Mechanisms in the Catalytic Reduction of N₂O by CO over the M₁₃@Cu₄₂ Clusters of Aromatic-like Inorganic and Metal Compounds

Abstract

Metal aromatic substances play a unique and important role in both experimental and theoretical aspects, and they have made tremendous progress in the past few decades. The new aromaticity system has posed a significant challenge and expansion to the concept of aromaticity. From this perspective, based on spin-polarized density functional theory (DFT) calculations, we systematically investigated the doping effects on the reduction reactions of N₂O catalyzed by CO for M₁₃@Cu₄₂ (M = Cu, Co, Ni, Zn, Ru, Rh, Pd, Pt) core–shell clusters from aromatic-like inorganic and metal compounds. It was found that compared with the pure Cu₅₅ cluster, the strong M–Cu bonds provide more structural stability for M₁₃@Cu₄₂ clusters. Electrons that transferred from the M₁₃@Cu₄₂ to N₂O promoted the activation and dissociation of the N–O bond. Two possible reaction modes of co-adsorption (L-H) and stepwise adsorption (E-R) mechanisms over M₁₃@Cu₄₂ clusters were thoroughly discovered. The results showed that the exothermic phenomenon was accompanied with the decomposition process of N₂O via L-H mechanisms for all of the considered M₁₃@Cu₄₂ clusters and via E-R mechanisms for most of the M₁₃@Cu₄₂ clusters. Furthermore, the rate-limiting step of the whole reactions for the M₁₃@Cu₄₂ clusters were examined as the CO oxidation process. Our numerical calculations suggested that the Ni₁₃@Cu₄₂ cluster and Co₁₃@Cu₄₂ clusters exhibited superior potential in the reduction reactions of N₂O by CO; especially, Ni₁₃@Cu₄₂ clusters are highly active, with very low free energy barriers of 9.68 kcal/mol under the L-H mechanism. This work demonstrates that the transition metal core encapsulated M₁₃@Cu₄₂ clusters can present superior catalytic activities towards N₂O reduction by CO.

1. Introduction

Nowadays, air pollution has gradually become a serious environmental problem. Fuel combustion, the emissions of exhaust gases, and excessive fertilization in agriculture have led to a huge production of large amounts of toxic and harmful gases in the atmosphere. Among them, nitrous oxide (N₂O) and carbon monoxide (CO) have been recognized as two common harmful gases among the emissions of exhaust gases. Specially, N₂O has been recognized as the main gas that causes the greenhouse effect because it has a global warming potential that is 300 times larger than that of CO₂ [1,2]. Moreover, it is also a stratospheric ozone depleter [3]. Meanwhile, CO is not only a potential greenhouse gas but can also cause serious harm to human health. In recent years, significant efforts have been devoted to the development and application of the reduction of the two harmful gases [4,5,6,7,8,9,10,11]. One of the most promising methods is to convert them into less harmful N₂ and CO₂ gases (N₂O + CO→N₂ + CO₂). This process involves two steps: firstly, a N₂O molecule reacts to form N₂ and an adsorbed O atom (N₂O→N₂ + O*), then the O* atom reacts with a CO molecule to form CO₂ (O* + CO→CO₂) [12]. Notably, the direct reaction of N₂O with CO molecules shows a high kinetic barrier (about 47.77 kcal/mol) [13], which seriously hinders the reaction’s ability to take place at room temperature. Therefore, it is necessary to develop catalysts that have the properties of being stable, economical, and highly active. Until now, many kinds of catalysts, including noble metal [14], metal zeolites/porphyrins [15], metal alloys, and perovskite-like catalysts [16,17], have been proven to achieve efficient conversions of N₂O and CO to N₂ and CO₂. However, the high cost and difficulties in the mining process (environment, working conditions) have led to a deep search for metal catalysts with similar or improved properties to replace them.

