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

Abstract

Various CO_x 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 MCO_x moieties are found to be stabilised in the order MCO < MCO₂ < MCO₃, similar to the trend for CO_x 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 CO_x 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.

1. Introduction

Ceria, as a component of catalysts containing transition metals (M) Pd or Ag, is used in numerous applications ranging from the abatement of soot, volatile organic compounds, and CO [1,2,3,4,5,6,7,8,9,10] to the production of syngas [11] and CO₂ activation [12,13]. As an active reducible support, ceria facilitates the dispersion of metals and MO_x phases on the surface [7,14,15,16,17] and provides lattice O atoms to oxidise reactants [2,9,17,18,19,20]. For instance, the interactions within Pd–ceria interfaces allow the synergistic oxidation/reduction of both subsystems [21], promote the oxidation of CO by lattice O atoms, and the oxidation of the reduced ceria by O atoms of CO₂ [22]. Supported transition metals can also enhance the redox performance and oxygen storage capacity of ceria [23]. Often, high catalytic efficiency is achieved using a nanostructured ceria support via enhanced metal–support interaction, which improves the dispersion of metal particles and suppresses their sintering at elevated temperatures [3,4,7,8,9,11,19,24,25,26,27].

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_xCe_1−xO_2−δ solutions [25,26,27,32,33,34,35], and dispersed M₁ or O_xM₁ ad-species [3,6,7,8,9,16,36,37]. Analysis of the crystalline environment of the Pd₁ ad-species revealed that each Pd²⁺ ion in Pd/CeO₂ catalysts prepared by the solution combustion method is coordinated, on average, by three O atoms [34]. This coordination mode of Pd₁ is a feature of adsorption complexes with CO such as O₂Pd₁-CO/CeO₂(111) [8], O₁Pd₁-CO/CeO₂(111) [8], and O₁Pd₁-CO/CeO₂(100) [9], while a Pd₁-CO/CeO₂(100) complex exhibits an O-Pd-O bridge [9]. In many cases, Pd₁ is in a square-planar environment. Pd₁ centres in Ce_1−xPd_xO_2−δ crystals (x ≤ 0.15) reside on O₄ 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 O₄ unit [23]. Furthermore, Pd₁ species are attached to the O₄ unit of the Pd_xCe_1−xO_2−x−δ lattice incorporating products of water dissociation [27]. Replacing every second upper-layer Ce⁴⁺ cation and one adjacent to it O²⁻ anion on the CeO₂(110) surface with Pd²⁺ leads to a complex reconstruction and a low-energy surface geometry, with the dopant ion residing close to the centre of the square-planar O₄ site [6]. Stable structures with square-planar O₄Pd are also communicated on Pd-doped CeO₂(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 O₄Pd structures on the CeO₂(110) surface [20] and {100} nanofacets [37]. The surface O₄ sites are also capable of suppressing the sintering of Ag₁ species, despite the fact that the Ag atom binds to the {100}-O₄ 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 CeO₂. For the ceria-supported metal catalysts of CO oxidation or CO₂ activation, of primary interest are the interactions of O₂, CO, and CO₂ 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 M₁-O₂, M₁-CO, and M₁-CO₂ entities on ceria [8,9,18,20,40]. The adsorption of CO on a single Pd atom embedded in the defect-free CeO₂(111) surface and that containing O vacancies followed by NO reduction with CO was explored [18,40]. Surface complexes of CO and CO₂ taking part in the catalytic cycle of CO oxidation on Pd₁/CeO₂(110), including Pd₁-CO, Pd₁-CO₂, O₁Pd₁-CO species on the stoichiometric CeO₂(110) surface and Pd₁-CO₂, Pd₁-O₂, O₂-Pd₁-CO ones on the O-deficient CeO₂(110) surface, were calculated [20]. The CO oxidation routes passing via O₁Pd₁-CO, Pd₁-CO, Pd₁-CO₂, O₂Pd₁-CO, and O₁Pd₁-CO₂ moieties on the defect-free CeO₂(111) surface [8] as well as on regular and O-deficient CeO₂(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 M₁-CO₂ structures, surface carbonate complexes can be formed on M₁–ceria interfaces before the desorption of CO₂. To this end, the formation of tridentate Pd₁-CO₃ carbonates upon CO₂ adsorption at the interface of Pd₁ and O-deficient CeO₂(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 Pd₁CO_x–ceria systems outlined above, no simulations of analogous Ag₁CO_x–ceria systems have been communicated so far to the best of our knowledge.

Previous studies have developed structural models of low-energy CeO₂ 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 Ce₂₁O₄₂ 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, CO₂, and CO₃²⁻ moieties resulting from the interaction of CO with Pd and Ag single atoms anchored to the O₄-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 M₁ centres, (iii) evaluate and rationalise the reactivity differences of Pd₁/NP{100} and Ag₁/NP{100} sites as active centres for CO oxidation (including the effect of M-atom on the formation of CO₃²⁻ prior to CO₂ 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.

2. Models and Details of Calculations

Surface sites of the CeO₂ substrate were represented by a putative global-minimum structure of stoichiometric NP Ce₂₁O₄₂ [46,47] exposing four O atoms on its top {100} nanofacet (a so-called O₄-pocket [49]); see Figure 1a. M₁/Ce₂₁O₄₂ models were created via anchoring a single M₁ atom (M = Pd or Ag) to the O₄-site of the NP; see Figure 1b,c. The removal of one O atom from the O₄-pocket results in an O-deficient M₁/Ce₂₁O₄₁ model with one O vacancy in ceria (not shown in Figures; see Supplementary Material for xyz-structures). CO adsorption does not change the number of O vacancies, whereas the oxidation of CO to CO₂ and further transformation to CO₃²⁻ require the expulsion of one or two O atoms from ceria, generating O vacancies. In the following, the number and origin of O vacancies in the NP Ce₂₁O₄₂ are labelled as NP[n/l], where n is a number of O vacancies present prior to CO adsorption (n = 0, 1) and l is a number of O vacancies created by the transfer of O atoms from ceria to the adsorbed CO to form CO₂ or CO₃²⁻ moieties (l = 0, 1, 2). For instance, the stoichiometric and O-deficient NP models M₁/Ce₂₁O₄₂ and M₁/Ce₂₁O₄₁ are referred to as M/NP[0/0] and M/NP[1/0], respectively.

