Adsorption and Oxidation of CO on Ceria Nanoparticles Exposing Single-Atom Pd and Ag: A DFT Modelling

Various COx species formed upon the adsorption and oxidation of CO on palladium and silver single atoms supported on a model ceria nanoparticle (NP) have been studied using density functional calculations. For both metals M, the ceria-supported MCOx moieties are found to be stabilised in the order MCO < MCO2 < MCO3, similar to the trend for COx species adsorbed on M-free ceria NP. Nevertheless, the characteristics of the palladium and silver intermediates are different. Very weak CO adsorption and the small exothermicity of the CO to CO2 transformation are found for O4Pd site of the Pd/Ce21O42 model featuring a square-planar coordination of the Pd2+ cation. The removal of one O atom and formation of the O3Pd site resulted in a notable strengthening of CO adsorption and increased the exothermicity of the CO to CO2 reaction. For the analogous ceria models with atomic Ag instead of atomic Pd, these two energies became twice as small in magnitude and basically independent of the presence of an O vacancy near the Ag atom. CO2-species are strongly bound in palladium carboxylate complexes, whereas the CO2 molecule easily desorbs from oxide-supported AgCO2 moieties. Opposite to metal-free ceria particle, the formation of neither PdCO3 nor AgCO3 carbonate intermediates before CO2 desorption is predicted. Overall, CO oxidation is concluded to be more favourable at Ag centres atomically dispersed on ceria nanostructures than at the corresponding Pd centres. Calculated vibrational fingerprints of surface COx moieties allow us to distinguish between CO adsorption on bare ceria NP (blue frequency shifts) and ceria-supported metal atoms (red frequency shifts). However, discrimination between the CO2 and CO32− species anchored to M-containing and bare ceria particles based solely on vibrational spectroscopy seems problematic. This computational modelling study provides guidance for the knowledge-driven design of more efficient ceria-based single-atom catalysts for the environmentally important CO oxidation reaction.

The M-containing surface phases of the aforementioned systems are represented by M m [6,7,16,24,28,29] and MO x [6,25,26,30] nanoparticles (NPs), charged metal clusters [7,24,31], solid M x Ce 1−x O 2−δ solutions [25][26][27][32][33][34][35], and dispersed M 1 or O x M 1 adspecies [3,[6][7][8][9]16,36,37]. Analysis of the crystalline environment of the Pd 1 ad-species revealed that each Pd 2+ ion in Pd/CeO 2 catalysts prepared by the solution combustion method is coordinated, on average, by three O atoms [34]. This coordination mode of Pd 1 is a feature of adsorption complexes with CO such as O 2 Pd 1 -CO/CeO 2 (111) [8], O 1 Pd 1 -CO/CeO 2 (111) [8], and O 1 Pd 1 -CO/CeO 2 (100) [9], while a Pd 1 -CO/CeO 2 (100) complex exhibits an O-Pd-O bridge [9]. In many cases, Pd 1 is in a square-planar environment. Pd 1 centres in Ce 1−x Pd x O 2−δ crystals (x ≤ 0.15) reside on O 4 units adjacent to Ce centres [32]. The doping of ceria with Pd results in a structure with the dopant ion displaced from the initial cationic position to the centre of the O 4 unit [23]. Furthermore, Pd 1 species are attached to the O 4 unit of the Pd x Ce 1−x O 2−x−δ lattice incorporating products of water dissociation [27]. Replacing every second upper-layer Ce 4+ cation and one adjacent to it O 2− anion on the CeO 2 (110) surface with Pd 2+ leads to a complex reconstruction and a low-energy surface geometry, with the dopant ion residing close to the centre of the square-planar O 4 site [6]. Stable structures with square-planar O 4 Pd are also communicated on Pd-doped CeO 2 (111) [33] and edges of ceria NPs at intersecting {111} and {100} nanofacets [35]. Four-fold coordinated Pd adatoms are identified in the most stable O 4 Pd structures on the CeO 2 (110) surface [20] and {100} nanofacets [37]. The surface O 4 sites are also capable of suppressing the sintering of Ag 1 species, despite the fact that the Ag atom binds to the {100}-O 4 pocket more weakly than other Group VIII-XI metal atoms [37,38]. The aforementioned thermally stable structures are relevant to the development of the single-atom catalysts [36,37,39].
To understand how the role of the ceria support varies in specific catalytic processes, it is crucial to examine the interactions of the involved reactants with various active centres of CeO 2 . For the ceria-supported metal catalysts of CO oxidation or CO 2 activation, of primary interest are the interactions of O 2 , CO, and CO 2 molecules with the metal-support interfaces [2,8,9,18,20,33,[40][41][42][43]. Thus, modelling based on density functional theory (DFT) has recently addressed a variety of sites with M 1 -O 2 , M 1 -CO, and M 1 -CO 2 entities on ceria [8,9,18,20,40]. The adsorption of CO on a single Pd atom embedded in the defectfree CeO 2 (111) surface and that containing O vacancies followed by NO reduction with CO was explored [18,40]. Surface complexes of CO and CO 2 taking part in the catalytic cycle of CO oxidation on Pd 1 /CeO 2 (110), including Pd 1 -CO, Pd 1 -CO 2 , O 1 Pd 1 -CO species on the stoichiometric CeO 2 (110) surface and Pd 1 -CO 2 , Pd 1 -O 2 , O 2 -Pd 1 -CO ones on the O-deficient CeO 2 (110) surface, were calculated [20]. The CO oxidation routes passing via O 1 Pd 1 -CO, Pd 1 -CO, Pd 1 -CO 2 , O 2 Pd 1 -CO, and O 1 Pd 1 -CO 2 moieties on the defectfree CeO 2 (111) surface [8] as well as on regular and O-deficient CeO 2 (100) surfaces [9] were also quantified. The catalytic CO oxidation according to the Mars-van-Krevelen mechanism combines the elementary steps of oxygen donation from a surface active centre to adsorbed CO and the subsequent replenishment of the support by stream oxygen; the much slower conversions of the first step are found to be rate-determining [8,9,19,20]. In addition to the M 1 -CO 2 structures, surface carbonate complexes can be formed on M 1 -ceria interfaces before the desorption of CO 2 . To this end, the formation of tridentate Pd 1 -CO 3 carbonates upon CO 2 adsorption at the interface of Pd 1 and O-deficient CeO 2 (111) surface was simulated [13] and the CO vibration frequencies of various ceria-supported Pd-CO species were calculated [8,9]. Unlike the quite extensive computational studies of Pd 1 CO xceria systems outlined above, no simulations of analogous Ag 1 CO x -ceria systems have been communicated so far to the best of our knowledge.
