Correspond to the models of Co₃-a, b, d, e, f, h respectively

According to previous studies, the Co₄ cluster had two stable configurations, the most stable planar rhombic structure (Co_4 − p), and the sub-stable space tetrahedron structure (Co_4 − t, Fig. S1) (Datta et al. 2007; Ma et al. 2006). In this work, we considered 22 and 9 initial adsorption sites of Co_4 − p and Co_4 − t, respectively, as shown in Fig. S5 and Fig. S6. After systematic optimization of different initial configurations and considering the symmetry breaking, seven and four stable adsorption configurations were obtained, respectively, as shown in Figs. 4a and c. Their corresponding adsorption energies were shown in Fig. 4b. For Co_4 − p, the initially adsorbed Co_4 − p-(a, b, k), Co_4 − p-(c, f, o, q), Co_4 − p-(e, g, j, p, r, t, u, v) and Co_4 − p-(l, m, n, s) models were structurally optimized to four stable adsorption configurations, i.e., Co_4 − p-a, Co_4 − p-c, Co_4 − p-e and Co_4 − p-l (Fig. 4a). While the remaining Co₄-p adsorption models were all optimized to form independent configurations, see Fig. 4a. For Co_4 − t, the initially adsorbed Co_4 − t-(a, c) and Co_4 − t-(b, j, h, i) sites were structurally optimized for the Co_4 − t-a and Co_4 − t-b models (Fig. 4c), respectively. The Co_4 − p-d and Co_4 − p-f adsorption models formed separate stable adsorption structures after surface relaxation, respectively, see Fig. 4c. Interestingly, both the planar and space structures of Co₄ cluster adsorption eventually form the identical most stable adsorption configurations (Co_4 − p-c in Fig. 4a and Co_4 − t-b in Fig. 4c) with adsorption energy of -11.87 eV.

a Stable adsorption configuration (top view and front view) of Co_4 − p/CeO₂(110) models. b Adsorption energy comparison of stable adsorption of Co₄ clusters. c Stable adsorption configuration (top view and front view) of Co_4 − t/CeO₂(110) models

The ability of Co atoms to grow on the CeO₂(110) surface to form a three-dimensional (3D) cluster structure may depend on the delicate balance between atom-atom interactions and atom-surface interactions (Mao et al. 2016). Therefore, to evaluate the stability of the Co_x/CeO₂(110) system and the growth pattern of Co on the CeO₂(110) surface, Table 2 calculated and summarized the E_B, E_Co−Co and E_Co−O(Ce) for the transition of Co clusters from planar to 3D structural configurations. Here, the two-dimensional adsorption structures of Co_x, i.e., Co₂, Co₃ and Co_4 − p, all of them had a larger E_Co−O(Ce) than E_Co−Co, which implied that the interaction of Co with the CeO₂(110) surface was stronger than the Co-Co interaction. In other words, the two-dimensional adsorption structure at this point was difficult to grow Co longitudinally along the surface due to the strong Co-O(Ce) bonding. Co_4 − t was the smallest 3D structure of cobalt, and although all four Co atoms of Co_4 − p interacted with surface oxygen, the E_B of Co_4 − t/CeO₂(110) was 0.8 eV larger than that of Co_4 − p/CeO₂(110), which may be due to the strong Co-Co interaction in Co_4 − t/CeO₂(110), implying that the Co_4 − t interaction with CeO₂(110) surface is stronger. The difference in E_Co−Co between Co_4 − t/CeO₂(110) and Co_4 − p/CeO₂(110) was very close to 0.8 eV, while E_Co−O(Ce) was almost equal. When Co_4 − t was loaded on CeO₂(110), the E_B was mainly contributed by E_Co−Co, and the Co-Co interaction was strong and the charge transfer was significant (0.25 vs. 0.23 e/per Co atom, Table 1). Additionally, E_Co−Co rapidly increased and approached more closely the metal cohesion energy of bulk phase Co (4.40 eV) (Singal and Das 1977) when the number of deposited Co atoms reached the conditions for the formation of 3D structures, implying that as Co-O(Ce) interactions weaken, Co-Co interatomic interactions increase (E_Co−Co > E_Co−O(Ce)) and clusters above Co₄ cluster structure preferentially forms a 3D stereo structure.