The Vienna ab initio simulation package (VASP) [52,53] was employed to determine equilibrium structures of various isomers of the MCO_x/NP[n/x − 1] complexes formed by the interaction of a CO molecule with Pd/NP[n/0] and Ag/NP[n/0] sites and transition state structures connecting selected equilibrium structures. The plane-wave basis with a 415 eV cutoff for the kinetic energy was used along with the projector-augmented wave description of the interactions of valence electrons (2s²2p⁴ for O, 4s¹4d⁹ for Pd, 5s¹4d¹⁰ for Ag and 5s²5p⁶6s²5d¹4f¹ for Ce) with the atomic cores [54,55]. The NP models were separated by a vacuum space of ~1 nm in the three Cartesian directions (typical cell dimensions 2 × 2 × 2 nm³) sufficient to eliminate the interaction between periodically repeated NP images [56,57]. All calculations were performed at the Γ-point of the reciprocal space. A generalised-gradient corrected (GGA) exchange-correlated functional PW91 [58] was utilised with the Hubbard-type on-site corrections U [59,60] for Ce4f states providing an improved description of Ce³⁺ ion formation in redox transitions [61,62]. The value of U = 4 eV (PW91 + U = 4 setup) were used in line with previous studies [45,48,61,63,64], though the usage of even such small U values may overestimate the formation energy of carbonates [62,65]. The minimum energy reaction paths MCO/NP[n/0] → MCO₂/NP[n/1] → MCO₃/NP[n/2] were represented with the points of the string method, and the transition states were approximated with polynomial splines [66,67].

Stabilities of the studied systems were quantified based on their formation energies E^f:

$$E^f=E\left(MC{O}_x/NP\left[0/x-1\right]\right)-E\left(CO\right)-E\left(M\right)-E\left(NP\left[0/0\right]\right)$$

(1)

for the MCO_x/NP models obtained from defect-free MCO/Ce₂₁O₄₂ structure and

$$E^f=E\left(MC{O}_x/NP\left[1/x-1\right]\right)-E\left(CO\right)-E\left(M\right)-E\left(NP\left[0/0\right]\right)+0.5\times E\left(O_2\right)$$

(2)

for the MCO_x/NP models obtained from O-deficient MCO/Ce₂₁O₄₁ structure, where E(O₂) is total energy of a free O₂ molecule. The binding energies E_b of CO and CO₂ molecules in the models under scrutiny were calculated as follows:

$$E_b\left(CO\right)=E\left(MC{O}_x/NP\left[n/x-1\right]\right)-E\left(CO\right)-E\left(M/NP\left[n/0\right]\right),x=1–3;n=0,1$$

(3)

$$E_b\left(C{O}_2\right)=E\left(MC{O}_x/NP\left[n/x-1\right]\right)-E\left(C{O}_2\right)-E\left(M/NP\left[n/1\right]\right),x=2,3;n=0,1$$

(4)

The energies (3) and (4) of the same MCO₂/NP complex were used to estimate the energy of the overall oxidation process CO(gas) + M/NP[n/0] → CO₂(gas) + M/NP[n/1]:

$$E_{ox}=E_b\left(CO\right)\left(MC{O}_2/NP\left[n/1\right]\right)-E_b\left(C{O}_2\right)\left(MC{O}_2/NP\left[n/1\right]\right)$$

(5)

or

$$E_{ox}=E_b\left(CO\right)\left(MCO/NP\left[n/0\right]\right)+E_{CO2}^{*}-E_b\left(C{O}_2\right)\left(MC{O}_2/NP\left[n/1\right]\right),n=0,1$$

(6)

where E*_CO2 is the energy of CO to CO₂ oxidation at a metal site; i.e., the heat of MCO/NP[n/0] → MCO₂/NP[n/1] transformation:

$$E_{CO2}^{*}=E\left(MC{O}_2/NP\left[n/1\right]\right)-E\left(MCO/NP\left[n/0\right]\right)$$

(7)

where, the asterisk indicates that CO and CO₂ molecules are adsorbed.

Harmonic vibrational frequencies of CO_x groups were calculated by diagonalising the mass-weighted Hessian matrix constructed of differences of the first derivatives of total energy, obtained by displacements by ±0.015 Å in all Cartesian directions of the M, C, and O_x atoms as well as neighbouring ceria atoms within 3.6 Å around them.

3. Results and Discussion

Lowest-energy geometries and formation energies E^f of metal-free CO_x/NP[n/x − 1] and metal-containing MCO_x/NP[n/x − 1] complexes are shown in Figure 2, Figure 3 and Figure 4 (for xyz-structures see Supplementary Material).

Table 1. Calculated parameters of the surface complexes shown in Figure 2, Figure 3 and Figure 4, created by the interaction of CO with the pristine ceria Ce₂₁O_42−n and metal–ceria M/Ce₂₁O_42−n sites (M = Pd, Ag; n = 0, 1): interatomic distances—r, number of the Ce³⁺ ions—N, difference between the numbers of spin-up and spin-down electrons—m, binding energies of CO—E_b(CO) (Equation (3)) and CO₂–E_b(CO₂) (Equation (4)). Negative energy values correspond to exothermic processes.