Aromaticity has attracted the most attention in recent years. Li et al. prepared a series of all metal clusters MAl₄⁻ (M = Li, Na, Cu) and investigated the valence molecular orbitals of Al₄²⁻ using photoelectron spectroscopy experiments combined with quantum chemical theory calculations [18]. Two π electrons occupied completely non-deterministic HOMO orbitals. This study identified MAl₄⁻ as an aromatic system, which has been confirmed in the scientific research. Zhu et al. reported the first synthesis of metallapentalyne having a transition metal-centered d orbital involved in conjugation in osmium metallapentalyne, thus converting the Hückel anti-aromatic nature of metallapentalyne into the Möbius aromatic nature of metallapentalyne [19]. These studies have generated great scientific importance in the extended concept of the aromaticity, which has extended the scope from organic chemistry to metal cluster systems and has opened up a new scientific frontier. In this context, Cu-based aromatic-like metal compound alloys have attracted considerable attentions because of copper’s low cost and excellent properties in various aspects, such as having high stability and long persistence in high-temperature conditions [20,21,22]. In recent years, metallic Cu nanoclusters or Cu-based alloy clusters have been widely applied in various catalytic processes, e.g., hydrogen evolution reaction (HER), NO_x reduction, dry reforming of methane (DRM), etc. [23,24,25,26,27]. As for the catalytic reduction of N₂O by CO reaction, Barabás et al. systematically investigated the performance of Cu_n (n = 4–15) cluster catalysts and found that Cu₁₂ and Cu₁₄ clusters were the best catalysts according to the thermodynamic analysis, even at ambient temperatures [28]. Lian et al. systematically studied M@Cu₁₂ (M = Cu, Pt, Ru, Pd, Rh) clusters and confirmed that Ru@Cu₁₂ and Pt@Cu₁₂ clusters exhibited superior catalytic activity via a co-adsorption mechanism [29].

As a medium-sized nanocluster (the diameter is about 1 nm) with a typical core–shell structure, the icosahedral Cu₅₅ cluster of aromatic-like inorganic and metal compounds is considered to be the global minimum of Cu₅₅ clusters [30]. Extensive studies have been carried out to reveal the physical and chemical properties and potentials in the catalysis of this nanocluster material [31,32,33,34,35,36]. Mao et al. reported a DFT-based high-throughput screening method to successfully screen Cu_55-nM_n (M = Co, Ni, Ru, and Rh) core–shell alloy clusters and identified Cu-Ni alloy clusters as a superior electrocatalyst for HER [31]. Cao et al. systematically studied a single Pd-doped Cu₅₅ nanoparticle towards propane dehydrogenation and demonstrated that this nanoparticle exhibited superior catalytic activity toward C–H bond activation and significantly reduced side reactions such as deep dehydrogenation [32]. Liu et al. identified a crown jewel-structured Pt₁₂Cu₄₃ cluster as a promising catalyst candidate for highly efficient and low lost oxygen reduction reaction (ORR) processes [33]. So far, pure or alloyed Cu₅₅ nanoclusters have been proven to own great potentials in HER [31], ORR [33], H₂ dissociation [35], propane dehydrogenation [32], and acetylene selective hydrogenation reactions [36]; however, to the best of our knowledge, no theoretical work has been carried out to investigate their activity towards the selective catalytic reduction of N₂O via CO (i.e., CO oxidation by N₂O). We aim to fill up that void with the current work.

In this paper, by means of DFT calculations, we systematically investigated the structural stability and catalytic performance of pure Cu₅₅ core–shell clusters and substituted M₁₃@Cu₄₂ (M = Co, Ni, Zn, Ru, Rh, Pd, Pt) clusters of aromatic-like inorganic and metal compounds by encapsulating the transition metal atoms as a core in a CO oxidation by N₂O reaction. The results confirm that the doping of the core metal atoms can greatly affect the structure and electronic and catalytic properties of Cu₅₅ clusters. By carefully examining the N₂O decomposition and CO oxidation processes of these core–shell clusters, we found that Ni₁₃@Cu₄₂ and Co₁₃@Cu₄₂ clusters can serve as promising candidates in CO oxidation by N₂O. The results also reveal that the different reaction mechanisms and the metal modification doping of M₁₃@Cu₄₂ clusters play a key role in CO oxidation. Our calculations reveal endoplasmically doped, medium-size Cu₅₅ clusters that can serve as stable, low-cost, and highly effective catalysts in the selective catalytic reduction of N₂O by CO.