Based on the above findings, we loaded simple 3D structure of Co₅ and Co₆ clusters on the surface of CeO₂(110) to determine an optimal Co_x/CeO₂(110) structure for studying the methane activation mechanism. Fifteen initial Co₅ adsorption configurations (Fig. S7) were structurally optimized to form ten stable adsorption models (Fig. 5). Specifically, the initial adsorption Co₅-(b, e), Co₅-(c, g, k), Co₅-(j, l) and Co₅-(m, o) sites correspond to the optimized models Co₅-b, Co₅-c, Co₅- j and Co₅-m in Fig. 5(c, d, i, j), respectively. While the remaining Co₅ adsorption models were all optimized to form independent structures, see Fig. 5(b, e, f, g, h, k). Comparison of the initial adsorption model and the final results reveals that the Co atoms in the initial adsorption structure interact strongly with the O atoms on the surface of CeO₂(110). Specifically, Co clusters would migrate from unstable positions to stable adsorption sites, with surface O ions detaching from the surface in the effect of Co, destroying the original structural symmetry. Comparison of the stable adsorption models revealed that Co₅-c (Fig. 5d) had the largest adsorption energy of -12.65 eV and was considered to be the most stable adsorption configuration. The four Co atoms of the bottom layer interact with six O atoms on the surface of CeO₂(110) with an average Co-O bond length of about 1.79 Å. Similar to Co₂, Co₃ and Co₄, two of the four Co atoms in the bottom layer remain in the double oxygen bridge site, while the other two Co atoms interact with the two O atoms in the lateral double oxygen bridge site and make them bulge on the surface. Furthermore, the Mulliken charge distribution analysis in Table 1 shows that the Co₅-c/CeO₂(110) model has the largest charge transfer (0.29 e/per Co atom) after adsorption of all Co clusters, which implies that Co has the strongest interaction with the substrate CeO₂(110) in this structure.

Adsorption energies a of Co₅ cluster on the CeO₂(110) surface and the top and front views of the corresponding stabilized adsorption configurations. b-k Correspond to the models of Co₅-a ~ d, f, h, i, j, m, n respectively

In this work, nine initial adsorption models of Co₆ on CeO₂(110) were considered (as shown in Fig. S8), and no identical stable adsorption model was found after surface relaxation (as shown in Fig. 6). Co₆-c/CeO₂(110) (Fig. 6d) exhibited the largest adsorption energy of all the Co₆ adsorbates, yet it was not the most stable structure we need for reasons consistent with the previously discussed unsuitability of Co₂-k (Fig. 2g), Co₃-e (Fig. 3e) and Co₃-f (Fig. 3f). Specifically, one of the Co atoms in the Co₆-f/CeO₂(110) structure had detached from the Co cluster and interacts with the surface alone, and its distanced from the closest O are approximately 1.81 Å, with distanced to the closest Co of 2.44 and 2.58 Å (d_Co−Co = 2.30 Å in the Co₆ cluster, Fig. S1). Therefore, Co₆-f/CeO₂(110) was considered to be the most stable adsorption model for the adsorption of Co₆ clusters on CeO₂(110) with an adsorption energy of -11.49 eV. The stable adsorption sites of the Co₆ cluster were similar to those of the other Co clusters, all belonging to the CeO₂(110) surface depression with the presence of more O ions. only four Co atoms in the Co₆-f/CeO₂(110 configuration were bonded to surface O, which implied that the surface interaction of the Co₆ cluster with CeO₂(110) is weaker than that of the Co₅ cluster. This was also supported by Mulliken charge distribution analysis (0.29 vs. 0.23 e/per Co atom). Moreover, the average bond length of the five Co atoms of Co₆ to the surface O ions was essentially the same as that in Co₅ (1.80 vs. 1.77 Å). It was noteworthy that Co₆ adsorption on CeO₂(110) was weaker than the most stable Co₅ adsorption on CeO₂(110) in all possible structures we considered, implying that the structural stability of Co clusters decreased as the number of Co atoms in Co_x/CeO₂(110) increased to 6. The Co₆-c/CeO₂(110) model with the largest adsorption energy accompanied by the detachment of one Co atom also supports this.

Adsorption energies a of Co₆ cluster on the CeO₂(110) surface and the top and front views of the corresponding stabilized adsorption configurations. b-j Correspond to the models of Co₆-a ~ i respectively

From the above discussion, we could conclude that the stable adsorption site of single-atom Co on the CeO₂(110) surface is the Double O-br site, Co prefers to form 3D clusters on the CeO₂(110) surface, and the stability of the clusters decreases when the number of atoms in the adsorbed Co clusters is more than six. Furthermore, the stable Co₅-c/CeO₂(110) structure has the largest adsorption energy, suitable Co-Co atomic interactions, and Co atom-CeO₂(110) surface interactions, which should be regarded as the optimal Co_x/CeO₂(110) structure for the study of methane activation mechanism.