System a	r(M-C)	r(M-O)	r(Ce-O) b	r(C-O) c	N	m	Eb(CO)	Eb(CO2)
	pm	pm	pm	pm			eV	eV
Complexes with CO
Pd1a	296 d	-	-	114	2	2	−0.26	-
Pd1b	241	-	-	115	2	2	−0.13	-
Pd1c	188	-	-	116	1	0	0.13	-
Pd1aV	187	-	-	116	4	4	−1.74	-
Ag1a	201	-	-	115	1	1	−0.80	-
Ag1aV	198	-	-	115	3	3	−0.78	-
1a	293 d	-	-	114	0	0	−0.26	-
1aV	297 d	-	-	114	2	2	−0.23	-
Complexes with CO2
Pd2a	206	-	247	2 × 127	2	0	−1.43	−1.20
Pd2b	-	-	314	2 × 118	2	0	−0.41	−0.18
Pd2aV	193	237	268	129; 124	4	4	−2.33	−0.72
Pd2bV	330	-	321	2 × 118	4	4	−1.77	−0.16
Ag2a	356	-	316	2 × 118	3	3	−1.37	−0.16
Ag2b	234	-	268	122; 121	3	1	−1.22	−0.01
Ag2aV	207	-	249	2 × 132	3	1	−1.13	−0.10
Ag2bV	342	-	348	2 × 118	5	1	−1.10	−0.07
2a	-	-	300	2 × 118	2	0	−1.69	−0.25
2aV	-	-	310	2 × 118	4	2	−1.16	−0.15
2bV	-	-	254	2 × 125	3	2	−0.42	0.59
Complexes with CO32−
Pd3a	249	207	260	2 × 133; 125	4	2	−1.68	−1.44
Pd3b	265	209	248	129; 135; 129	3	2	−0.99	−0.75
Pd3c	-	212	245	133; 143; 121	2	0	−0.74	−0.50
Pd3aV	275	211	258	132; 132; 128	4	2	−2.67	−1.06
Pd3bV	288	211	247	131; 143; 122	4	0	−2.28	−0.67
Ag3a	277	221	245	130; 135; 127	3	1	−2.72	−1.49
Ag3b	289	233	247	132; 141; 122	3	1	−2.09	−0.86
Ag3aV	273	216	265	130; 132; 130	5	1	−2.36	−1.40
Ag3bV	291	211	255	129; 146; 122	5	1	−2.09	−1.13
3a	-	-	237	133; 138; 122	2	0	−2.59	−1.15
3b	-	-	250	129; 132; 129	2	2	−2.28	−0.84
3aV	-	-	262	130; 131; 130	4	2	−3.23	−2.22
3bV	-	-	229	133; 137; 122	4	2	−2.53	−1.52

^a For notations, see Figure 2, Figure 3 and Figure 4; ^b Average distances of the O of CO_x moiety and nearest neighbour Ce atom; ^c Bond lengths within CO_x moiety; ^d Ce-C contact.

displays the parameters used to specify attachment modes (coordination) of the CO_x groups. Along with the notations MCO_x/NP[n/x − 1], shorter ones MxL and MxLV were used for complexes with n = 0 and n = 1, respectively, where L is a sequential identifier of the relative energy of a given isomer among isomers with the same M, x, and n (a—the most stable, b—the second most stable, c—the third most stable). Ce ions with magnetic moments close to 1, at a variance to 0 for most of the cations, were qualified as Ce³⁺ ions resulting from the reduction of Ce⁴⁺ by electrons of MCO_x moieties or O vacancies.

To specify the coordination modes of CO₂ in MCO₂/NP[n/1] and of CO₃²⁻ in MCO₃/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 CO₃²⁻ 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 CO₃²⁻ (corresponding to a and b or b and c, respectively) form a bidentate bond with one atom of the substrate. Dotless abc identifiers designate CO₃²⁻ groups with each O atom coordinated to a different substrate atom. When the three-digits notation is used to specify coordination of CO₂ in MCO₂/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 CO₂ in structure 111-Pd2a contacts different ions of the Pd/Ce₂₁O₄₁ subsystem, and in complex 1.21-Pd2aV, one of the O atoms of CO₂ attaches to Pd and Ce atoms of Pd/Ce₂₁O₄₀, and C atom also to Pd.

3.1. Structure, Charge State, and Relative Energies of Surface Complexes with CO_x

3.1.1. Adsorption Sites

The particle Ce₂₁O₄₂ exposes a {100} nanofacet (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 O₄-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]. The distances between the O₄-pocket atoms and the neighboring Ce atoms, 214–215 pm, are shortened versus the Ce-O distances of three-coordinated surface O atoms and four-coordinated inner O atoms, 230–250 pm.

The Ag atom binds by 2.27 eV to the O₄-site (Figure 1b), making the two diagonals of the latter almost equal. The two types of Ag-O bond lengths, 236 and 242 pm, agree with Ag-O distances of 239 and 241 pm calculated at the same theory level on a larger Ce₄₀O₈₀ NP [37]. Furthermore, the present location of the Ag atom 96 pm above the O₄-plane is close to the elevation by 90 pm on Ce₄₀O₈₀ [37]. A slightly larger above-plane elevation, by 102 pm, was calculated for a two-fold coordinated Ag single atom adsorbed on the Fe₃O₄(001) surface with energy 2.75 eV [69]. Ag atom adsorption moves O₄ 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 O₄ 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/Ce₄₀O₈₀ model [37]. The formation of PdO₄ species moves O atoms closer to Pd, contracting diagonals of the O₄ 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 O₄-site of larger ceria NPs [37]. Two Ce³⁺ ions appeared upon Pd adsorption, indicating the oxidation state Pd²⁺.

An O-deficient site is created by the removal of the weakest bonded O atom (with E(O_V) = 1.87 eV,

Table 2. Reaction and activation energies (E^≠) on the pristine ceria Ce₂₁O_42−n and metal–ceria M/Ce₂₁O_42−n models (M = Pd, Ag; n = 0, 1) depicted in Figure 2, Figure 3 and Figure 4. Oxygen vacancy formation energies E(O_V) are also shown. Negative energy values correspond to exothermic processes. All energies are in eV.

Model a		CO → CO2			CO2 → CO3
	E(OV)	Eox b	E*CO2 c	E≠	E*CO3 d	E≠
Ce21O42	1.87	−1.44	−1.43	1.02	−0.90	0.27
Ce21O41	2.31	−1.01	−0.92	0.82	−2.07	0.82
Ag/Ce21O42	2.08	−1.21	−0.52	0.88	−1.50	0.78
Ag/Ce21O41	2.28	−1.03	−0.35	0.53	−1.23	1.73
Pd/Ce21O42	3.08	−0.23	−1.30	0.51	−0.25	1.83
Pd/Ce21O41	1.70	−1.61	−0.59	1.06	−0.34	1.80

^a System on which initial CO adsorption takes place; ^b reaction energy of the CO oxidation CO(gas) + NP[n/0] → CO₂(gas) + NP[n/1] or CO(gas) + M/NP[n/0] → CO₂(gas) + M/NP[n/1]; ^c reaction energy of the CO₂ formation CO/NP[n/0] → CO₂/NP[n/1] or MCO/NP[n/0] → MCO₂/NP[n/1]; ^d reaction energy of CO₂/NP[n/1] → CO₃/NP[n/2] or MCO₂/NP[n/1] → MCO₃/NP[n/2] conversion.

