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

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.


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 (N 2 O) and carbon monoxide (CO) have been recognized as two common harmful gases among the emissions of exhaust gases. Specially, N 2 O 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 CO 2 [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 N 2 and CO 2 gases (N 2 O + CO→N 2 + CO 2 ). This process involves two steps: firstly, a results confirm that the doping of the core metal atoms can greatly affect the structure and electronic and catalytic properties of Cu 55 clusters. By carefully examining the N 2 O decomposition and CO oxidation processes of these core-shell clusters, we found that Ni 13 @Cu 42 and Co 13 @Cu 42 clusters can serve as promising candidates in CO oxidation by N 2 O. The results also reveal that the different reaction mechanisms and the metal modification doping of M 13 @Cu 42 clusters play a key role in CO oxidation. Our calculations reveal endoplasmically doped, medium-size Cu 55 clusters that can serve as stable, low-cost, and highly effective catalysts in the selective catalytic reduction of N 2 O by CO.

Computational Details
All spin-polarized DFT calculations in this paper were performed using the generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof (PBE) exchangecorrelation 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 M 13 @Cu 42 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: where E M 13 @Cu 42 , E Cu, and E M are the total energy of M 13 @Cu 42 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): 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 N 2 O, CO, CO 2 , and N 2 . The Cu-Cu average bond length of the Cu 55 cluster was calculated to be 2.32 Å, which is fairly consistent with the experimental result of 2.37 Å [42].

Structure
The structure of the aromatic-like inorganic and metal compounds Cu 55 cluster is presented in Figure 1, which had icosahedral (I h ) symmetry and a diameter size of approximately 9.77 Å. The Cu 55 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 Cu 55 consisted of 20 equivalent triangular fcc (111) facets. The fcc (111) facet in Cu 55 clusters and aromatic structures are similar. Each facet contained two types of nonequivalent atoms, namely three Cu 1 atoms at the intersection of five fcc (111) facets (vertex, T) and three Cu 2 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 Cu 1 -Cu 2 and 2.59 Å of d Cu 2 -Cu 2 . The distance of the Cu 1 atoms to the inner layer atom was 4.77 Å with a coordination number of six, while that of the Cu 2 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 Cu 55 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 M 13 @Cu 42 (M = Co, Ni, Zn, Ru, Rh, Pd, Pt) clusters exhibited no obvious structural deformation. shown in Figure 1, the surface of Cu55 consisted of 20 equivalent triangular fcc (111) facets.  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. 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 outlayer 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. Furthermore, the structural stability of the M 13 @Cu 42 clusters was examined from the binding energy point ( Figure 2). The binding energy of the pure Cu 55 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 Cu 55 except for Zn 13 @Cu 42 , indicating the strong M-Cu bonds and structural stability of these core-doped clusters, as listed in Table 1. 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.

Catalytic Properties of M 13 @Cu 42 Cluster
Before analyzing the CO oxidation by N 2 O, the adsorption of N 2 O on the catalysts was explored. For the neutral state, the N 2 O molecules presented a linear geometry with a N-O bond length of 1.20 Å. Generally, there were two types of geometries for N 2 O adsorption on the catalyst, namely N terminal and O terminal geometries. After geometric optimization, the adsorption energies of N 2 O 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 N 2 O molecule exceeded −0.9|e|; meanwhile, there was no significant charge transfer in the N terminal adsorbed systems. The related parameters and structure of N 2 O adsorption on the Cu 55 cluster are shown in Table S1 and Figure S1.