2. Computational Details

All spin-polarized DFT calculations in this paper were performed using the generalized gradient approximation (GGA) of the Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional while adopting the Vienna ab initio simulation package (VASP 5.4.4) software package [37,38,39]. The electron–ion exchange correlation interactions were calculated by using the projector augmented wave (PAW) method. Grimme’s semiempirical DFT-D3 scheme of dispersion correction was implemented to elaborate the van der Waals (vdW) interaction [40]. A plane wave basis was accompanied by a kinetic energy cut-off of 500 eV. The convergence criteria for the structure optimizations were set to 10⁻⁵ eV, and the Hellmann–Feynman force was less than 0.02 eV Å⁻¹. Cluster structures with a vacuum space of 25 Å were applied to ensure negligible interactions within neighboring unit clusters. For the optimized geometries, the K-points was set to be 3 × 3 × 1; they were set to 9 × 9 × 1 for the density of states (DOSs) calculations. The minimum reaction paths for each step of the reaction were considered to be using the climbing image advancement elastic band (CI–NEB) method [41].

In order to characterize the stability of the transition metal (TM) core atoms-substituted M₁₃@Cu₄₂ clusters, the average binding energy (E_b) was adopted to evaluate the structural stability of core–shell bimetallic clusters, which was calculated according to the following equation:

$$E_b=\left(13E_M+42E_{Cu}-E_{M_{13}@C{u}_{42}}\right)/55$$

(1)

where $E_{M_{13}@C{u}_{42}}$, E_Cu, and E_M are the total energy of M₁₃@Cu₄₂ cluster, energy of the Cu atom, and doped metal atom, respectively.

The adsorption energies (E_ads) of the adsorption species on these clusters were defined by the following Equation (2):

$$E_{ads}=E_{total}-E_{species}-E_{cluster},$$

(2)

where E_total, E_species, and E_cluster are the total energies of the total adsorbed systems, isolated adsorption species, and clusters, respectively. A Bader population analysis was adopted to quantify the charge population in each atom in our calculation.

To support the choice of the functional combinations and the computational detail of the basis set described, we provided benchmark calculations of the geometrical parameters for N₂O, CO, CO₂, and N₂. The Cu–Cu average bond length of the Cu₅₅ cluster was calculated to be 2.32 Å, which is fairly consistent with the experimental result of 2.37 Å [42].

3. Results and Discussion

3.1. Structure

The structure of the aromatic-like inorganic and metal compounds Cu₅₅ cluster is presented in Figure 1, which had icosahedral (I_h) symmetry and a diameter size of approximately 9.77 Å. The Cu₅₅ cluster possessed a multishell structure, in which the outer layer was composed of 42 Cu atoms and the I_h core was formed by 13 copper central atoms. As shown in Figure 1, the surface of Cu₅₅ consisted of 20 equivalent triangular fcc (111) facets. The fcc (111) facet in Cu₅₅ clusters and aromatic structures are similar. Each facet contained two types of nonequivalent atoms, namely three Cu₁ atoms at the intersection of five fcc (111) facets (vertex, T) and three Cu₂ atoms in two contiguous fcc (111) facets (bridge site, B). The different Cu atoms induced different Cu–Cu bond lengths, such as 2.51 Å of d_Cu1–Cu2 and 2.59 Å of d_Cu2–Cu2. The distance of the Cu₁ atoms to the inner layer atom was 4.77 Å with a coordination number of six, while that of the Cu₂ atoms to the inner layer atom was 4.18 Å with a coordination number of eight. Compared with bulk copper, the different bond lengths in the Cu₅₅ cluster endowed its atoms and bonds with higher activity, showing potential in certain catalysis reactions. After the substitution of the core atom, all of the M₁₃@Cu₄₂ (M = Co, Ni, Zn, Ru, Rh, Pd, Pt) clusters exhibited no obvious structural deformation.