) from the O₄-pocket of the Ce₂₁O₄₂ particle (Figure 1). Two Ce³⁺ centres resulting from the O removal in the second Ce layer cause the elongation of the Ce³⁺-O bonds by ~0.1 Å. O vacancy formation in the Ag/Ce₂₁O₄₂ model requires 2.08 eV (Table 2), nearly the same amount as for the metal-free O₄-site. Thus, an extra energy cost due to breaking the Ag-O bond (in addition to two Ce-O bonds of Ce₂₁O₄₂) is estimated at ~0.2 eV. Two Ag-O bonds are contracted to 2.15 Å upon O removal, whereas the third bond is elongated from 2.36 to 2.49 Å. A similar bonding situation has been found in our previous work, where an Ag single atom was anchored to the bottom {100} nanofacet of Ce₂₁O₄₂ NP [38]. Alternatively, the creation of an O-deficient Pd/Ce₂₁O₄₁ site requires substantial energy costs of 3.08 eV (Table 2).

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 PdO₄ site of Pd/Ce₂₁O₄₂. No reduction of Ag⁺ and Pd²⁺ ions occurs upon O vacancy creation, since the leaving O atom donates two electrons to two Ce⁴⁺ ions, increasing the number of Ce³⁺ centres by two (to three for Ag/NP and to four for Pd/NP).

Figure 2. Structures and formation energies E^f (in eV) of the complexes created by the interaction of CO with the Ce₂₁O_42−n sites (n = 0, 1): CO/Ce₂₁O₄₂ (1a), CO/Ce₂₁O₄₁ (1aV), CO₂/Ce₂₁O₄₁ (2a), CO₂/Ce₂₁O₄₀ (2aV, 2bV), CO₃/Ce₂₁O₄₀ (3a, 3b) and CO₃/Ce₂₁O₃₉ (3aV, 3bV). Activation energies (E^≠) of selected transition states are shown near the dashed arrows connecting corresponding initial reagent and product. The C atoms are shown in dark grey. O atoms numbered with “1”, “2”, and “3” enter CO, CO₂, and CO₃ moieties, respectively. For further explanations, refer to the main text and the Figure 1 caption.

Figure 2. Structures and formation energies E^f (in eV) of the complexes created by the interaction of CO with the Ce₂₁O_42−n sites (n = 0, 1): CO/Ce₂₁O₄₂ (1a), CO/Ce₂₁O₄₁ (1aV), CO₂/Ce₂₁O₄₁ (2a), CO₂/Ce₂₁O₄₀ (2aV, 2bV), CO₃/Ce₂₁O₄₀ (3a, 3b) and CO₃/Ce₂₁O₃₉ (3aV, 3bV). Activation energies (E^≠) of selected transition states are shown near the dashed arrows connecting corresponding initial reagent and product. The C atoms are shown in dark grey. O atoms numbered with “1”, “2”, and “3” enter CO, CO₂, and CO₃ moieties, respectively. For further explanations, refer to the main text and the Figure 1 caption.

3.1.2. 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 Ce⁴⁺ 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) was calculated for the Pd-containing Pd1a structure with the CO molecule bound to a Ce⁴⁺ ion (Figure 3), indicating that the filling of the O₄-pocket by the Pd atom mainly affects the local structure of the PdO₄ site.

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.

Figure 3. Structures and formation energies E^f (in eV) of the complexes created by the interaction of CO with the PdCe₂₁O_42−n sites (n = 0, 1): PdCO/Ce₂₁O₄₂ (Pd1a, Pd1b, Pd1c), PdCO/Ce₂₁O₄₁ (Pd1aV), PdCO₂/Ce₂₁O₄₁ (Pd2a, Pd2b), PdCO₂/Ce₂₁O₄₀ (Pd2aV, Pd2bV), PdCO₃/Ce₂₁O₄₀ (Pd3a, Pd3b, Pd3c) and PdCO₃/Ce₂₁O₃₉ (Pd3aV, Pd3bV). Activation energies (E^≠) of selected transition states are shown near the dashed arrows connecting corresponding initial reagent and product. For further explanations, refer to the main text and the captions to Figure 1 and Figure 2.

Figure 3. Structures and formation energies E^f (in eV) of the complexes created by the interaction of CO with the PdCe₂₁O_42−n sites (n = 0, 1): PdCO/Ce₂₁O₄₂ (Pd1a, Pd1b, Pd1c), PdCO/Ce₂₁O₄₁ (Pd1aV), PdCO₂/Ce₂₁O₄₁ (Pd2a, Pd2b), PdCO₂/Ce₂₁O₄₀ (Pd2aV, Pd2bV), PdCO₃/Ce₂₁O₄₀ (Pd3a, Pd3b, Pd3c) and PdCO₃/Ce₂₁O₃₉ (Pd3aV, Pd3bV). Activation energies (E^≠) of selected transition states are shown near the dashed arrows connecting corresponding initial reagent and product. For further explanations, refer to the main text and the captions to Figure 1 and Figure 2.

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, E_b(CO) < −0.2 eV was calculated for coordinatively saturated Pd atoms in PdO(100). Thus, a very low E_b(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 Pd²⁺ 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 Pd²⁺, except for Pd1c with an endothermic mode by 0.13 eV CO adsorption (Table 1), where a Ce³⁺ → Ce⁴⁺ 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 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) [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 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), E_b(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 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—AgO₄ or AgO₃—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 Ag₁/Fe₃O₄(001) site and −0.94 eV for the two-fold coordinated Ag atom at the AgO₂(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) coincides with the value computed for the Ag₁CO moiety at Fe₃O₄(001). The C-O bond, 115 pm, is 1 pm longer than that in the free CO molecule. The Ag-C-O angle of ~170° points to slight deviation from the typically favoured linear bonding geometry. In both structures, CO adsorption triggers a further displacement of Ag atom out-of-plane of neighbouring O atoms, reaching values of 132 and 152 pm for Ag1a and Ag1aV, respectively (vs. 96 and 60 pm for CO-free structures). Ag-O bond lengths vary substantially, ranging from 237 to 258 pm for the AgO₄ unit and from 224 to 264 pm for the AgO₃ unit. The notable distortions at the Ag/CeO₂ interface are not reflected in CO adsorption energies. This finding is in line with the quite weak Ag-O bonding estimated at 0.2 eV (see Section 3.1.1).

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 PdO₄ site is almost inactive towards CO adsorption, whereas the PdO₃ unit with a vacant coordination place readily traps CO with a substantial energy gain. In contrast, AgO₄ and AgO₃ centres with weak Ag-O bonds and a more flexible geometry are more prone to adsorb CO molecules with equally moderate energies.