3.2 Electronic structures of Co_x (x = 1 ~ 6) on CeO₂(110) surface

It is well known that density of states (DOS) is a very helpful tool for electronic structure analysis in flat plate model calculations. Here, we have analyzed the partial density of states (PDOS) for the most energetically favorable Co_x/CeO₂(110) structure and further elucidated the Co_x and CeO₂(110) interactions by electronic structure properties. The PDOS of the stabilized Co_x/CeO₂(110) structure was illustrated in Fig. 7. The dashed and solid lines in the PDOS describing Co_x indicated the electronic states of Co in the gas phase and adsorbed on the surface of CeO₂(110), respectively. The dashed and solid lines in the PDOS of CeO₂(110) described the electronic states of O and Ce, respectively. The contributions of the basal Ce and O atoms to TDOS after adsorption of Co atoms or clusters were essentially unchanged significantly (not shown in the paper). However, a shift in their electron-occupying states toward lower energies can be clearly observed, which is consistent with the results for other transition metals after adsorption (Chutia et al. 2018; Qin and Su 2021; Tian et al. 2018). In contrast to the pure CeO₂(110) surface PDOS, new occupied states appeared between the top of the valence band and the bottom of the Ce-4f band. This occupied state is almost entirely contributed by the 4f orbital of the reduced Ce³⁺ ion, the 3d orbital of the Coⁿ⁺ ion, and the 2p orbital of the O²⁻ ion (Li et al. 2016). This is in agreement with the work reported by Zhang et al. (2021) studying the surface of Co-doped CeO₂(110).

When Co_x was adsorbed to the surface, the occupied 4s state of Co_x near the Fermi energy level disappeared almost completely, implying that the transfer of Co-4s electrons occurs upon adsorption (Cui et al. 2012). The Co-3d states can be observed to spread over a wider energy range above the Fermi level, indicating strong interactions between Co_x and on the support surface with greater charge transferred between Co and O atoms (Reddy and Deshpande, 2022). The asymmetry of the Co-3d spin states was observed in the PDOS, suggesting the presence of a non-zero magnetic moment on the Co atom. Co loading resulted in the formation of occupied d-type Co orbitals in the bandgap of the semiconducting properties of the CeO₂(110) surface, which was consistent with the f-type orbitals that were previously found to be occupied upon Ni loading (Hahn et al. 2015). The PDOS area and height of Co orbitals increased with the number of Co atoms, indicating that the electron density increased with the number of Co atoms (Xu et al. 2016). The increase in the electronic occupation state of Co-3d orbitals resulted in a decrease in the band gap, which completely disappeared from Co₃ onwards (Fig. 7c). Similar to the results of Pintos et al. (2013), we found new unoccupied states above the Fermi energy level of the PDOS curve, mainly contributed by O-2p orbitals and Co-3d orbitals. The crossover between O-2p and Co-3d orbitals indicated that some O atoms in CeO₂(110) were activated by some Co atoms in the Co cluster, leading to the formation of Co-O bonds. As depicted by PDOS in Fig. 7e, the contribution of O-2p orbitals in the interstitial state (-2 to -0.8 eV) after the adsorption of Co₅ largely overlapped with that of Co₃-d orbitals, whereas the contribution from the O-2p orbitals after the adsorption of all Co_x except Co₁ were smaller than those from the Co-3d orbitals. The stronger interaction between O and Co atoms in the Co₅/CeO₂(110) structure was explained, which was consistent with the result that Co₅ exhibited the maximum adsorption energy after adsorption. It is remarkable that the contribution of O-2p orbitals in the interstitial state (-2 to -1.5 eV) after Co₁ adsorption was larger than that of Co-3d orbitals, which was due to the interaction of Co₁ with the four O atoms on the surface after stable adsorption, and the transfer of electrons from surface Ce ions to Co via O. In addition, the asymmetric behavior of the electron-occupying states of Co near the Fermi energy level indicated the metallic character of the Co_x/CeO₂(110) system (Hahn et al. 2015; Xu et al. 2016).