Previous studies have developed structural models of low-energy CeO 2 NPs [44][45][46][47] and established that their {100} nanofacets notably stabilise single d-metal atoms [38,41,44,[48][49][50][51]. In this work, we consider monoatomic Pd and Ag species located on a Ce 21 O 42 NP [49] as models appropriately describing surface composites formed by single-atom Pd and Ag with nanostructured ceria. These two metals, which are neighbouring in the Periodic Table, interact very differently with ceria and behave as M-based species involved in CO oxidation. The quantification and in-depth understanding of such differences are still missing in the literature.
This study aims to (i) determine the structures of the lowest-energy complexes with CO, CO 2 , and CO 3 2− moieties resulting from the interaction of CO with Pd and Ag single atoms anchored to the O 4 -pocket sites of the stoichiometric and O-deficient ceria NPs, (ii) analyse the structure and properties of these nanostructured adsorption systems versus earlier investigated analogues formed on extended ceria surface containing M 1 centres, (iii) evaluate and rationalise the reactivity differences of Pd 1 /NP{100} and Ag 1 /NP{100} sites as active centres for CO oxidation (including the effect of M-atom on the formation of CO 3 2− prior to CO 2 desorption), and (iv) examine the vibrational fingerprints of the CO x units accompanying the formation of various surface species. Obtained results related to all these aspects are summarised in the Conclusions section.

Models and Details of Calculations
Surface sites of the CeO 2 substrate were represented by a putative global-minimum structure of stoichiometric NP Ce 21 O 42 [46,47] (3)) and CO 2 -E b (CO 2 ) (Equation (4)). Negative energy values correspond to exothermic processes. To specify the coordination modes of CO 2 in MCO 2 /NP[n/1] and of CO 3 2− in MCO 3 /NP[n/2] complexes, additional three-digit indices were used [68] resulting in the notation that being invoked only when discussing the coordination modes of CO x species. For carbonate complexes, a notation abc (integer a, b and c range from 0 to 3) determines numbers of substrate atoms, to which each O atom in CO 3 2− is coordinated. The middle digit b corresponds to the O atom with the highest coordination. A dot in indices a.bc or ab.c specifies that two O atoms of CO 3 2− (corresponding to a and b or b and c, respectively) form a bidentate bond with one atom of the substrate. Dotless abc identifiers designate CO 3 2− groups with each O atom coordinated to a different substrate atom. When the three-digits notation is used to specify coordination of CO 2 in MCO 2 /NP[n/1] complexes, the first digit a gives the number of substrate atoms coordinated to C atom. For instance, in Figure 3, each of the atoms of CO 2 in structure 111-Pd2a contacts different ions of the Pd/Ce 21 (Figure 1a), which can bind metal atoms much stronger than its {111} nanofacets do [38]. We anchored single Pd and Ag atoms to the {100} nanofacet composed of four nearly coplanar two-coordinated oxygen centres forming an O 4 -pocket with diagonals of 459 and 443 pm. This arrangement is appropriate for accommodating transition metal cations with typical M-O bond lengths of 185-210 pm [37].  [37]. Furthermore, the present location of the Ag atom 96 pm above the O 4 -plane is close to the elevation by 90 pm on Ce 40 O 80 [37]. A slightly larger above-plane elevation, by 102 pm, was calculated for a two-fold coordinated Ag single atom adsorbed on the Fe 3 O 4 (001) surface with energy 2.75 eV [69]. Ag atom adsorption moves O 4 centres upwards, elongating the involved Ce-O distances to 218-223 pm. One Ce ion reduced to +3 state, pointing to the Ag + oxidation state.
The Pd adatom is located nearly in the O 4 plane (Figure 1c), with an out-of-plane displacement of 18 pm, adopting a favourable planar coordination. All four Pd-O bonds are equal to 205 pm-exactly the same as for the Pd/Ce 40 O 80 model [37]. The formation of PdO 4 species moves O atoms closer to Pd, contracting diagonals of the O 4 square to 408 pm and elongating the corresponding Ce-O distances to 230 pm-the value typical for three-coordinated O centres. The high adsorption energy of the Pd atom, 4.24 eV, further increases upon interactions with the O 4 -site of larger ceria NPs [37]. Two Ce 3+ ions appeared upon Pd adsorption, indicating the oxidation state Pd 2+ .
An O-deficient site is created by the removal of the weakest bonded O atom (with E(O V ) = 1.87 eV,    (Table 1). No geometry changes are calculated upon bringing together the CO molecule and ceria species. In particular, the C-O Evidently, an extra energy of~1.2 eV is needed to cleave one Pd-O bond. Note that the Pd atom remains after O removal in a virtual square-planar environment with one coordination site empty and the lengths of the remaining three Pd-O bonds unchanged, 206-209 pm, vs. the PdO 4 site of Pd/Ce 21 O 42 . No reduction of Ag + and Pd 2+ ions occurs upon O vacancy creation, since the leaving O atom donates two electrons to two Ce 4+ ions, increasing the number of Ce 3+ centres by two (to three for Ag/NP and to four for Pd/NP).