3.1.3. Carbon Dioxide Species

For the metal-free ceria, only weakly adsorbed CO₂ 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 CO₂ at extended CeO₂(100), (110), and (111) surfaces [71,72,73,74,75,76]. In both complexes, the linear geometry of CO₂ as in the gas-phase molecule is preserved: C-O bond lengths are 118 pm and the O-C-O angle is 178°. The C atoms of CO₂ molecules are located above the O vacancy parallel to the surface of NP (Figure 2); in case of 2a, the O atom from the low-lying layer moves up and forms an O-C contact of 288 pm (vs. 390 pm in 2aV).

Figure 4. Structures and formation energies E^f (in eV) of the complexes created by the interaction of CO with the Ag/Ce₂₁O_42−n sites (n = 0, 1): AgCO/Ce₂₁O₄₂ (Ag1a), AgCO/Ce₂₁O₄₁ (Ag1aV), AgCO₂/Ce₂₁O₄₁ (Ag2a, Ag2b), AgCO₂/Ce₂₁O₄₀ (Ag2aV, 2bV), AgCO₃/Ce₂₁O₄₀ (Ag3a, Ag3b) and AgCO₃/Ce₂₁O₃₉ (Ag3aV, Ag3bV). Activation energies (E^≠) of selected transition states are shown near the dashed arrows connecting corresponding initial reagent and product. For further explanations, refer to the main text and the captions to Figure 1 and Figure 2.

Figure 4. Structures and formation energies E^f (in eV) of the complexes created by the interaction of CO with the Ag/Ce₂₁O_42−n sites (n = 0, 1): AgCO/Ce₂₁O₄₂ (Ag1a), AgCO/Ce₂₁O₄₁ (Ag1aV), AgCO₂/Ce₂₁O₄₁ (Ag2a, Ag2b), AgCO₂/Ce₂₁O₄₀ (Ag2aV, 2bV), AgCO₃/Ce₂₁O₄₀ (Ag3a, Ag3b) and AgCO₃/Ce₂₁O₃₉ (Ag3aV, Ag3bV). Activation energies (E^≠) of selected transition states are shown near the dashed arrows connecting corresponding initial reagent and product. For further explanations, refer to the main text and the captions to Figure 1 and Figure 2.

The contacts of O atoms of the CO₂ 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 CO₂ moiety have led to carbonate moieties (described in detail in Section 3.1.4). No minima corresponding to bent CO₂ structures of carboxylate type were found. The only located structure with distorted CO₂ (2bV at Figure 2) was found to be 0.75 eV less stable relative to the linear 2aV model. It features C-O bond lengths of 125 pm and an O-C-O angle of 131°. The O atoms of CO₂ are at 252 and 257 pm from Ce atoms. The positive CO₂ binding energy in 2bV of 0.6 eV (Table 1) indicates exothermic CO₂ release. Since only one Ce³⁺ ion is present after CO to CO₂ transformation, CO₂ in 2bV is negatively charged, forming a CO₂⁻ anion. Thus, CO₂ binds weakly and easily desorbs from bare Ce₂₁O_42−x NP.

The metal-containing Pd/NP and Ag/NP models also feature structures with “linear” and “bent” CO₂ (Figure 3 and Figure 4). Similar to the bare ceria, linear CO₂ is weakly bound in Pd2b, Pd2bV, Ag2a, and Ag2bV, by less than 0.2 eV (Table 1). All distances between atoms of CO₂ molecule and ceria are longer than 300 pm. In contrast, in “bent” CO₂ structures Pd2a, Pd2aV, Ag2b, and Ag2aV, CO₂ 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 CO₂) does not require substantial energy (limited to 0.2 eV). The bonds of CO₂ in Ag2b are symmetrically stretched to 121 pm and the O-C-O angle is reduced to 145°, thus indicating the formation of a weakly-bound carboxylate-like complex. CO₂ is coordinated to Ag via the C atom at a distance of 234 pm and forms an (O)C-Ag-O angle of 175° with the Ag-O bond in trans-position. The Ag atom in AgCO₂/Ce₂₁O₄₁ rises above the O₃-plane by 52 pm (vs. 132 pm in AgCO/Ce₂₁O₄₂), similar to O-deficient adsorbate-free Ag/Ce₂₁O₄₁ complex (60 pm). Thus, the surrounding of the Ag center in Ag2b is nearly square-planar. The formation of the CO₂ moiety in Ag2aV does not lead to the entire detachment of the surface O* atom by adsorbed CO (Figure 4). Rather, the Ag2aV model can be viewed as a complex with CO inserted into the O*-Ag bond; as a result, the O*-Ag distance is stretched from 227 to 287 pm. Upon this insertion, Ce-O* bonds of the Ce-O*-Ce bridge are elongated from 218–233 pm in Ag1aV to 249–257 pm in Ag2aV (Table 1). The shortest Ce-O* distance in Ag2b is 268 pm. The CO₂ 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-CO₂ distance (207 pm) is typical for metal–CO₂ complexes with an η¹-C type of CO₂ coordination [77]. Energies of Ag2b and Ag2aV models differ by 1.9 eV, the value close to the O vacancy formation energy at the O₄-pocket (Table 2).

The PdCO₂-containing complexes, Pd2a and Pd2aV, with a “bent” CO₂ moiety (Figure 3) are characterised by substantial CO₂ binding energies of −1.2 and −0.7 eV, respectively (Table 1). Both models exhibit a carboxylate-like structure of CO₂: C-O bonds are 124–130 pm long and the O-C-O angle is 130 ± 3°. In the Pd2a structure, CO₂ is η¹-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 CO₂ molecule is η²-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 PdO₃ structures with calculated CO₂ binding energies more than −0.4 eV (by module) were found in the literature [8,9,20]. The larger values −0.82 eV [20] and −0.96 eV [8] were calculated for PdO₂ units at CeO₂(110) and CeO₂(111) surfaces. In part, this can be explained by a favourable square-planar geometry within the O₃Pd-CO₂ fragment formed at the {100} nanofacet of Ce₂₁O₄₂ NP. Indeed, such structures are hindered at extended CeO₂ surfaces by geometrical constrains.

Thus, similar to the CO case, the strongest bonding is calculated for the PdO₃ site with one vacant coordination place. This is followed by the PdO₂ unit with two vacant valences, which binds CO₂ in a side-on fashion. Both structures are characterised by CO₂ bending. The adsorption of CO₂ 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, AgO₃ and AgO₂ sites again do not show differences in adsorption properties, whereas their Pd analogs do.