Furthermore, the structural stability of the M₁₃@Cu₄₂ clusters was examined from the binding energy point (Figure 2). The binding energy of the pure Cu₅₅ cluster was calculated to be 70.10 kcal/mol, which agrees well with a previous report [43]. The average binding energies of the subsequent clusters were even larger than those of intrinsic Cu₅₅ except for Zn₁₃@Cu₄₂, indicating the strong M–Cu bonds and structural stability of these core-doped clusters, as listed in

Table 1. Structural, energetic, and electronic properties of M₁₃@Cu₄₂ clusters, including the average M–M and M–Cu bond lengths (d_Cu–Cu, d_M–Cu), binding energies (E_b), magnetic moment (Mag), average charges transferred from M to Cu atoms (CT_M), average charges transferred from the shell-Cu atoms to the core-M metal atoms (CT_Cu), d orbital centers (ε_d), and HOMO–LUMO gaps (Eg).

M	dCu-M (Å)	dM-M (Å)	Eb (kcal/mol)	Mag (μB)	CTM (e)	CTCu (e)	εd (eV)	Eg (eV)
Cu	2.42	2.49	−70.10	3	+0.06	−0.017	2.42	0.1
Co	2.42	2.45	−77.48	21	−0.05	0.017	2.21	0.01
Ni	2.43	2.45	−77.48	8	−0.01	0.003	2.07	0.01
Zn	2.44	2.59	−55.81	2	−0.16	0.052	3.51	0.59
Ru	2.62	2.61	−90.40	4	+0.01	−0.002	2.45	0.02
Rh	2.48	2.69	−81.86	9	+0.12	−0.035	2.22	0.02
Pd	2.48	2.70	−70.79	2	+0.18	−0.054	2.11	0.17
Pt	2.65	2.82	−80.71	0	+0.28	−0.086	2.26	0.16

. This is reasonable from the viewpoint of the melting points of these metals, e.g., [44]. The energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of these clusters ranged from 0.01 eV to 0.59 eV. The bond lengths between the M dopants and out-layer Cu atoms ranged from 2.42 Å to 2.65 Å, which was accompanied by an average charge transfer of about 0.01 |e|~0.28 |e| from the TM atoms to the adjacent Cu atoms, as shown in Table 1. Such electron transfers greatly affected the clusters’ catalytic performances, as discussed in the following sections.

3.2. Catalytic Properties of M₁₃@Cu₄₂ Cluster

Before analyzing the CO oxidation by N₂O, the adsorption of N₂O on the catalysts was explored. For the neutral state, the N₂O molecules presented a linear geometry with a N–O bond length of 1.20 Å. Generally, there were two types of geometries for N₂O adsorption on the catalyst, namely N terminal and O terminal geometries. After geometric optimization, the adsorption energies of N₂O binding to clusters through the N terminus were smaller than those through the O terminus (about 43.81 kcal/mol). The charge transfer from the system with O terminals to the N₂O molecule exceeded −0.9|e|; meanwhile, there was no significant charge transfer in the N terminal adsorbed systems. The related parameters and structure of N₂O adsorption on the Cu₅₅ cluster are shown in Table S1 and Figure S1.