Projected density of states (PDOS) on the atoms involved for a Co₁/CeO₂(110), b Co₂/CeO₂(110), c Co₃/CeO₂(110), d Co₄/CeO₂(110), e Co₅/CeO₂(110) and f Co₆/CeO₂(110) surface. E_F is the Fermi energy level and is taken as the zero point of DOS. Upper and lower panels represent spin up and spin down, respectively

According to Mulliken charge analysis (Table 1), the strong interaction of the Co clusters with the CeO₂(110) surface led to a significant charge transfer from the metal atoms as well as a partial oxidation of Co atoms close to the surface of the supported CeO₂(110) (Li et al. 2019), with Q_Co ranging from 0.20 to 0.44 e/per Co atom. The charge transfer on each Co atom was 0.29 and 0.23 e for the CeO₂-supported Co₅ and Co₆ systems, respectively, i.e., the Co₅/CeO₂(110) configuration had more electron transfer, which could lead to stronger interactions (Qu and Wang 2022). Noteworthy, although the maximum charge transfer after single-atom Co adsorption would have implied a stronger cobalt-support interaction, the disappearance of the highly localized d-orbital contribution in PDOS after single-atom Co adsorption implied that the low-activity d-orbital electrons might have reduced the redox capacity of the catalyst (Shi et al. 2021). Moreover, the average distance between Ce and the nearest neighboring O ion near the adsorption site of the Co₅ cluster was calculated to be 2.49 Å, which is similar to the experimentally found Ce³⁺-O bond length (2.50 Å) (Ganduglia-Pirovano et al. 2009). The optimized Co₅/CeO₂(110) structure was selected as the optimal configuration for the study of methane activation mechanism by considering the adsorption energy, binding energy and Co atom- CeO₂(110) surface electron interactions comprehensively.

3.3 Adsorption of CH_x(x = 0 ~ 4) over Co₅/CeO₂(110)

Stable adsorption sites for CH_x* species were identified via the most stable CH₄ adsorption sites, which can overcome the high energy barrier to long-range migration of CH_x* species during CH₄ dissociation (Singha et al. 2019). The Ni₅/CeO₂(110) model identified for the study of methane activation has three possible CH₄ molecular adsorption sites: (i) surface adsorption site, (ii) interfacial adsorption site, (iii) active metal Co adsorption site (see Fig. S9). There are five stable structures of CH₄ after adsorption at the surface adsorption site (Fig. S10) with adsorption energies ranging from -0.07 to -0.19 eV, while there is only one stable structure at both the interfacial adsorption site and the metal site. The stable structure of CH₄ after adsorption at the interfacial adsorption site with an adsorption energy of -0.12 eV is shown in Fig. S10. The CH₄ adsorbed on the top of Co₅ had the largest adsorption energy of -0.45 eV, which was considered to be the most stable adsorption model for methane, as shown in Fig. 8a. The C-H₁, C-H₂, C-H₃ and C-H₄ bond lengths after CH₄ adsorption are 1.14, 1.13, 1.10 and 1.10 Å, respectively; the H-C-H angles are 104.83-114.65° (the C-H bond length of methane molecule in the gas phase is 1.10 Å and the H-C-H angle is 109.47° (Horn and Schlögl 2015). It implied that the CH₄ molecule was effectively activated during the adsorption process (Guo and Wang 2017). The most stable adsorption structures and adsorption energies of CH_x* and H* at the Co metal sites are shown in Figs. 8b-f, respectively, which could be used to determine the final structures of the methane dissociation products. In addition, other adsorption configurations of CH_x* species and H* species after methane dissociation are also shown in the Supplementary material.

Stable adsorption sites and adsorption energies of a CH₄* b CH₃* c CH₂* d CH* e C* and f H* species on the surface of Co₅/CeO₂(110) catalyst. Includes top view (top) and front view (bottom)

3.4 Energetics of dissociation CH₄

To understand the activation mechanism of CH₄ on the surface of Co₅/CeO₂(110) catalyst, the activation energy (E_a) and reaction energy (E_re) for the sequential dehydrogenation of methane at the above adsorption sites have been investigated. The energy information of the stepwise dehydrogenation process of methane and the structural information of the transition state were summarized in Table 3. Methane adsorbed on the top of Co₅ was used as the initial state (IS), and the first efficiently activated C-H bond (C-H₁) dissociated on the metal to form the transition state (TS, see Fig. 9a) with a C–H distance of 1.67 Å. Here, the H atom of the dissociated first C-H bond is extracted by the active Co metal and combined with the bridge of the Co-Co bond to form two Co-H bonds, while the CH₃* fragment adsorbs to the Co metal on the other side to form two Co-C bonds. The transition state search revealed that the E_a to be overcome by methane to dissociate the first C-H bond at the active metal site of Co₅-CeO₂(110) was only 0.44 eV(about 10.10 Kcal/mol), which is much lower than the E_a (23.70 Kcal/mol) of CH₄ dissociation catalyzed by Ni₄ cluster supported on cerium oxide reported by Singha et al. (2019), and is close to the E_a of 0.55 eV reported by Lustemberg et al. (2020) for the dissociation of CH₄ on the Co₄/Ce₂O₃. Moreover, the E_re for the dissociation of the first C-H bond was − 0.41 eV, implying that the process is thermodynamically favorable.