3.1.4. Carbonate Species

Carbonate species are formed upon the coordination of the CO₂ molecule via the C atom to an O center of ceria NP. Thus, CO₃²⁻ formation can be considered as a form of CO₂ adsorption, and CO₂ binding energy can be applied to the estimation of the stability of these carbonate species.

The carbonate-like CO₂ adsorption at bare ceria NPs with binding energies of 0.84–2.22 eV (Table 1) is the most exothermic of all types of CO₂ coordination discussed above. The strongest binding of 2.22 eV is calculated for the tridentate 2.2.2-structure (3aV, Figure 2), with each O atom of the CO₃ moiety coordinated to two Ce ions. The flat-lying carbonate fragment of 3aV fills two O vacancies with its oxygen atoms; i.e., all O atoms of the CO₃ moiety are in neighbouring O-positions of the O₄-pocket. The E_b(CO₂) energy for 3aV is between –1.9 and –2.3 eV, respectively, calculated for its formal 2.2.2-CO₃ analog on regular CeO₂(100) [78] and bidentate 220-CO₃ on O-deficient CeO₂(110) [74]. The 2.2.2-model features three C-O bonds equally stretched to 130 pm and O-C-O angles of 118 ± 2°. Three of four Ce³⁺ ions are located in the Ce₄ square just below the O₄-pocket of the {100} nanofacet. The other tridentate 1.21-structure 3b is stabilised by only 0.84 eV relative to the sum CO₂ + NP (Table 1). Here, each of the two O atoms of CO₂ has only one contact with Ce ions of 238 and 247 pm. As in the 3aV model, the CO₃ fragment in 3b has a slightly distorted C_3V symmetry, with C-O bonds of 130 ± 2 pm and O-C-O angles of 117–122°. Its CO₃ plane is tilted by 40° relative to the Ce₄ layer. The CO₂ binding energy in the 1.21-carbonate is comparable to value −0.72 eV calculated for the flat-lying 2.21-CO₃ structure [71] formed upon CO adsorption at the stoichiometric CeO₂(100) surface with every second atom of the O layer removed. The deletion of an O atom from 1.21-3b to give 2.2.2-3aV costs only 0.67 eV. Thus, energy for the removal of a lattice O atom (~2.3 eV for formation of a 2nd O vacancy) is compensated by the formation of two new O-Ce contacts in 3aV with ~1.6 eV energy gain. At variance, the energy difference between two 1.20-structures 3a → 3bV, with a bidentate coordination, 1.68 eV, does not decrease with respect to E(O_v) for Ce₂₁O₄₂ → Ce₂₁O₄₁ transition, since both models have a similar bonding pattern of carbonate species. Thus, not surprisingly, the CO₂ binding energies for 3a and 3bV models are not very different, at –1.15 and −1.52 eV, respectively (Table 1). In both 3a and 3bV models, the CO₃ 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 CO₃ moieties oriented parallel and perpendicular to the O-defective CeO₂ (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 (Figure 3 and Figure 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 CO₃ 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⋯CO₂ contact by 4–9 pm, which probably weakens CO₂ 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 CO₂ adsorption in a “standing” mode is weaker than adsorption in carboxylate PdCO₂ form. Notably, Pd is in a zero-oxidation state in both types of complexes.

Stronger CO₂ 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 CO₃ 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 CO₃ moiety leave their lattice positions to form short Pd-O bonds (Figure 3). This leads to the creation of a CO₃²⁻ 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 PdO₄ 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 O₃PdCO₂ unit. The plane of the CO₃ subsystem forms a small angle of about 20^° with the O₃M 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 CO₃ is the most favourable Ag-carbonate structure with a CO₂ adsorption energy of −1.49 eV (Table 1). Similar to the 1.30-model Ag3b, the CO₂ 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⋯CO₂ 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 CeO₂; 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(CO₂) of −0.86 eV and reaches a CO₂ adsorption energy of −1.52 eV of the metal-free “standing” 3bV model. 1.21-Ag3a complex has a nearly identical CO₂ 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 CO₃ 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 CO₂ 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 Pd⁰.

In summary, carbonate CO₃²⁻ species show coordination patterns different from CO and CO₂ 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 CO₂ binding energies at the metal-free and M-containing sites, it follows that CO₂ binds slightly more strongly in MCO₃/NP[0/2] structures than in CO₃/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.

3.2. Reaction Energies

In this section, we consider the energies of CO to CO₂ oxidation, E*_ox, and of CO₂ to CO₃ 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 CO₂ yield energies of 0.9–1.4 eV and require 0.8–1.0 eV of activation (Table 2). Because of the low CO₂ desorption barriers, 0.15–0.25 eV (Table 1, E_des(CO₂) = −E_b(CO₂) for 2a and 2aV), the formed CO₂/Ce₂₁O₄₂ and CO₂/Ce₂₁O₄₁ complexes can quite easily decompose. Otherwise, they are expected to exothermically transform into carbonates with activation barriers ranging from low—0.27 eV (for CO₂/NP[0/1])—to moderate—0.82 eV (for CO₂/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 PdO₄ site of the Pd/NP[0/0] complex with an adsorption energy of −0.1 eV (Pd1b in Table 1). CO₂ 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 CO₂ molecule is quite strongly bound, with a desorption energy of 1.2 eV (Table 1, E_des(CO₂) = −E_b(CO₂) 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 CO₂ to CO₃²⁻, which is exothermic by only 0.25 eV. CO is strongly, by 1.7 eV, adsorbed at the O-deficient PdO₃ site (Pd1aV in Table 1). The formed stable O₃PdCO species can transform to O₂PdCO₂ 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(CO₂) for Pd2aV in Table 1) is required to desorb the CO₂ molecule into the gas phase. Thus, the most likely ceria-supported Pd-intermediates to be detected in reaction medium are saturated square-planar O₃PdCO/NP (Pd1aV) and O₃PdCO₂/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 defect-free and O-deficient Ag/NP systems occurs with a moderate energy gain of 0.8 eV (Table 1). The formed O₄AgCO and O₃AgCO species are converted into the corresponding O₃AgCO₂ and O₂AgCO₂ species with a similar exothermicity around 0.4 eV, but the activation barrier for the more O-saturated complex O₄AgCO, 0.9 eV, is 0.4 eV higher than that for O₃AgCO (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 CO₂ desorption should proceed quite readily (see −E_b(CO₂) values for Ag2b and Ag2aV in Table 1). Thus, the carbonyl complexes O₄AgCO/NP (Ag1a) and O₃AgCO (Ag1aV), which are easily formed with notable energy gains, are expected to be detectable in a reaction medium. The detection of carboxylate AgCO₂/NP (Ag2b and Ag2aV) complexes seems problematic due to their instability with respect to CO₂ desorption.