Six different adsorption sites on the surface of the pure Cu₅₅ cluster were investigated to determine the optimal adsorption configuration for the reaction, including the hollow of the fcc (H₁, H₂) facets, top of the Cu₁ atom (T₁), top of the Cu₂ atom (T₂), bridge of the bond between Cu₁ and Cu₂ (B₁), and bridge of the bond between Cu₂ and Cu₂ (B₂). After geometric optimization with the O terminal, the N₂O was decomposed to the N₂ molecule, and the remaining O atom was adsorbed on the Cu₅₅ cluster. The average distance of Cu–O was shortened from 2.20 Å to 1.90 Å, while the bond length of N–O was lengthened from 1.20 to 3.19 Å. Clearly, the N–O bond was broken, and the adsorbed O atom prepared for the subsequent oxidation reaction of CO on the cluster. The adsorption energy between the Cu₅₅ cluster and N₂O was obtained as ranging from −48.43 to −53.27 kcal/mol, as shown in Table S1. The adsorption energies of the H₁ and H₂ adsorption sites were comparable on the Cu₅₅ cluster, but the H₂ configuration was more easily activated than the H₁ configuration. The optimization results indicated that the optimized structure of N₂O adsorption at the B₁, T₂, and B₂ sites was consistent with that located at the H₂ sites. The subsequent CI–NEB calculation also showed that the remaining O atom was biased to be adsorbed at the H₂ site after the N₂ dissociation for the Cu₅₅ cluster. The Bader charge analysis proved that approximately 0.96|e| to 0.97|e| was transferred from the clusters to the N₂O molecule (H₂ approximately 0.97|e|). Therefore, the H₂ configuration served as the preferred adsorption site of N₂O on the Cu₅₅ cluster, which is consistent with the literature [45]. For further calculations, the H₂ site adsorbed to the clusters by the O terminal was selected as the most stable adsorption geometry.

Similarly, the configurations of N₂O at the H₂ active site on the doped M₁₃@Cu₄₂ clusters were studied. The geometry of the N₂O adsorbs was greatly changed. The atomic average distance of Cu–O was 1.92 Å, while the length of the N–O bond was elongated, ranging from 3.17 Å to 3.58 Å for the M₁₃@Cu₄₂ clusters. These changes indicated that the N₂O absorbed by the M₁₃@Cu₄₂ clusters decomposed to N₂ and an adsorbed O atom on the M₁₃@Cu₄₂ cluster for the follow-up reaction. All adsorption energies were negative (−46.12 to −70.33 kcal/mol), suggesting that the adsorption processes for all catalysts were favorable in terms of thermodynamic stability. The Bader charge analysis showed that the M₁₃@Cu₄₂ clusters transferred 0.97|e| to 1.11|e| charges to N₂O molecule, which caused its reduction. In other words, the M₁₃@Cu₄₂ clusters significantly assisted in withdrawing charges from the N₂O molecule, as indicated in

Table 2. Adsorption energies of N₂O and CO molecules on M₁₃@Cu₄₂ clusters (ΔE_N2O, ΔE_CO), adsorption energies of co-adsorbed N₂O and CO molecules on M₁₃@Cu₄₂ clusters (ΔE_N2O-CO, ΔE_O-CO), charge transfer between the molecule and cluster (CT), and energy barriers of the CO oxidation (TS).

	E-R				L-H
M13@Cu42	ΔEN2O (kcal/mol)	ΔECO (kcal/mol)	CT (e)	TS (kcal/mol)	ΔEN2O-CO (kcal/mol)	ΔEO-CO (kcal/mol)	CT (e)	TS (kcal/mol)
Cu	−53.27	−27.44	0.97	11.64	−72.87	−7.61	1.09	10.58
Co	−50.04	−28.59	1.07	14.75	−77.48	−2.77	1.10	9.80
Ni	−46.12	−32.51	1.08	10.97	−74.02	−5.53	1.08	9.68
Zn	−50.27	−28.36	0.97	17.35	−78.40	−2.31	1.09	19.58
Ru	−50.04	−28.36	1.11	12.90	−86.71	−5.77	1.12	11.99
Rh	−50.96	−27.67	1.10	13.99	−84.40	−2.54	1.13	12.53
Pd	−70.33	−20.06	1.09	22.37	−97.77	−0.92	1.18	18.22
Pt	−57.88	−20.75	1.11	14.93	−75.41	−4.84	1.12	12.47

.