The energy and structure diagrams for the continued dehydrogenation of CH₃* to form CH₂*+H* were shown in Fig. 9b. The E_a for the continued dehydrogenation of CH₃* was 0.55 eV, which is higher than that for the first C-H bond dissociation of CH₄, implying that that the rate-determining step (RDS) for methane activation in the Co₅/CeO₂(110) catalyst system studied in this paper was no longer the activation of the first C-H of CH₄ as previously widely reported (Egawa 2018; Wei and Iglesia 2004). One surprising result was that the continued dehydrogenation of CH₃* was an exothermic reaction with a E_re of -0.11 eV, which was contrary to the results of previous studies on Ni (Xie et al. 2021) and Pt (Niu et al. 2016) as reactive metals. The activated C-H bond was extended from 1.12 Å to 1.66 Å in the TS where CH₃* continued to dissociate and dehydrogenate, and the distances between the dissociated H atom and Co are 2.13 Å and 1.51 Å, respectively, implying that the H atom forms a strong bond with Co (Li et al. 2014).

The dissociation process of CH₂* was shown in Fig. 9c, in which the hydrogen atom directed towered the top Co atom was stretched to its top and directed towered the hcp site of the three Co atoms in the rear side, and eventually the hydrogen atom was firmly bonded to the three Co atoms in the rear hcp sites. While the hydrogen atoms on CH* fragment moved to the top of C atom, and the whole CH* fragment was still adsorbed at the hcp site on the upper part of Co₅ cluster. DFT calculations of the transition state structure revealed that the C-H bond was pulled from 1.10 Å to 2.26 Å, and the CH₂* dehydrogenation to CH* required to overcome an E_a of 0.31 eV (about 7.13 kcal/mol), the E_re is -0.11 eV. This E_a is greater than the recently reported Pt(111) surface CH₂* dehydrogenation barrier(6.20 kcal/mol) (Yoshida et al. 2022), which is very consistent with the Ni(111) surface CH₂* dehydrogenation barrier(0.30 eV) reported by Blaylock et al. (2009).

Energy diagrams for complete dissociation of methane. The initial, transition and final states of the reaction for each dehydrogenation step were inserted separately into the blanks of each energy diagrams

The E_a for CH* dehydrogenation is 1.20 eV (see Fig. 9d), which agreed well with Li et al. (2014) (1.36 eV). The transition state configuration showed that the hydrogen atom was pulled from the top of the C atom to the Co-Co bridge site, and the C-H bond was pulled from 1.10 Å to 1.57 Å. In the configuration of the product, C and H atoms were located at two hcp sites, respectively, which was the same as CH* dehydrogenation. In addition, CH* dehydrogenation was calculated to be an endothermic reaction with a E_re of 0.54 eV. The dehydrogenation of CH* was the RDS in this research system, which was consistent with the previous reports on the difficulty of further dissociation of carbon deposits after methane activation (Niu et al. 2016; Xie et al. 2021).

In this work, we investigated the growth mode of small-sized Co clusters on the surface of CeO₂(110) using density-functional theory and determined the most favorable Co cluster structure to be formed on CeO₂(110). Co clusters grew most favorably at the step positions enriched with oxygen ions which are near the double-oxygen bridge sites. Single-atom Co, Co₂ clusters and two Co atoms in Co₃ clusters were all stable adsorbed at double-oxygen bridge sites on the surface of CeO₂(110), while the third Co atom in Co₃ clusters grew along the side and adsorbed at the O bridge sites. The fourth Co atom in the Co₄ cluster grew along the direction away from the surface of CeO₂(110) and formed a three-dimensional cluster, suggesting that Co clusters on CeO₂(110) were more inclined to form three-dimensional rather than planar clusters. The Co₅ clusters formed on CeO₂(110) were the most competitive among all the small-sized Co clusters considered. The primary reasons were that Co₆ cluster formation on CeO₂(110) was thermodynamically limited compared to Co₅ clusters, as well as the Co atoms in Co₆ clusters had the ability to grow independently from the clusters with the structure being thermodynamically more favorable than other Co₆ clusters. The adsorption and activation mechanism of methane was investigated using the optimal Co₅/CeO₂(110) model. The energetics of methane dissociation implied that the catalyst model had a methane activation capacity comparable to that of metallic nickel and platinum, with a dissociation energy barrier for the first C-H bond of only 0.44 eV. In addition, the high energy barrier for the dissociation of the CH* fragments provided an efficient route for selective methane activation.