Carbonyl Species
Let us first consider the adsorption of a CO molecule on a Ce ion of bare ceria particles ( Figure 2). For both the pristine and O-deficient structures, CO adsorption energy is very small, at −0.26 and −0.23 eV, respectively (Table 1). No geometry changes are calculated upon bringing together the CO molecule and ceria species. In particular, the C-O bond is retained at 114 pm as in the free CO molecule. The C end of the CO adsorbate is 293 (1a) and 297 pm (1aV) away from the nearest Ce 4+ ion of NP (Table 1). CO forms angles at 176 • and 172 • with the Ce site. Thus, CO is rather physisorbed than chemisorbed on the Ce site of the pristine and reduced forms of the metal-free NP. The same geometry and adsorption energy of −0.26 eV (Table 1) [6,27,32]. Note that CO adsorption on all Pd-containing models does not change the oxidation state Pd 2+ , except for Pd1c with an endothermic mode by 0.13 eV CO adsorption (Table 1), where a Ce 3+ → Ce 4+ transition indicated a reduction to Pd + .
In an O-deficient structure, Pd1aV (Figure 3), the adsorbed CO occupies one of four places around Pd. This results in Pd-C bond shortening to 187 pm (Table 1), as in Pd 1 -CO/CeO 2 (110) complexes bonded with two (Pd-C = 184 pm) and three O surface atoms (Pd-C = 188 pm) [20]. The Pd-C-O angle in Pd1aV is close to 180 • . The elongation of the C-O distance from 114 to 116 pm indicates noticeable d → 2π* back-donation. In Pd1aV, CO binds at a vacant coordination site around Pd, no bonds are broken, and adsorption induced geometry changes are minor. As a result, PdCO/Ce 21 O 41 is stabilised by 1.7 eV with respect to separated Pd/Ce 21 O 41 and CO fragments (Table 1). Interestingly, similarly strong CO binding as that for Pd1aV, 1.77 eV, and a Pd-C distance of 186 pm were calculated for the two-fold coordinated single Pd atom in Pd 1 /Fe 3 O 4 (001) [69]. The CO bond to the isolated Pd atom is also similarly strong, at 1.8 eV [70]. The values of 1.6 eV [8] and 1.9 eV [9] were calculated for Pd 1 -CO/CeO 2 (111) and O 1 Pd 1 -CO/CeO 2 (100) complexes, respectively, with Pd 1 coordinated to three O atoms including that of isolated O 1 Pd 1 species. A CO adsorption energy of −1.5 eV was calculated for the Pd 1 -CO/CeO 2 (110) complex with the Pd + ion between two three-fold O atoms [20]. In the series of complexes Pd 1 -CO/CeO 2 (111), O 1 Pd 1 -CO/CeO 2 (111), and O 2 Pd 1 -CO/CeO 2 (111), E b (CO) decreases (by module) with the growth of the Pd 1 coordination number from 1.6 to 0.9 and to 0.6 eV [8].
An even smaller CO adsorption energy, −0.13 eV, was calculated for the coordinatively saturated Pd centre of the PdO4 site of the unreduced model (Pd1b, Figure 3). Here, CO binds the Pd atom at an angle of 131° and rather long Pd-C contact of 241 pm. CO adsorption causes minor distortions in the Pd/Ce21O42 structure: Pd-O bonds extend from 205 to 207 pm, and Pd moves by 27 pm above the O4 plane. The C-O bond elongates by just 1 pm vs. gas-phase CO. No CO adsorption was reported on Pd atoms in the PdO4 environment saturated by two O centres of the CeO2{100} surface and two O adatoms [9]. Furthermore, Eb(CO) < −0.2 eV was calculated for coordinatively saturated Pd atoms in PdO(100). Thus, a very low Eb(CO) for Pd1b is related to the saturation of the coordination sphere of the Pd atom in the O4-pocket of the {100} nanofacet by O atoms; the formation of an additional Pd-C bond competes with quite strong Pd-O bonds. The exceptional stability of Pd 2+ ions in square-planar oxygen environment in CeO2 materials is also claimed in other experiments [6,27,32]. Note that CO adsorption on all Pd-containing models does not change the oxidation state Pd 2+ , except for Pd1c with an endothermic mode by 0.13 eV CO adsorption (Table 1), where a Ce 3+ → Ce 4+ transition indicated a reduction to Pd + .
In an O-deficient structure, Pd1aV (Figure 3), the adsorbed CO occupies one of four places around Pd. This results in Pd-C bond shortening to 187 pm (Table 1), as in The binding of CO to O-defect-free Ag1a and O-deficient Ag1aV complexes is moderately strong, at about 0.8 eV (Table 1), and essentially independent of the coordination-AgO 4 or AgO 3 -of the Ag atom. This adsorption energy value fits the calculated values of −0.85 eV for CO adsorption at the two-fold coordinated Ag single atom in the Ag 1 /Fe 3 O 4 (001) site and −0.94 eV for the two-fold coordinated Ag atom at the AgO 2 (111) surface well [69]. Structures of the AgCO fragments in Ag1a and Ag1aV are very similar ( Figure 4). The Ag-C distance of~200 pm (Table 1)  In summary, the modification of the ceria NP with single Pd and Ag atoms strongly affects its affinity to CO. Effects of Pd and Ag atoms are different. Due to strong Pd-O bonds, the saturated PdO 4 site is almost inactive towards CO adsorption, whereas the PdO 3 unit with a vacant coordination place readily traps CO with a substantial energy gain. In contrast, AgO 4 and AgO 3 centres with weak Ag-O bonds and a more flexible geometry are more prone to adsorb CO molecules with equally moderate energies.