After the analysis of N₂O adsorption, the entire CO oxidation mechanisms as a result of the N₂O reaction were investigated by combining the elementary steps associated with all eight kinds of potential catalysts. There were a total of two possible reaction mechanisms, including the E-R and L-H pathways. For the above eight potential catalysts, the most favorable potential energy curves of the CO oxidation as a result of N₂O processes for all of the possible reaction pathways are presented in Figures S2–S7. The corresponding structures of the reaction intermediates were also explored; the important information is summarized in Table 2.

Under the L-H mechanism, N₂O and CO were first co-adsorbed (*N₂O–*CO) on the catalyst surface, bonding to the underlying two adjacent Cu atoms. Subsequently, the N₂ was desorbed from the active sites to generate a gaseous N₂ molecule, and the remaining O atoms were adsorbed on the Cu₅₅ cluster. The average distance between *C and Cu was 1.84 Å, and the N–O bond length was 3.04 Å. The adsorption energies of the co-adsorbed CO and N₂O molecules for the eight types of catalysts were calculated to range from −72.87 to −97.77 kcal/mol. The remaining O atom approached an adsorbed CO molecule and reacted to form CO₂, which was also exothermic. The adsorption energies of the CO and absorbed O atom ranged from −0.92 to −7.61 kcal/mol. The barrier of the transition state (TS²⁺) for the formation of *O*CO ranged from 9.68 kcal/mol to 19.58 kcal/mol. The transition state involved *O and *CO adsorbates having a distance of 1.93–2.27 Å between them for the M₁₃@Cu₄₂ clusters. The CO₂ molecule was directly dissociated from the M₁₃@Cu₄₂ clusters, indicating the accomplishment of the reaction. By examining the overall CO oxidation as a result of N₂O processes via the L-H mechanism, the CO oxidation step was considered as the rate-limiting step in the eight catalysts (M₁₃@Cu₄₂ clusters), which was consistent with the results of the Cu_n (n = 4–15) clusters [28]. Before the rate-limiting step, the barriers for the N₂O reduction steps on these eight catalysts were relatively exothermic and barrierless. The released energy ranged from −72.87 to −97.77 kcal/mol for the exothermic reaction of N₂O reduction. As shown in Figure 3 and Figure 4, the Cu₅₅ and Ni₁₃@Cu₄₂ clusters of catalysts successfully produced N₂ and CO₂ with barrier energies of 10.58 and 9.68 kcal/mol, respectively. Notably, the Ni₁₃@Cu₄₂ cluster possessed the lowest barrier for catalyzing the CO oxidation by the N₂O reaction.

CO oxidation on the M₁₃@Cu₄₂ clusters by the E-R mechanism followed similar procedures as those occurring by the L-H mechanism; the difference is whether the CO reactant was physisorbed on the catalyst or not. In the transition state, only one O atom of the reaction intermediates was bound with Cu atoms. As a result, the corresponding barriers were 10.97 kcal/mol and 22.37 kcal/mol, which was higher than those of the L-H mechanism, as shown in Table 2.

Figure 5 summarizes the energy barriers of the rate-limiting step to CO oxidation by the Cu₅₅, Co₁₃@Cu₄₂, Ni₁₃@Cu₄₂, and Ru₁₃@Cu₄₂ clusters in this work along with some other reported atomically dispersed catalysts. The barriers of the rate-limiting step to CO oxidation via the L-H mechanism for these four kinds of nanoclusters were obviously lower than that of Cu₁₃ (16.60 kcal/mol) [29], Cu-graphene (CuG:19.14 kcal/mol), [46] and Fe-graphene (FeG:19.37 kcal/mol) [47] systems and were comparable with that of a Ru@Cu₁₂ (11.66 kcal/mol) [29] catalyst. In addition, the barriers of the rate-limiting step to CO oxidation via the E-R mechanism for these four catalysts were also lower than that of Cu₁₂ (18.45 kcal/mol) [28] and SiN₄G (16.60 kcal/mol) [48], comparable with that of Pt@Cu₁₂ (14.81 kcal/mol) [29] and V@Au₁₂ (15.68 kcal/mol) [49], and higher than that of Cr@Au₁₂ (4.15 kcal/mol or 6.23 kcal/mol) [49], showing great potential in the reaction.