We estimated the propensity of CO to CO₂ transformation by the energy of the CO(gas) + M/NP[n/0] → CO₂(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 O₄-site of CeO₂ NP with the calculated energies for clean ceria surfaces [65,71,74,79,80] and the Pd₁–ceria interfaces [8,9,20]. This reaction was found to be slightly, by 0.4–0.6 eV, exothermic on bare CeO₂(111) [74,79] and notably more exothermic on CeO₂(110) [65,74,78,79], at 1.1–1.8 eV. The calculated reaction exothermicity further drastically increases to 3.1 eV for the CeO₂(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 CeO₂(100) surface, but in a similar range to that for CeO₂(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 Pd₁/CeO₂(100) and O₁Pd₁/CeO₂(100) sites, the conversion of CO to CO₂ was characterised by energy yields of 0.6 and 1.2 eV [9], respectively—markedly lower than at the pristine CeO₂(100) surface. The reaction is also moderately exothermic at the Pd₁/CeO₂(110) interface, by 1.2 eV [20], and highly exothermic at the isolated O₁Pd₁ and O₂Pd₁ species on the CeO₂(111) surface, by 2.9 and 2.7 eV [8]—much more exothermic than at the regular CeO₂(111) surface because of exposing weakly bonded O atoms. Compared to the above-mentioned transformations, that at Pd/NP[0/0] has the lowest E_ox of −0.23 eV. There, the formal migration of an O-atom of the O₄Pd moiety to become a part of CO₂ molecule is difficult even in comparison with the three-coordinated O centre of the regular CeO₂(111) surface. For the conversion at the Pd/NP[1/0] site with E_ox = −1.61 eV, the relocation of the second O atom of the O₄Pd moiety is more favourable than of the O atom of the isolated O₁Pd₁ moiety on CeO₂(100) or Pd₁ at CeO₂(110), but less beneficial than that of O₁Pd₁ or O₂Pd₁ ad-species on CeO₂(111). For the reactions on Ag/NP[n/0] sites, the energy E_ox, −1.0–1.2 eV, is slightly lower than on the Pd/NP[1/0] site, thus approaching E_ox values for O₁Pd₁/CeO₂(100) and Pd₁/CeO₂(110) systems. Therefore, our model ceria particle with the Pd atom adsorbed on the O-defective {100} nanofacet appears to be more reactive in CO to CO₂ oxidation than its formal analogue of the Pd-doped extended CeO₂(100) surface.

Thus, the trend for lowering E_ox in bare and M-containing ceria systems is Pd/NP[1/0] > NP[n/0] ≈ Ag/NP[n/0] > Pd/NP[0/0], which correlates with the growth of the O vacancy formation energy in the same row (Table 2). Note that the reactivity in CO oxidation of both Ag/NP complexes—with and without an O vacancy near the Ag atom—is 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/Ce₂₁O₄₂ nanoparticle problematic. Such characteristics of the studied models as moderately strong CO adsorption, exothermic overall CO oxidation process, sufficiently low barriers of MCO to MCO₂ transformations, and ease of CO₂ 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 CO₂ and CO₂ to CO₃ conversions for M-containing ceria NPs, we conclude that the most probable species to be observed experimentally are AgCO and PdCO carbonyls and carboxylate PdCO₂ 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.

3.3. CO_x Vibrational Fingerprints

Several studies reported measured [7,9,16,25,26,28,68,81] and calculated [8,9,68,82,83,84] vibrational frequencies of CO, CO₂, and CO₃²⁻ groups in the complexes formed by the interaction of CO or CO₂ with cerium-based substrates. The calculated frequencies for selected stretching vibrations of CO_x subsystems of the structures displayed in Figure 2, Figure 3 and Figure 4 are collected in

Table 3. Calculated vibrational frequencies ν(CO), ν(CO₂) and ν(CO₃) for the systems depicted in Figure 2, Figure 3 and Figure 4 along with the corresponding frequency shifts Δν(CO) and Δν(CO₂) with respect to calculated vibrational frequencies of free molecules CO (ν(free CO) = 2131 cm⁻¹) and CO₂ (ν_asym(free CO₂) = 2363 cm⁻¹).

System a	ν(CO) cm−1	Δν(CO) cm−1	ν(CO2) cm−1	Δν(CO2) cm−1	ν(CO3) cm−1
Complexes with CO
Pd1a	2158	27	-	-	-
Pd1b	2047	−84	-	-	-
Pd1c	2022	−109	-	-	-
Pd1aV	2018	−113	-	-	-
Ag1a	2081	−50	-	-	-
Ag1aV	2070	−61	-	-	-
1a	2162	31	-	-	-
1aV	2165	34	-	-	-
Complexes with CO2
Linear O-C-O
Pd2b	-	-	2323	−40	-
Pd2bV	-	-	2332	−31	-
Ag2a	-	-	2348	−15	-
Ag2bV	-	-	2350	−13	-
2a	-	-	2354	−9	-
2aV	-	-	2360	−3	-
Bent O-C-O
Pd2a	-	-	1535	−828	-
Pd2aV	-	-	1628	−735	-
Ag2aV	-	-	1332	−1031	-
Ag2b	-	-	1950	−413	-
2bV	-	-	1657	−706	-
Complexes with CO32−
Tridentate
Pd3a	-	-	-	-	1573; 1221
Pd3b	-	-	-	-	1451; 1243
Pd3aV	-	-	-	-	1442; 1309
Ag3a	-	-	-	-	1511; 1233
Ag3aV	-	-	-	-	1434; 1337
3b	-	-	-	-	1442; 1280
3aV	-	-	-	-	1400; 1353
Bidentate
Pd3c	-	-	-	-	1746; 1118
Pd3bV	-	-	-	-	1729; 1122
Ag3b	-	-	-	-	1689; 1126
Ag3bV	-	-	-	-	1752; 1169
3a	-	-	-	-	1714; 1082
3bV	-	-	-	-	1704; 1101

^a For system designations see Figure 2, Figure 3 and Figure 4.