Carbon Dioxide Species
For the metal-free ceria, only weakly adsorbed CO 2 species were calculated: binding energies are −0.25 and −0.15 eV for 2a and 2aV models, respectively (Table 1). These energies are comparable with the values calculated for linearly-adsorbed CO 2 at extended CeO 2 (100), (110), and (111) surfaces [71][72][73][74][75][76]. In both complexes, the linear geometry of CO 2 as in the gas-phase molecule is preserved: Pd1-CO/CeO2(110) complexes bonded with two (Pd-C = 184 pm) and three O surface atoms (Pd-C = 188 pm) [20]. The Pd-C-O angle in Pd1aV is close to 180°. The elongation of the C-O distance from 114 to 116 pm indicates noticeable d → 2π* back-donation. In Pd1aV, CO binds at a vacant coordination site around Pd, no bonds are broken, and adsorption induced geometry changes are minor. As a result, PdCO/Ce21O41 is stabilised by 1.7 eV with respect to separated Pd/Ce21O41 and CO fragments (Table 1). Interestingly, similarly strong CO binding as that for Pd1aV, 1.77 eV, and a Pd-C distance of 186 pm were calculated for the two-fold coordinated single Pd atom in Pd1/Fe3O4(001) [70]. The CO bond to the isolated Pd atom is also similarly strong, at 1.8 eV [71]. The values of 1.6 eV [8] and 1.9 eV [9] were calculated for Pd1-CO/CeO2(111) and O1Pd1-CO/CeO2(100) complexes, respectively, with Pd1 coordinated to three O atoms including that of isolated O1Pd1 species. A CO adsorption energy of −1.5 eV was calculated for the Pd1-CO/CeO2(110) complex with the Pd + ion between two three-fold O atoms [20]. In the series of complexes Pd1-CO/CeO2(111), O1Pd1-CO/CeO2(111), and O2Pd1-CO/CeO2(111), Eb(CO) decreases (by module) with the growth of the Pd1 coordination number from 1.6 to 0.9 and to 0.6 eV [8].  The contacts of O atoms of the CO 2 group with Ce atoms are~300 pm in 2a and 304-331 pm in 2aV (Table 1). All attempts to locate more stable structures with a bent CO 2 moiety have led to carbonate moieties (described in detail in Section 3.1.4). No minima corresponding to bent CO 2 structures of carboxylate type were found. The only located structure with distorted CO 2 (2bV at Figure 2) was found to be 0. 75 (Table 1) indicates exothermic CO 2 release. Since only one Ce 3+ ion is present after CO to CO 2 transformation, CO 2 in 2bV is negatively charged, forming a CO 2 − anion. Thus, CO 2 binds weakly and easily desorbs from bare Ce 21 O 42−x NP. The metal-containing Pd/NP and Ag/NP models also feature structures with "linear" and "bent" CO 2 (Figures 3 and 4). Similar to the bare ceria, linear CO 2 is weakly bound in Pd2b, Pd2bV, Ag2a, and Ag2bV, by less than 0.2 eV ( Table 1). All distances between atoms of CO 2 molecule and ceria are longer than 300 pm. In contrast, in "bent" CO 2 structures Pd2a, Pd2aV, Ag2b, and Ag2aV, CO 2 approaches more closely to the NP surface and forms C-M and O-Ce bonds at 193-234 and 250-270 pm, respectively. Interestingly, despite the sizable changes at the metal-adsorbate interface when going from "linear" to "bent" structures, the pairs Ag2aV/Ag2bV and Ag2a/Ag2b are isoenergetic within 0.15 eV. This observation supports our earlier finding that the formation of a new Ag-ligand bond (e.g., Ag-C with CO 2 ) does not require substantial energy (limited to 0.  (Table 1). The shortest Ce-O* distance in Ag2b is 268 pm. The CO 2 fragment in Ag2aV is more strongly distorted than in Ag2b: C-O bonds are 130 pm and the O-C-O angle is quite small, at 114 • . The Ag-CO 2 distance (207 pm) is typical for metal-CO 2 complexes with an η 1 -C type of CO 2 coordination [77]. Energies of Ag2b and Ag2aV models differ by 1.9 eV, the value close to the O vacancy formation energy at the O 4 -pocket ( Table 2).
The PdCO 2 -containing complexes, Pd2a and Pd2aV, with a "bent" CO 2 moiety (Figure 3) are characterised by substantial CO 2 binding energies of −1.2 and −0.7 eV, respectively (Table 1). Both models exhibit a carboxylate-like structure of CO 2 : C-O bonds are 124-130 pm long and the O-C-O angle is 130 ± 3 • . In the Pd2a structure, CO 2 is η 1 -coordinated to the Pd atom with the Pd-C distance, 206 pm, comparable to three Pd-O bonds around the metal center, 208-220 pm. In the Pd2aV complex, the CO 2 molecule is η 2 -coordinated to Pd via the short Pd-C bond, 193 pm, and long Pd-O contact of 237 pm; two other Pd-O bond lengths are 205-220 pm. The Pd atom in both Pd2a and Pd2aV complexes is nearly in a square-planar environment with Pd shifting from the ligand plane by 25-30 pm. Interestingly, no ceria-supported PdO 3 structures with calculated CO 2 binding energies more than −0.4 eV (by module) were found in the literature [8,9,20] Thus, similar to the CO case, the strongest bonding is calculated for the PdO 3 site with one vacant coordination place. This is followed by the PdO 2 unit with two vacant valences, which binds CO 2 in a side-on fashion. Both structures are characterised by CO 2 bending.
The adsorption of CO 2 in linear mode results in an energy gain less than 0.2 eV for both Pd and Ag derivatives. In contrast to the Pd derivatives, both "linear" and "bent" modes have similar small adsorption energies for the Ag systems. Thus, AgO 3 and AgO 2 sites again do not show differences in adsorption properties, whereas their Pd analogs do.

Carbonate Species
Carbonate species are formed upon the coordination of the CO 2 molecule via the C atom to an O center of ceria NP. Thus, CO 3 2− formation can be considered as a form of CO 2 adsorption, and CO 2 binding energy can be applied to the estimation of the stability of these carbonate species.