To date, computations refer to hypothetically ideal conditions, where finite temperature and constant pressure are generally desired in experiments. Thus, the Gibbs free energy (ΔG) of N₂O reduction by the CO reaction at 1 atm pressure was calculated and served as a function of a temperature of 298.15 K for each basic procedure; it was computed as:

$$\mathrm{\Delta }G=\mathrm{\Delta }E+\mathrm{\Delta }{E}_{ZPE}-T\mathrm{\Delta }S,$$

(3)

where ΔE and ΔE_ZPE are the calculated DFT total energy, calculated zero-point energy, and entropic corrections (T$\mathrm{\Delta }$S) at T = 298.15 K. For gas phase molecules, the values of ZPE and S came from the NIST database [50]. The ΔG, ZPE, and S of the reactant by the thermodynamics systems were calculated (Tables S2 and S3). The reaction occurred readily under ambient conditions in the case of the M₁₃@Cu₄₂ cluster clusters (except for Pd₁₃@Cu₄₂), as shown in Figure 6.

The results clearly indicated that Cu₅₅ and doped M₁₃@Cu₄₂ clusters (M = Co, Ni, Zn, Ru, Rh, Pt) enable the reaction process to properly proceed under ambient conditions. Therefore, Cu₅₅ and doped M₁₃@Cu₄₂ clusters are promising catalysts that benefited from the fact that the nitrogen-oxygen bonds were broken without an energy barrier and that the nitrogen molecule readily separated from the cluster. At the same time, these catalysts were able to perform at low temperatures.

The CO oxidation by N₂O reaction evaluation results showed that doping with different elements of the M₁₃@Cu₄₂ clusters and different reaction mechanisms had an important effect on the reaction activity. Extensive previous theoretical and experimental works have demonstrated that the rate-limiting step of CO oxidation by the N₂O reaction depended on the properties of the catalysts. For example, N₂O reduction possessed a higher energy barrier than CO oxidation on the Ag₇Au₆ catalyst [51]. Notably, the potential energy curve analysis indicated that the catalytic activity was tuned by controlling the different active mechanisms. Compared with the E-R mechanism, the bimetallic cluster catalyst under the L-H mechanism reduced the energy barrier of the CO oxidation process. According to the charge transfer in the two mechanisms, more electrons were transferred (approximately 0.20|e|) in the presence of CO, which was favorable compared with the absence of CO. The co-adsorbed CO promoted the conduction of the reaction to some extent. Therefore, the structural robustness and chemical tunability are the prominent advantages of the doped metal cage clusters, making them become a promising family of nanometer catalysts with practical application prospects.

3.3. Electronic Structure Analysis

The electronic structure of these bimetallic clusters was deeply analyzed to further understand the catalytic activity of the M₁₃@Cu₄₂ cluster. The surfaces of all of these clusters exhibited significant charge densities, which corresponded to the electronic states near the Fermi energy level. The electron configuration of N₂O was ${\left(7\mathsf{\sigma }\right)}^2{\left(2\mathsf{\pi }\right)}^4{\left(3\mathsf{\pi }\right)}^0$, and the frontier molecular orbitals (FMOs) consisted of $\mathsf{\pi }$–orbitals, where the $2\mathsf{\pi }$–HOMO orbital was the bonding orbital of the N–N bond and the antibonding orbital of the N–O bond. $3\mathsf{\pi }$–LUMO was the strong antibonding orbital between all atoms [52].

