Full Paper
The Mechanism of Low-Temperature CO Oxidation on IB Group Metals and Metal Oxides
Article first published online: 23 NOV 2011
DOI: 10.1002/cctc.201100298
Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Additional Information
How to Cite
Wei, Z.-Z., Li, D.-C., Pang, X.-Y., Lv, C.-Q. and Wang, G.-C. (2012), The Mechanism of Low-Temperature CO Oxidation on IB Group Metals and Metal Oxides. ChemCatChem, 4: 100–111. doi: 10.1002/cctc.201100298
Publication History
- Issue published online: 27 DEC 2011
- Article first published online: 23 NOV 2011
- Manuscript Received: 26 AUG 2011
Funded by
- National Natural Science Foundation of China. Grant Numbers: 20273034, 20673063
- Abstract
- Article
- References
- Cited By
Keywords:
- CO oxidation;
- copper;
- density functional calculations;
- gold;
- metal oxides;
- reaction mechanism;
- silver
Abstract
- Top of page
- Abstract
- Introduction
- Calculation Methods and Models
- Results and Discussion
- Conclusions
- Acknowledgements
CO oxidation on the IB group metals [Cu(111), Ag(111), and Au(111)] and corresponding metal oxides [Cu2O(100), Ag2O(100), and Au2O(100)] has been studied by means of density functional theory calculations with the aim to shed light on the reaction mechanism and catalytic activity of metals and metal oxides. The calculated results show that 1) the molecular oxygen mechanism is favored on Ag(111) and Au(111), but the atomic oxygen mechanism is favored on Cu(111); 2) the metal-terminated metal oxide shows very low activity for CO oxidation; 3) the lattice oxygen can react either with gas phase CO or the absorbed CO molecule on oxygen-terminated metal oxides; and 4) the reaction barrier for CO oxidation follows the order of M2O(100)–O<M(111)<M2O(100)–M (M=Cu, Ag, Au); namely the M2O(100)–O shows higher activity than does the corresponding metal. By analyzing the factor that controls the energy barrier, it was found that the interaction energy between two CO molecules and one O atom at the transition state plays an important role in determining the trend in the barrier.
Introduction
- Top of page
- Abstract
- Introduction
- Calculation Methods and Models
- Results and Discussion
- Conclusions
- Acknowledgements
CO oxidation reaction, as one of the simplest association reactions on surfaces, is of great importance both technologically and theoretically. The CO oxidation on transition-metal (TM) surfaces is a very important catalytic reaction in many industrial processes, primarily for two reasons:1 Technologically, it is the main reaction in car-exhaust emission control, CO2 lasers, sensors, and so on; and theoretically, it can be widely used as the model system to study the mechanism of the heterogeneous catalysis process. Because CO adsorption and activation on the TM surface has a significant meaning for many catalytic processes that involve CO (such as Fischer–Tropsch synthesis, CO methanation, water–gas shift reaction for hydrogen, and methanol decomposition), CO oxidation is regarded as the prototype reaction and has been widely studied.2–4 German and Sheintuch studied CO adsorption and desorption kinetics on (111) surfaces of TMs (Ru, Ir, Pd, Rh, and Pt) by using the ab initio density functional theory (DFT) method with two correlation-exchange functionals; they found that the top site is the most favorable for CO adsorption on Ru, Rh, and Ir surfaces and the hollow position is preferable for CO on the Pd surface.3 Su et al. systematically studied the promotion effect of water for CO oxidation on Ag(111) and Au(111) surfaces by means of DFT and found that the presence of water greatly stabilizes the adsorption of reactants, such as O2, atomic oxygen, and CO, through the formation of the hydrogen bonds and/or the interactions between the substrates and the adsorbates.1 Moreover, they also found that adsorbed water molecules stabilize the transition states (TSs) and various intermediates by similar interactions.1
During realistic reaction conditions, the metal catalysts would potentially be oxidized to form metal oxide, which could affect the activity of catalysts for CO oxidation. Thus, CO oxidation on TM oxide surfaces has led to a number of studies. The research emphases are on the intrinsic properties of metal oxide and the comparisons of catalytic activity with their corresponding metallic states.5 Ertl and co-workers performed a series of experiments of CO oxidation on RuO2 surfaces, and they found that RuO2 exhibits enhanced catalytic activity toward CO oxidation under steady-state flow condition relative to the low activity of metallic Ru.6–8 White et al. studied CO oxidation at a relatively low temperature by using copper oxide nanoparticles loaded onto silica gel as an exceptional catalyst, and they found that it is very efficient for the oxidation of CO to CO2.9 Theoretically, Gong et al. systematically studied and reported that the barriers for CO oxidation on TM oxides (RuO2, RhO2, PbO2, OsO2, IrO2, and PtO2) are generally lower than the barriers for CO oxidation on metal surfaces (Ru, Rh, Pb, Os, Ir, and Pt).10 However, there are few studies that concern the difference of CO oxidation on IB group metals (Cu, Ag, and Au) and metal oxides (Cu2O, Ag2O, and Au2O).11 In this work, the detailed reaction process of CO oxidation on IB group metals and metal oxides is investigated by performing DFT calculations. First, many important elementary steps of CO oxidation on these metal and metal oxide surfaces are considered. Then, the TS of CO oxidation on each surface is located, and the reaction barriers can be determined. Finally, the electronic and the physical nature of energy barrier are discussed.