The carbonate-like CO 2 adsorption at bare ceria NPs with binding energies of 0.84-2.22 eV (Table 1) is the most exothermic of all types of CO 2 coordination discussed above. The strongest binding of 2.22 eV is calculated for the tridentate 2.2.2-structure (3aV, Figure 2 (Table 1). In both 3a and 3bV models, the CO 3 moiety is tied by three O-Ce bonds at 227, 238, and 245 pm. The three O-C bond lengths are different and increase from 122 to 133 and to 137 pm with the growing coordination number of O atom from 0 to 1 and to 2, respectively. Notably, at the O-deficient ceria, the flat-lying structure 3aV is preferred over the standing one 3bV by 0.7 eV. A similar difference of 0.84 eV was calculated for CO 3 moieties oriented parallel and perpendicular to the O-defective CeO 2 (100) facet [71]. The trend of destabilising carbonate species at ceria substrates upon surface enrichment by O atoms [71] is also supported by the present data.
Three types of carbonate structures-standing (perpendicular), tilted and flat-lying (parallel)-were also located for metal-containing ceria NPs (Figures 3 and 4). The "standing"-type carbonate species is coordinated in a bidentate way in 1.30-models Pd3c, Pd3bV, Ag3b, and Ag3bV. These structures are very similar to 1.20-carbonates 3a and 3bV at bare ceria NPs, with the difference that the CO 3 moiety is additionally bound with the M center via one short M-O bond of 211 pm (233 pm in Ag3b). This extra metal-oxygen bond induces the elongation of other three O-Ce contacts by 5-15 pm as well as elongates O· · · CO 2 contact by 4-9 pm, which probably weakens CO 2 binding from −1.15-1.52 eV in metal-free models to −0.86-1.13 and −0.39-0.50 eV in Ag-and Pd-carbonates, respectively (Table 1). Thus, for Pd-systems, carbonate-like CO 2 adsorption in a "standing" mode is weaker than adsorption in carboxylate PdCO 2 form. Notably, Pd is in a zero-oxidation state in both types of complexes.
Stronger CO 2 bindings, of −1.44 and −1.40 eV, were calculated for the "flat-lying" structures 2.2.1-Pd3a and 2.2.2.-Ag3aV, respectively ( Table 1). The CO 3 fragment is bidentately coordinated with two M-O contacts: almost equal in Pd3a (207 and 211 pm) and asymmetric in Ag3aV (216 and 265 pm). In the Pd3a structure, all O atoms of the CO 3 moiety leave their lattice positions to form short Pd-O bonds (Figure 3). This leads to the creation of a CO 3 2− unit with a formal charge of −2 and oxidation of Pd to the +2 oxidation state. Even shorter M-O bonds are formed between metal centres and O atoms of the ceria support: 201-202 pm for Pd-O and 206 pm for Ag-O bonds. Thus, the Pd atom is four-coordinated whereas Ag is three-coordinated by O ligands. Importantly, the PdO 4 unit in Pd3a is in a slightly distorted stable square-planar configuration. Likely, this contributes greatly to making Pd3a the most energetically favourable among all studied ceria-supported PdCO x species. The Pd3a complex is even 0.25 eV more stable than another square-planar structure: carboxylate Pd2a complex with O 3 PdCO 2 unit. The plane of the CO 3 subsystem forms a small angle of about 20 • with the O 3 M plane. The "lying" Ag3aV structure is only 0.27 eV stabilised with respect to "standing" Ag3bV, whereas the analogous stabilisation for Pd3a → Pd3c transition reaches 0.87 eV. The Ag3a 1.21-complex with the "tilted" coordination mode of CO 3 is the most favourable Ag-carbonate structure with a CO 2 adsorption energy of −1.49 eV (Table 1). Similar to the 1.30-model Ag3b, the CO 2 moiety in the Ag3a structure is tied in an η-C,O fashion with ceria support by means of two bonds. While the distance O-C-O· · · Ce is the same in Ag3a and Ag3b, the O· · · CO 2 contact in Ag3a is shortened to 135 pm from 141-146 pm in Ag3b. The shorter Ag-O contact of 221 pm (vs. 233 pm in Ag3b) is formed with the O atom, which has no bonds with CeO 2 ; this is comparable to the Ag-O bond length of 218 pm with ceria. Remarkably, "tilted" 1.21-complex Ag3a is by 0.63 eV stabilised with respect to "standing" 1.30-model Ag3b with an E(CO 2 ) of −0.86 eV and reaches a CO 2 adsorption energy of −1.52 eV of the metal-free "standing" 3bV model. 1.21-Ag3a complex has a nearly identical CO 2 adsorption energy (within 0.1 eV) to the "lying" 2.2.2-Ag3aV model. In both complexes, the cationic Ag + center is three-coordinated. Despite the closer contact of the CO 3 unit with ceria support in the 2.2.2-model, its formation from the Ag3a structure by the removal of O bound to the Ag atom requires a substantial energy of 2.18 eV. In contrast, O deletion from 1.21-Pd3b to give 2.2.1-Pd3aV is endothermic by only 1.55 eV. Both "tilted" complexes, Pd3b and Pd3aV, have CO 2 adsorption energies of −0.75 and −1.06 eV, respectively, bracketing the value for the "tilted" metal-free 3b complex. Note that the Pd3b → Pd3aV transition is associated with the reduction of the Pd centre from Pd + to Pd 0 .
In summary, carbonate CO 3 2− species show coordination patterns different from CO and CO 2 moieties: they tie to the ceria support or metal centres via O atoms, whereas the C atom does not participate in adsorbate-substrate interaction. From the comparison of CO 2 binding energies at the metal-free and M-containing sites, it follows that CO 2 binds slightly more strongly in MCO 3 /NP[0/2] structures than in CO 3 /NP[0/2]. Conversely, the creation of an extra O vacancy stronger stabilises the formation of the carbonates at metal-free NPs than that at metal-containing NPs.

