The calculated most stable structures of MSi n O 2 n + 1 – clusters are presented in Figure 1. Clusters with three kinds of metal atoms (Au, Ag, Cu) have similar geometric structures and the same electronic states, except for the slight differences in bond lengths and bond angles. All the MSiO 3 – and MSi 2 O 5 – clusters have C_2V symmetry and ¹A₁ electronic state, while MSiO 3 – clusters have C₁ symmetry and ¹A electronic state. Details of the M-O bond lengths and M-O-Si bond-angles are shown in Table 1.

The most stable adsorption structures of O₂ on optimized MSi n O 2 n + 1 – clusters are shown in Figure 2 and some data are listed in Table 2. The triplet states of the adsorption structures for each cluster are considered at first, since the ground state of O₂ is a triplet. On Au/Ag-containing clusters, O₂ takes end-on adsorption coordination to the metal atom, while on the Cu-containing clusters, O₂ takes side-on coordination to Cu. After the adsorption, the electronic state may be changed due to spin flip. Therefore, the singlet states are also considered. In all the singlet state structures, O₂ takes side-on coordination on metal atoms. A spin-crossover may occur in the potential energy surfaces of singlet and triplet states when O₂ adsorbs onto the metal atoms in MSi n O 2 n + 1 – . The minimum energy crossing points (MECP) were determined by the sobMECP program combined with the Gaussian 09 package, and the conversion from the triple-state to the singlet state is shown in Figure 2. The triplet state is less stable than the singlet state for n = 1, 2 clusters, and the conversion from the triplet to the singlet state is quite easy, with low energy barriers (i.e., the relative energy of MECP with respect to the triplet state) as about 0.2 eV for Au-containing clusters and less than 0.1 eV for Ag/Cu-containing clusters. For the relatively larger clusters (n = 3), the triplet state is more stable and the conversion from the triplet to the singlet need additional energy, and the

barriers of Au/Ag-containing clusters are quite large (1.78 and 1.25 eV, respectively), while that of CuSi 3 O 7 – is still small (−0.21 eV). Note that the energies in Figure 2 are without ZPE corrections since harmonic vibrational frequency calculations can not be performed on MECPs which are not stationary points.

The adsorption energy (E_ad) of O₂ on MSi n O 2 n + 1 – clusters was calculated as E_ad = E ( MSi n O 2 n + 1 – ) + E (O₂) – E ( MSi n O 2 n + 1 – -O 2 ), where E is the energy of free singlet MSi n O 2 n + 1 – , triplet O₂, and the adsorption complex MSi n O 2 n + 1 – -O 2 with either singlet or triplet states, respectively. Four types of energies were considered, namely, E_e (electronic energies), E_ZPE (sum of electronic and zero-point energies), E_H (sums of electronic and thermal enthalpies) and E_G (sum of electronic and Gibbs free energies) at the standard temperature (298.15 K) and

pressure (1 atm). The results are given in Table 2. Generally, Cu-containing clusters and smaller clusters have higher E_b values than Au/Ag-containing clusters and larger clusters. The values of E_ZPE are close to or more than 1 eV for most clusters, indicating that O₂ can be firmly adsorbed on these clusters. AuSi 3 O 7 – -O 2 (S₁) and AgSi 3 O 7 – -O 2 (S₃) have small values for E_ZPE as about 0.6 eV, and AgSi 3 O 7 – -O 2 (S₁) has the smallest E_ZPE as 0.11 eV. Because the adsorption of O₂ on clusters leads to the decrease of entropy, the values of E_G are smaller than those of E_ZPE by about 0.4 eV. Therefore, AgSi 3 O 7 – -O 2 (S₁) has a negative value (−0.38 eV) for E_G, indicating that this complex can not be formed at standard conditions.

Vibrational frequencies of O-O (v_O-O) in the adsorption complexes MSi n O 2 n + 1 – -O 2 are useful information to evaluate the activation of O₂ after adsorption. The calculated results are shown in Table 2. Upon adsorption, the O-O bond will be weakened, leading to the decrease of v_O-O in the adsorption complexes, accompanied by the increase of O-O bond lengths (R_O-O). For the triplet state, comparing with Au/Ag-containing clusters, the v_O-O of Cu-containing clusters is smaller than those of Au/Ag-containing clusters. Accordingly, the R_O-O of Cu-containing clusters is between 1.33 Å and 1.35 Å, which is longer than those of Au/Ag-containing clusters, about 1.28 Å and 1.33 Å. Relatively larger clusters (n = 3) have larger v_O-O and shorter R_O-O than n = 1, 2 clusters. For example, the v_O-O of AuSi 3 O 7 – is 1138.0 cm⁻¹, which is 37.8 and 49.6 cm⁻¹ larger than AuSi 2 O 5 – and AuSiO 3 – , respectively, and their R_O-O is 1.33, 1.34, and 1.35 Å, respectively. After the transition from triplet to singlet states, the v_O-O decreases remarkably and the R_O-O increases significantly, indicating high activation of O₂ in the singlet states. For the singlet state, different from the triplet state, the R_O-O values of Au-containing clusters are the biggest, which are between 1.41 Å and 1.44 Å, while those of Cu/Ag-containing clusters are between 1.37 Å and 1.41 Å. Accordingly, the v_O-O of Au-containing clusters is the smallest. Similar to the situation for triplet states, the v_O-O of the relatively larger clusters (n = 3) is larger than that of n = 1, 2 clusters. Note that the calculated S² values before and after annihilation indicate that all electronic states we obtained have no spin pollution.