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,   Six different adsorption sites on the surface of the pure Cu 55 cluster were investigated to determine the optimal adsorption configuration for the reaction, including the hollow of the fcc (H 1 , H 2 ) facets, top of the Cu 1 atom (T 1 ), top of the Cu 2 atom (T 2 ), bridge of the bond between Cu 1 and Cu 2 (B 1 ), and bridge of the bond between Cu 2 and Cu 2 (B 2 ). After geometric optimization with the O terminal, the N 2 O was decomposed to the N 2 molecule, and the remaining O atom was adsorbed on the Cu 55 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 Cu 55 cluster and N 2 O was obtained as ranging from −48.43 to −53.27 kcal/mol, as shown in Table S1. The adsorption energies of the H 1 and H 2 adsorption sites were comparable on the Cu 55 cluster, but the H 2 configuration was more easily activated than the H 1 configuration. The optimization results indicated that the optimized structure of N 2 O adsorption at the B 1 , T 2 , and B 2 sites was consistent with that located at the H 2 sites. The subsequent CI-NEB calculation also showed that the remaining O atom was biased to be adsorbed at the H 2 site after the N 2 dissociation for the Cu 55 cluster. The Bader charge analysis proved that approximately 0.96|e| to 0.97|e| was transferred from the clusters to the N 2 O molecule (H 2 approximately 0.97|e|). Therefore, the H 2 configuration served as the preferred adsorption site of N 2 O on the Cu 55 cluster, which is consistent with the literature [45]. For further calculations, the H 2 site adsorbed to the clusters by the O terminal was selected as the most stable adsorption geometry.
Similarly, the configurations of N 2 O at the H 2 active site on the doped M 13 @Cu 42 clusters were studied. The geometry of the N 2 O 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 M 13 @Cu 42 clusters. These changes indicated that the N 2 O absorbed by the M 13 @Cu 42 clusters decomposed to N 2 and an adsorbed O atom on the M 13 @Cu 42 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 M 13 @Cu 42 clusters transferred 0.97|e| to 1.11|e| charges to N 2 O molecule, which caused its reduction. In other words, the M 13 @Cu 42 clusters significantly assisted in withdrawing charges from the N 2 O molecule, as indicated in Table 2. After the analysis of N 2 O adsorption, the entire CO oxidation mechanisms as a result of the N 2 O 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 N 2 O 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, N 2 O and CO were first co-adsorbed (*N 2 O-*CO) on the catalyst surface, bonding to the underlying two adjacent Cu atoms. Subsequently, the N 2 was desorbed from the active sites to generate a gaseous N 2 molecule, and the remaining O atoms were adsorbed on the Cu 55 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 N 2 O 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 CO 2 , 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 (TS 2+ ) 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 M 13 @Cu 42 clusters. The CO 2 molecule was directly dissociated from the M 13 @Cu 42 clusters, indicating the accomplishment of the reaction. By examining the overall CO oxidation as a result of N 2 O processes via the L-H mechanism, the CO oxidation step was considered as the rate-limiting step in the eight catalysts (M 13 @Cu 42 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 N 2 O 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 N 2 O reduction. As shown in Figures 3  and 4, the Cu 55 and Ni 13 @Cu 42 clusters of catalysts successfully produced N 2 and CO 2 with barrier energies of 10.58 and 9.68 kcal/mol, respectively. Notably, the Ni 13 @Cu 42 cluster possessed the lowest barrier for catalyzing the CO oxidation by the N 2 O reaction.   CO oxidation on the M 13 @Cu 42 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. 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 Fegraphene (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.  Figure 5 summarizes the energy barriers of the rate-limiting step to CO oxidation by the Cu 55 , Co 13 @Cu 42 , Ni 13 @Cu 42 , and Ru 13 @Cu 42 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 Cu 13 (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@Cu 12 (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 Cu 12 (18.45 kcal/mol) [28] and SiN 4 G (16.60 kcal/mol) [48], comparable with that of Pt@Cu 12 (14.81 kcal/mol) [29] and V@Au 12 (15.68 kcal/mol) [49], and higher than that of Cr@Au 12 (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: where ΔE and ΔEZPE are the calculated DFT total energy, calculated zero-point energy, and entropic corrections (T∆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. To date, computations refer to hypothetically ideal conditions, where finite temperature and constant pressure are generally desired in experiments. Thus, the Gibbs free energy (∆G) of N 2 O 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: where ∆E and ∆E ZPE are the calculated DFT total energy, calculated zero-point energy, and entropic corrections (T∆S) at T = 298.15 K. For gas phase molecules, the values of ZPE and S came from the NIST database [50]. The ∆G, 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 M 13 @Cu 42 cluster clusters (except for Pd 13 @Cu 42 ), as shown in Figure 6. The results clearly indicated that Cu 55 and doped M 13 @Cu 42 clusters (M = Co, Ni, Zn, Ru, Rh, Pt) enable the reaction process to properly proceed under ambient conditions. Therefore, Cu 55 and doped M 13 @Cu 42 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 N 2 O reaction evaluation results showed that doping with different elements of the M 13 @Cu 42 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 N 2 O reaction depended on the properties of the catalysts. For example, N 2 O reduction possessed a higher energy barrier than CO oxidation on the Ag 7 Au 6 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. 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.

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 (7σ) 2 (2π) 4 (3π) 0 , and the frontier molecular orbitals (FMOs) consisted of π-orbitals, where the 2π-HOMO orbital was the bonding orbital of the N-N bond and the antibonding orbital of the N-O bond. 3π-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

Electronic Structure Analysis
The electronic structure of these bimetallic clusters was deeply analyzed to further understand the catalytic activity of the M 13 @Cu 42 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 N 2 O was (7σ) 2 (2π) 4 (3π) 0 , and the frontier molecular orbitals (FMOs) consisted of π-orbitals, where the 2π-HOMO orbital was the bonding orbital of the N-N bond and the antibonding orbital of the N-O bond. 3π-LUMO was the strong antibonding orbital between all atoms [52].
There was a small charge transfer from the N 2 O molecule to the metallic clusters when the N 2 O molecule was attached to the surface of clusters through its O end. When N 2 O 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 N 2 O compared with pure Cu 55 clusters. The adsorbability of the M 13 Cu 42 cluster was better than that of the Cu 55 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 Cu 55 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 M 13 @Cu 42 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 N 2 O to obtain electrons, meaning that the N-O bond of N 2 O 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 M 13 @Cu 42 clusters can be further associated with the d orbital center of the cluster, defined as [54]: 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 M 13 @Cu 42 clusters are shown in Figures 7b and S8. tallic 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]: 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 Figures 7b and 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 M 13 @Cu 42 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.

Conclusions
In conclusion, M 13 @Cu 42 (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 N 2 O via CO, were systematically investigated using periodic spin-polarized first-principles calculations. The results show that the stability of these M 13 @Cu 42 clusters are significantly higher than that of the intrinsic Cu 55 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 M 13 @Cu 42 clusters that had suitable binding capacities comprised a low potential barrier. Especially, the kinetic barrier of Ni 13 @Cu 42 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 M 13 @Cu 42 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.