Reaction Energies
In this section, we consider the energies of CO to CO 2 oxidation, E* ox , and of CO 2 to CO 3 transformation, E* CO3 , along with the corresponding activation barriers, E = , calculated for Pd/NP and Ag/NP models in comparison with the bare NP model. Data in Table 2 show that i) all these reactions are exothermic and ii) activation barriers for the carbonate formation are often higher than for the oxidation of CO.
Bare NPs adsorb CO very weakly, by less than 0.3 eV (Table 1, Figure 2). The extraction of lattice O and the formation of ceria-supported CO 2 yield energies of 0.9-1.4 eV and require 0.8-1.0 eV of activation ( Table 2). Because of the low CO 2 desorption barriers, 0.15-0.25 eV (Table 1, E des (CO 2 ) = −E b (CO 2 ) for 2a and 2aV), the formed CO 2 /Ce 21 O 42 and CO 2 /Ce 21 O 41 complexes can quite easily decompose. Otherwise, they are expected to exothermically transform into carbonates with activation barriers ranging from low-0.27 eV (for CO 2 /NP[0/1])-to moderate-0.82 eV (for CO 2 /NP[1/1])-values. The thermodynamic stability of such surface carbonate complexes makes them most probable candidates for experimental detection [68].
CO binds very weakly at the defect-free PdO 4 site of the Pd/NP[0/0] complex with an adsorption energy of −0.1 eV (Pd1b in Table 1). CO 2 can form via the interaction of the adsorbed CO with a lattice O atom. The process, which is exothermic by 1.3 eV, requires the overcoming of a barrier of 0.5 eV ( Table 2). The formed CO 2 molecule is quite strongly bound, with a desorption energy of 1.2 eV (Table 1, E des (CO 2 ) = −E b (CO 2 ) for Pd2a).
Overcoming an even higher barrier of 1.8 eV ( Table 2) is needed to extract one more lattice O centre and activate the transformation of CO 2 to CO 3 2− , which is exothermic by only 0.25 eV. CO is strongly, by 1.7 eV, adsorbed at the O-deficient PdO 3 site (Pd1aV in Table 1). The formed stable O 3 PdCO species can transform to O 2 PdCO 2 with an activation barrier of 1.1 eV and moderate reaction exothermicity of 0.6 eV ( Table 2). Slightly exothermic by 0.3 eV, the formation of carbonate is hindered by a high energy barrier of 1.8 eV. A much lower energy barrier of 0.7 eV (−E b (CO 2 ) for Pd2aV in Table 1) is required to desorb the CO 2 molecule into the gas phase. Thus, the most likely ceria-supported Pd-intermediates to be detected in reaction medium are saturated square-planar O 3 PdCO/NP (Pd1aV) and O 3 PdCO 2 /NP (Pd2a) complexes whose formation proceeds with a sizable energy release (1.3-1.7 eV) and moderate activation barriers of 0.5 eV and whose decomposition is hindered by substantial barriers of about 1.1-1.2 eV.
The reactivity of Ag-containing systems is different (Table 2). CO adsorption on defectfree and O-deficient Ag/NP systems occurs with a moderate energy gain of 0.8 eV ( Table 1) (Table 2). Despite the high exothermicity of 1.2-1.5 eV, the transformation to carbonates is hindered by barriers of~0.8-1.7 eV. Alternatively, the decomposition with CO 2 desorption should proceed quite readily (see −E b (CO 2 ) values for Ag2b and Ag2aV in Table 1). Thus, the carbonyl complexes O 4 AgCO/NP (Ag1a) and O 3 AgCO (Ag1aV), which are easily formed with notable energy gains, are expected to be detectable in a reaction medium. The detection of carboxylate AgCO 2 /NP (Ag2b and Ag2aV) complexes seems problematic due to their instability with respect to CO 2 desorption.
We estimated the propensity of CO to CO 2 transformation by the energy of the CO(gas) + M/NP[n/0] → CO 2 (gas) + M/NP[n/1] oxidation reaction, E ox (Equations (5) and (6)). It is directly connected with the ease of O release from the ceria lattice and O vacancy creation ( Table 2).
Let us compare the oxidation reaction energy E ox calculated for the O 4 -site of CeO 2 NP with the calculated energies for clean ceria surfaces [65,71,74,79,80] and the Pd 1 -ceria interfaces [8,9,20]. This reaction was found to be slightly, by 0.4-0.6 eV, exothermic on bare CeO 2 (111) [74,79] and notably more exothermic on CeO 2 (110) [65,74,78,79], at 1.1-1.8 eV. The calculated reaction exothermicity further drastically increases to 3.1 eV for the CeO 2 (100) surface with the most exposed O atoms [71]. Our calculated E ox energies for the stoichiometric and O-deficient NP{100} sites, −1.44 and −1.01 eV, respectively (Table 2), are considerably lower than those for the CeO 2 (100) surface, but in a similar range to that for CeO 2 (110) (assuming that the E ox value should increase by ca. 0.5 eV when the U value is increased from 4 to 5 eV [62]).
At the Pd 1 /CeO 2 (100) and O 1 Pd 1 /CeO 2 (100) sites, the conversion of CO to CO 2 was characterised by energy yields of 0.6 and 1.2 eV [9], respectively-markedly lower than at the pristine CeO 2 (100) surface. The reaction is also moderately exothermic at the Pd 1 /CeO 2 (110) interface, by 1.2 eV [20], and highly exothermic at the isolated O 1 Table 2). Note that the reactivity in CO oxidation of both Ag/NP complexes-with and without an O vacancy near the Ag atomis similar. Conversely, the presence of an O vacancy in the vicinity of Pd atom is mandatory for CO oxidation at Pd/NP systems to proceed. This makes two consequent steps of CO oxidation at the Pd/Ce 21 O 42 nanoparticle problematic. Such characteristics of the studied models as moderately strong CO adsorption, exothermic overall CO oxidation process, sufficiently low barriers of MCO to MCO 2 transformations, and ease of CO 2 desorption render CO oxidation by lattice ceria oxygen atoms more favourable at the sites with Ag than with Pd. Comparing the reaction and activation energies of CO to CO 2 and CO 2 to CO 3 conversions for M-containing ceria NPs, we conclude that the most probable species to be observed experimentally are AgCO and PdCO carbonyls and carboxylate PdCO 2 species. Unlike purely ceria nanoparticles, the formation of silver and palladium carbonates is prohibited by high activation barriers. We note, however, that for precise information on the species present in the reaction medium at equilibrium, a microkinetic modelling is required, which is out of the scope of the present study.