There was a small charge transfer from the N₂O molecule to the metallic clusters when the N₂O molecule was attached to the surface of clusters through its O end. When N₂O was adsorbed, a sizeable electron density rearrangement appeared on the shell atoms; the core atoms were not significantly affected. In the alloy metal clusters, the electrons on the shell Cu atoms were transferred to the core dopant atom. Due to the reduction of electrons in the shell Cu atoms, the electrophilicity of the Cu atoms was enhanced, which makes it easier for alloy metal clusters to adsorb N₂O compared with pure Cu₅₅ clusters. The adsorbability of the M₁₃Cu₄₂ cluster was better than that of the Cu₅₅ cluster in the presence of greater electron transfer, which was consistent with the adsorption energy analysis. CO oxidation served as the rate-limiting step during the reaction, and a cluster complex with residual O was produced in both mechanisms; therefore, the interaction between O and CO played an important role. The CO molecule was attached to the metallic clusters through the C atom, and the electron of the CO molecule was transferred to the metallic clusters. For example, the number of charge transfers from CO to the bimetallic clusters was larger than that from CO to the pure Cu₅₅ cluster, which led to a higher catalytic performance for CO oxidation on the alloy clusters.

All of these clusters show prominent charge densities on the Cu cage surface, which correspond to the electronic states near the Fermi level and are responsible for the chemical reactivity. As shown in Figure 7a, the M₁₃@Cu₄₂ cluster with a lower d orbital center provided a stronger adsorption strength with the CO molecule. Such a trend of activity was also observed in previous studies [49,53]. This interaction makes it easier for N₂O to obtain electrons, meaning that the N–O bond of N₂O is more easy to break. Intuitively, less charge transfer between M–Cu indicates a weaker bonding between M and Cu atoms and an enhanced unsaturation of the Cu outer cage, resulting in a higher reactivity of the surface Cu atoms to CO. The activity of the M₁₃@Cu₄₂ clusters can be further associated with the d orbital center of the cluster, defined as [54]:

$${\mathsf{\epsilon }}_{\mathrm{d}}=\frac{{{\displaystyle \int }}_{-\infty }^{0}ED\left(E\right)dE}{{{\displaystyle \int }}_{-\infty }^{0}D\left(E\right)dE},$$

(4)

where D€ is the local density of states (LDOSs) of the d orbitals of the cluster at a given energy E; the integral is taken from all occupied states, and the highest occupied molecular orbital (HOMO) is set to zero. The LDOSs of the M₁₃@Cu₄₂ clusters are shown in Figure 7b and Figure S8.

According to the picture of the extended Hückel theory [55], a deeper d orbital level of the catalyst leads to a lower hopping matrix element and stronger binding strength with the adsorbate. Therefore, the binding ability and activity of the M₁₃@Cu₄₂ clusters are related to the d orbital centers of the clusters, and the catalytic performance can be optimized by selecting suitable doping elements and even by designing ideal catalysts for various reactions.

4. Conclusions

In conclusion, M₁₃@Cu₄₂ (M = Cu, Co, Ni, Zn, Ru, Rh, Pd, Pt) core–shell clusters of aromatic-like inorganic and metal compounds, where transition metal atoms acted as the core for the selective catalytic reduction of N₂O via CO, were systematically investigated using periodic spin-polarized first-principles calculations. The results show that the stability of these M₁₃@Cu₄₂ clusters are significantly higher than that of the intrinsic Cu₅₅ cluster. Meanwhile, the total charge transfers from the shell to the central doped atoms were shown to increase. The doping of the central metal atom affected the catalytic and electronic properties of the clusters. A portion of the M₁₃@Cu₄₂ clusters that had suitable binding capacities comprised a low potential barrier. Especially, the kinetic barrier of Ni₁₃@Cu₄₂ was 9.68 kcal/mol for CO oxidation under the L-H mechanism. The L-H mechanism, which stemmed from gas molecule co-adsorption on the M₁₃@Cu₄₂ clusters and transition metal modification doping, played a key role in the adsorption of CO oxidation. Our calculations revealed the use of endoplasmically doped copper clusters as a novel stable subnanocatalyst, which is a promising material for high-performance catalytic media.