.

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 Ce⁴⁺ centres of the nanostructured CeO₂ [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 M₁-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 Pd₁ species, the Pd1b complex with Pd²⁺ 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 Pd²⁺ cations (Table 3). For the earlier examined systems with Pd-CO bonds, the redshifts Δν(CO) were calculated to increase from 6 to 96 cm⁻¹ in the order O₂Pd₁/CeO₂(111) < O₁Pd₁/CeO₂(100) ≈ O₁Pd₁/CeO₂(111) < Pd₁/CeO₂(100) < Pd₁/CeO₂(111) [8,9]. These values are comparable with those attributed to the CO molecule contacting one Pd atom in experimental studies of Pd/CeO₂, 13–123 cm⁻¹ [7,28] and 10–69 cm⁻¹ [9,16,25] and PdO/CeO₂, 58 cm⁻¹ [26]. Note that the Δν(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 Pd₁-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 Pd²⁺ cations anchored to ceria [83].

The highest frequencies of CO₂ stretching vibrations in 2a, 2aV, Ag2a, Ag2bV, Pd2b, and Pd2bV complexes with a linear CO₂ moiety are close to that of the IR active CO₂ asymmetric stretching frequency of the free molecule; the negative shift Δν(CO₂) does not exceed 40 cm⁻¹ (Table 3). The redshift Δν(CO₂) for a bent CO₂ fragment in 2bV, 706 cm⁻¹, is comparable to the experimental value for the free anion CO₂⁻, 691 cm⁻¹ [88] (vs. measured ν(CO₂) of free molecule 2349 cm⁻¹ [76]) and CO₂⁻ species at TiO₂ surface, 709 cm⁻¹ [89]. The redshift Δν(CO₂) for the MCO₂/NP[n/1] systems having the M-C bond from 413 to 1031 cm⁻¹ is associated with the bending of the CO₂ moiety and C-O bond elongation by 3 to 14 pm. The redshifts for PdCO₂/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 CO₂ attached to a single d-metal atom [76], while redshift Δν(CO₂) in Ag2b is smaller, at only 413 cm⁻¹. Δν(CO₂) for the CO₂²⁻ group in Ag2aV with CO bonds elongated by 14 pm compared to those of free CO₂ matches the measured redshifts of 1020–1079 cm⁻¹ for carbonite ions at CeO₂ [90] and in Cs₂CO₂ [91]. Thus, the increased redshift Δν(CO₂) 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 CO₃²⁻ stretching vibrations [68]. In tridentate CO₃/NP[n/2] and MCO₃/NP[n/2] complexes, the C-O bond lengths are 125–135 pm for the 1.11- and 1.21-modes, and in less symmetrical bidentate 1.20- and 1.30-structures, the C-O bonds cover a wider interval 121–146 pm.

Overall, the splitting of C-O frequencies is lower for more symmetrical species. In particular, for the two highest frequencies (ν₁ and ν₂), it is only 47 cm⁻¹ for 2.2.2-structures, increasing to 97–133 cm⁻¹ for 2.2.1-isomers and 162–252 cm⁻¹ for 1.2.1- and 1.1.1-isomers (Table 3). For 1.20- and 1.30-carbonates, the splitting becomes as high as 563–632 cm⁻¹. According to earlier calculations, carbonate groups attached to nanostructured ceria surface by three oxygen atoms, represented by sets of 1.21-, 1.2.1- and 1.3.1-structures, are characterised by ν₁ values from 1590 to 1490 cm⁻¹ [68]. With the inclusion of ν₁ values for tridentate structures 3b and 3aV, this range extends to 1400 cm⁻¹. The calculated ν₁ 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 ν₁ 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 ν₁ 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 ν₁ 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 CO₃²⁻ on M-free ceria substrates.

The calculated ν₂ 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 ν₂ 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 ν₂ 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 ν₂ for the CO₃ 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 CO₃/NP and MCO₃/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 ceria-supported 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 CO₂ asymmetric stretching frequency of the M-CO₂ fragments are much higher, up to ~830 cm⁻¹ for carboxylate MCO₂ and further increasing by ~200 cm⁻¹ for carbonite AgCO₂. The two highest ν(CO₃) stretching frequencies of M-CO₃ structures lie in intervals 1755–1690 cm⁻¹ and 1170–1120 cm⁻¹ for the CO₃ moiety coordinated in a bidentate fashion and 1575–1430 cm⁻¹ and 1340–1220 cm⁻¹ for the CO₃ in the tridentate coordination.

4. Conclusions

CO_x intermediates formed upon CO adsorption and oxidation on single M = Pd and Ag atoms coordinated to the O₄-site on the {100} facet of a Ce₂₁O₄₂ 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 < MCO₂ < MCO₃, 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 O₄-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 MO₄ to MO₃ for a particular metal: Ag/Ce₂₁O₄₂ (50 cm⁻¹) < Ag/Ce₂₁O₄₁ (61 cm⁻¹) < Pd/Ce₂₁O₄₂ (84 cm⁻¹) < Pd/Ce₂₁O₄₁ (113 cm⁻¹).

Carboxylate CO₂⁻ and carbonite CO₂²⁻ (for Ag-doped NP with an O vacancy) complexes featuring a bent CO₂ moiety are formed upon CO oxidation at the M/ceria interface. Contrary to AgCO₂-species, which are easily decomposed via CO₂ detachment, PdCO₂ moieties are prone to withstand decomposition due to significant CO₂ desorption energies of 0.7–1.2 eV. These PdCO₂ moieties anchored to ceria particles could be experimentally detected by the red shifts of the CO₂ asymmetric stretching frequency (vs. that of free CO₂ 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 CO₂ desorption due to the high barriers of CO₂ transformation to CO₃²⁻ (up to 1.8 eV for PdCO₃ moieties) and weak CO₂ binding (below ~0.2 eV for AgCO₃ moieties). Detailed analysis of the vibrational spectra of MCO₃/NP complexes has shown that the two highest ν(CO₃) stretching frequencies lie in the well-resolved intervals 1755–1690 and 1170–1120 cm⁻¹ for the CO₃ 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 CO₃/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 MCO₂ transformations, and ease of CO₂ desorption render CO oxidation by lattice ceria oxygen atoms more favourable at the sites with Ag than with Pd.