Our modelling revealed that the CO stretching frequency, ν(CO), for the molecule attached to a cerium ion in M-free systems 1a and 1aV and Pd-containing model Pd1a shifts by 27-34 cm −1 to the short-wave region, which agrees with the measured blue shifts of 27-32 cm −1 (vs. 2143 cm −1 for free molecule [85]) for CO interacting with the Ce 4+ centres of the nanostructured CeO 2 [19,86]. Note that the quantitatively precise reproduction of measured vibrational frequencies of CO on ceria requires going beyond the U-corrected generalised-gradient exchange-correlation functionals to hybrid-type functionals [81]. In contrast, ν(CO) for the fragments with M 1 -CO bonding formed on M/NP[n/0] substrates shows redshifts of 50-113 cm −1 , consistent with the C-O bond elongation by 1-2 pm. Among the models containing Pd 1 species, the Pd1b complex with Pd 2+ cation coordinated by four two-coordinated O anions reveals a medium redshift of 84 cm −1 , and the maximum redshifts of 109-113 cm −1 are identified for the other two complexes, Pd1c and Pd1aV, with three-fold coordinated Pd + and Pd 2+ cations (Table 3). For the earlier examined systems with Pd-CO bonds, the redshifts ∆ν(CO) were calculated to increase from 6 to 96 cm −1 in the order O 2 Pd 1 /CeO 2 (111) < O 1 Pd 1 /CeO 2 (100) ≈ O 1 Pd 1 /CeO 2 (111) < Pd 1 /CeO 2 (100) < Pd 1 /CeO 2 (111) [8,9]. These values are comparable with those attributed to the CO molecule contacting one Pd atom in experimental studies of Pd/CeO 2 , 13-123 cm −1 [7,28] and 10-69 cm −1 [9,16,25] and PdO/CeO 2 , 58 cm −1 [26]. Note that the ∆ν(CO) redshifts for CO coordinated to the supported Pd cations are opposite to the blue shift for the free PdCO + ion, measured at 63 cm −1 and calculated at 75 cm −1 (B3LYP), but approach a redshift for the neutral PdCO molecule, measured at 87 cm −1 and calculated at 99 cm −1 [70]. The redshifts of ν(CO) for Ag1a and Ag1aV complexes, at 50 and 61 cm −1 , respectively, are smaller than those for the Pd 1 -CO moieties and correspond to about one-third of the calculated redshift for the AgCO molecule, 144 cm −1 [87]. Similarly large frequency redshifts to those obtained for CO on single Ag and Pd cations on a ceria NP were calculated for CO adsorbed on Pt + and Pd 2+ cations anchored to ceria [83]. Table 3. Calculated vibrational frequencies ν(CO), ν(CO 2 ) and ν(CO 3 ) for the systems depicted in Figures 2-4 along with the corresponding frequency shifts ∆ν(CO) and ∆ν(CO 2 ) with respect to calculated vibrational frequencies of free molecules CO (ν(free CO) = 2131 cm −1 ) and CO 2 (ν asym (free CO 2 ) = 2363 cm −1 ). The highest frequencies of CO 2 stretching vibrations in 2a, 2aV, Ag2a, Ag2bV, Pd2b, and Pd2bV complexes with a linear CO 2 moiety are close to that of the IR active CO 2 asymmetric stretching frequency of the free molecule; the negative shift ∆ν(CO 2 ) does not exceed 40 cm −1 ( Table 3). The redshift ∆ν(CO 2 ) for a bent CO 2 fragment in 2bV, 706 cm −1 , is comparable to the experimental value for the free anion CO 2 − , 691 cm −1 [88] (vs. measured ν(CO 2 ) of free molecule 2349 cm −1 [76]) and CO 2 − species at TiO 2 surface, 709 cm −1 [89]. The redshift ∆ν(CO 2 ) for the MCO 2 /NP[n/1] systems having the M-C bond from 413 to 1031 cm −1 is associated with the bending of the CO 2 moiety and C-O bond elongation by 3 to 14 pm. The redshifts for PdCO 2 /NP systems, 828 cm −1 (Pd2a) and 735 cm −1 (Pd2aV), are in the range of values 610-850 cm −1 reported for coordination compounds with CO 2 attached to a single d-metal atom [76], while redshift ∆ν(CO 2 ) in Ag2b is smaller, at only 413 cm −1 . ∆ν(CO 2 ) for the CO 2 2− group in Ag2aV with CO bonds elongated by 14 pm compared to those of free CO 2 matches the measured redshifts of 1020-1079 cm −1 for carbonite ions at CeO 2 [90] and in Cs 2 CO 2 [91]. Thus, the increased redshift ∆ν(CO 2 ) seems to correlate with C-O bond elongation, Ag2b < Pd2aV < Pd2a < Ag2aV (Table 1).