Bond order analysis is a direct way to evaluate the bonding strength between two atoms. We calculated the Fuzzy bond order (FBO) of O-O in the adsorption complexes MSi n O 2 n + 1 – -O 2 , and compared with that of free O₂ molecule obtained at the same theoretical level. After adsorption, FBO decreases from 2.47 for free O₂ to values less than 2 for the triplet states. Cu-containing clusters and smaller clusters have lower FBO values than Au/Ag-containing clusters and larger clusters, which is consistent with the conclusion that Cu-containing clusters and smaller clusters have higher ability to activate O₂ according to the analysis basis on R_O-O and v_O-O. After the transition from triplet to singlet states, FBO decrease to low values about 1.4, indicating that O-O in the singlet MSi n O 2 n + 1 – -O 2 is highly activated, which is consistent with the long R_O-O and small v_O-O for them.

The activation of O-O bonds in the adsorption complexes MSi n O 2 n + 1 – -O 2 can also be reflected by the electron transfer from MSi n O 2 n + 1 – to O₂. The O₂ molecule obtains electrons after adsorption and these electrons will fill into the π^* anti-bonds of O-O, leading to the weakening of O-O bond. Natural population analysis (NPA) was performed to get the charges on O₂ (q_O2), and the results are shown in Figure 4. It is clear that q_O2 of the triplet states is smaller (for absolute

values) than that of the singlets. The oscillation of the curve shows that for each case (a certain metal and a certain electronic state), q_O2 decreases as n increases from 1 to 3. For the triplet state, Cu-containing clusters have larger q_O2 than Au/Ag-containing clusters with the same cluster sizes, while for the singlet state, q_O2 of Au-containing clusters is the largest for each n. All these findings agree well with the previous discussion on the activation of O₂ based on R_O-O, v_O-O, and FBO.

Oxidation of CO is often used as a probe reaction to evaluate the oxidation ability of oxidants. Considering the high energy barriers of spin flip from the triplet state to singlet state for the adsorption complexes AuSi n O 2 n + 1 – -O 2 and AgSi n O 2 n + 1 – -O 2 , a systematical study was performed on the oxidation of CO on Cu-containing clusters, which may be the most promising catalysts for CO oxidation. Because the ground states of CuSiO 3 – and CuSi 2 O 5 – are the singlet state and the ground state of CuSi 3 O 7 – clusters is the triplet state, both singlet and triplet states along the reaction paths were calculated. The sum of the energy of infinite separated CO and the ground state of CuSi n O 2 n + 1 – -O 2 was set to zero. Figure 5(a) shows the reaction path of CuSiO 3 – -O 2 (IS1) with CO. It can be started from the singlet ¹IS1 with CO, because ¹IS1 is lower in energy than ³IS1 by 0.155 eV, and the transition from ³IS1 to ¹IS1 is very easy (the energy barrier is only 0.01 eV, Figure 2). The CO is then weakly adsorbed on an O atom to form ¹I1 with a low adsorption energy −0.066 eV. The distance between the C and the O in ¹IS1 (d_C…O) is quite far (2.724 Å) at this moment. Then the CO moves much more close to the cluster and climbs over a transition state (¹TS1), whose overall relative energy is as high as 0.747 eV and d_C…O in ¹TS1 is 1.540 Å. After the transition state, a CO₂ moiety is formed as in ¹I2 which is very stable with a low relative energy (−2.739 eV). In the last step, the system desorbs a CO₂, forming 3 CuSiO 4 − (−2.119 eV) through a spin-crossover, or 1 CuSiO 4 − (−1.744 eV). The whole path of the singlet stats is below that of the triplet, except the products, indicating that the singlet states are preferred for CuSiO 3 – -O 2 (IS1) with CO. Similarly situations are found for the reaction of CuSi 2 O 5 – -O 2 (IS2) with CO, as shown in Figure 5(b). Differently, the reaction path of CuSi 3 O 7 – -O 2 (IS3) with CO prefers triplet states (Figure 5(c)). Consistent with the previous discussion, the smallest system CuSiO 3 – -O 2 has the lowest energy barrier and therefore the highest oxidation ability toward CO. These three paths are compared with our previous work in which AuVO 1 , 2 + were used to catalyse the reaction of CO to CO₂ by O₂. [39] The difference between the two works is CO attack site. In our work, CO prefers O site of the activated oxygen, while CO prefers mental site in AuVO 1 , 2 + system. Rate-determining step (RDS) barrier means a lot when study reaction. The RDS barrier of previous work is from 1.100 eV to 2.470 eV, while that is from 0.817 eV to 0.992 eV in this work.