Differences in the length of the intramolecular C-O bonds are considered among the main factors determining the frequency splitting of CO 3 2− stretching vibrations [68]. In tridentate CO 3 [68]. With the inclusion of ν 1 values for tridentate structures 3b and 3aV, this range extends to 1400 cm −1 . The calculated ν 1 for tridentate carbonates corresponds to a broad experimental region of 1620-1450 cm −1 attributed to the high-frequency vibrations of the carbonate groups formed on surfaces with oxygen vacancies, as well as on facet, edge, and corner sites of ceria particles [68]. The ν 1 frequencies for tridentate carbonate Ag3a, Pd3a, Pd3b, Ag3aV, and Pd3aV complexes, of 1573-1434 cm −1 , fall between the limits of the clean surface of the nanostructured ceria. The ν 1 values for 1.20-carbonate groups in 3a and 3bV systems are in a narrow range of 1718-1698 cm −1 for bidentate carbonates [68] corresponding to the measured frequency interval of 1732-1722 cm −1 [68]. The ν 1 frequencies of the M-containing 1.30-complexes Pd3c, Pd3bV, Ag3b, and Ag3bV are in a broader range of 1752-1689 cm −1 , which includes the interval for bidentate CO 3 2− on M-free ceria substrates. The calculated ν 2 frequency range of the complexes on the clean ceria surface is 1353-1227 cm −1 . This corresponds to the experimental frequencies of 1380 and 1280 cm −1 [68]. The ν 2 values for tridentate 1.21-and 2.2.1-carbonates P3b, Pd3aV, Ag3a, and Ag3aV for M-containing systems, at 1340-1220 cm −1 , are between these limits, and that for the 1.11-Pd3a isomer is only 6 cm −1 below the low-end threshold. The ν 2 frequencies are distributed between 1194 and 1082 cm −1 for bidentate carbonates depicted in Figure 2 and those examined in [68]; the related experimental values are 1147-1133 cm −1 [68].
The range of ν 2 for the CO 3 moieties coordinated in a bidentate way at M/NP systems is 1170-1120 cm −1 . Thus, the frequency ranges are similar for the metal-free CO 3 /NP and MCO 3 /NP sites, making the discrimination between the metal-containing and bare ceria particles solely on the basis of the vibrational spectroscopy data problematic.
In summary, our calculations show that the C-O stretching vibrations of the ceriasupported PdCO and AgCO fragments feature redshifts up to~110 cm −1 , which is at variance with the blue shift at metal-free ceria. Redshifts of CO 2 asymmetric stretching frequency of the M-CO 2 fragments are much higher, up to~830 cm −1 for carboxy-late MCO 2 and further increasing by~200 cm −1 for carbonite AgCO 2 . The two highest ν(CO 3 ) stretching frequencies of M-CO 3 structures lie in intervals 1755-1690 cm −1 and 1170-1120 cm −1 for the CO 3 moiety coordinated in a bidentate fashion and 1575-1430 cm −1 and 1340-1220 cm −1 for the CO 3 in the tridentate coordination.

Conclusions
CO x intermediates formed upon CO adsorption and oxidation on single M = Pd and Ag atoms coordinated to the O 4 -site on the {100} facet of a Ce 21 O 42 nanoparticle have been studied computationally. Equilibrium structures, CO x vibrational frequencies, and energetic parameters of various MCO x -containing complexes have been determined. The influence of the creation of an O vacancy nearby the M atom has been also investigated. The stability of the CO x moieties anchored to the ceria-supported M atom is found to increase in the order MCO < MCO 2 < MCO 3 , similar to the trend for CO x species adsorbed on M-free ceria NP.
Except for the Pd atom saturated by four O atoms of the ceria surface O 4 -site, which is unable to properly adsorb CO, the doping of the ceria nanoparticle with Pd and Ag atom increases its propensity to bind the CO molecule with respect to bare ceria material. In particular, the CO adsorption energy value reaches −1.7 eV for a PdCO unit on a ceria nanoparticle with a nearby O vacancy. CO binding in AgCO complexes, regardless of the presence or absence of a nearby O vacancy, is moderately strong, at −0.8 eV. All these species are the most probable candidates to be detected experimentally, also due to the presence of moderate barriers for CO oxidation (0.5-1.0 eV). In contrast to the blue shift for CO adsorbed on pristine ceria, red shifts of the C-O stretching (vs. free CO) have been calculated for MCO species anchored to ceria. The red shifts of the CO stretching frequency are higher for complexes of Pd and increase with the decreasing coordination of M from MO 4 to MO 3 for a particular metal: Ag/Ce 21  Carboxylate CO 2 − and carbonite CO 2 2− (for Ag-doped NP with an O vacancy) complexes featuring a bent CO 2 moiety are formed upon CO oxidation at the M/ceria interface. Contrary to AgCO 2 -species, which are easily decomposed via CO 2 detachment, PdCO 2 moieties are prone to withstand decomposition due to significant CO 2 desorption energies of 0.7-1.2 eV. These PdCO 2 moieties anchored to ceria particles could be experimentally detected by the red shifts of the CO 2 asymmetric stretching frequency (vs. that of free CO 2 molecule) by 828 cm −1 (one O vacancy nearby Pd) and 735 cm −1 (two O vacancies nearby Pd).
Unlike pristine ceria, carbonate structures at ceria-supported Pd and Ag atoms are hardly formed before CO 2 desorption due to the high barriers of CO 2 transformation to CO 3 2− (up to 1.8 eV for PdCO 3 moieties) and weak CO 2 binding (below~0.2 eV for AgCO 3 moieties). Detailed analysis of the vibrational spectra of MCO 3 /NP complexes has shown that the two highest ν(CO 3 ) stretching frequencies lie in the well-resolved intervals 1755-1690 and 1170-1120 cm −1 for the CO 3 moiety coordinated in a bidentate fashion and 1575-1430 and 1340-1220 cm −1 for the carbonate groups in the tridentate coordination. These frequency ranges are similar to those for the M-free CO 3 /NP sites. Thus, discrimination between the M-containing and bare ceria particles solely using vibrational spectroscopy data seems hardly possible.
In summary, such characteristics of the studied models as moderately strong CO adsorption, an exothermic CO oxidation process, sufficiently low barriers of MCO to MCO 2 transformations, and ease of CO 2 desorption render CO oxidation by lattice ceria oxygen atoms more favourable at the sites with Ag than with Pd.