Calculation Methods and Models
- Top of page
- Abstract
- Introduction
- Calculation Methods and Models
- Results and Discussion
- Conclusions
- Acknowledgements
To study the energy and structure details of CO oxidation on metal and metal oxide surfaces, the periodic, self-consistent DFT calculation was performed by using the Vienna ab initio simulation package (VASP).12–14 The electronic structures were calculated by using DFT within the generalized gradient approximation (GGA-PW91).15–17 The project-augment wave (PAW)16, 17 scheme was used to describe the inner cores, and the electronic wavefunctions were expended in a plane wave basis with a kinetic cutoff energy of 400 eV. The climbing-nudged elastic band method was employed to locate the TS18–20 and the frequency analysis was performed for a confirmation of the TS. Vibrational frequencies are calculated by using numerical differentiation of the forces using a second-order finite difference approach with a step size of 0.015 Å. The surfaces of metal oxides [Cu2O(100), Ag2O(100), and Au2O(100)] are polar and have the square symmetry. They also consist of planes parallel to the surface with either metal cations or O anions: the metal planes have two metal cations with a net charge of 2+ per unit cell; the O planes have two O anions with a net charge of 2− per unit cell. A two-plane repeat pattern is necessary to maintain stoichiometry and charge neutrality. The surface could thus be either metal- or O-terminated [named as M2O(100)–M or M2O(100)–O (M=Cu, Ag, Au) in this study]. To meet the symmetry requirement, the slab was comprised of alternate O and Cu layers (three of O and four of Cu), with four atoms in the O layer and eight atoms in the Cu layer. The calculated results indicated that the energy has no difference on the symmetric slab, both with and without the polarity corrected. However, the polarity correction can affect the adsorption energy of CO on metal oxides. The calculation results indicated that the adsorption energy of CO on the nonsymmetric slab (with four layers of oxygen and four layers of metal) with polarity is higher [−1.79 on the Cu2O(100) surface] than that on the symmetric slab without polarity [−1.52 on the Cu2O(100) surface]. This rule is also applicable to the symmetric slabs with symmetrically adsorbed species. Namely, the adsorption energy of nonsymmetrically adsorbed species of the nonsymmetric slab (i.e., the CO molecule was put on one side of the slab) with polarity is higher [−1.79 eV on the Cu2O(100) surface] than that of the symmetrically adsorbed species (i.e., CO molecules were put on both sides of the slab) on the symmetric slab without polarity [−1.42 eV on the Cu2O(100) surface]. Therefore, to improve the convergence for structural relaxation of the polar surface of metal oxides, the nonsymmetric slab with dipole correction to the total energy of the system is included.11 In our calculations, the lattice constant of 4.18 Å is used for Ag(111) and Au(111) and 3.64 Å is used for Cu(111) whereas the lattice constant of 4.72 Å21 is used for Ag2O(100) and Au2O(100) and 4.30 Å22 is used for Cu2O(100).
For metal and metal oxide surfaces, the surface is modeled by a symmetric periodic slab model and the p (2×2) unit cell is used. In the case of metals [Cu(111), Ag(111), and Au(111)], the surfaces are modeled by four layers of metals and the top two layers are relaxed until the atomic forces are less than 0.03 eV Å−1, while the bottom two layers are held fixed in their bulk position. We calculated that the oxygen atom adsorbs on the different models (two relaxed layers and three relaxed layers), and the energy difference is found to be less than 0.06 eV. The calculated results indicate that four-layer-thick metal slabs, with only two surface layers relaxed, are sufficient for an adequate convergence of the reported adsorption characteristics. Consequently, the two surface layers relaxed model was used in this work. In the calculations performed on metal oxides [Cu2O(100), Ag2O(100), and Au2O(100)], the surfaces are modeled by eight layers of metal oxides, with the uppermost four layers relaxed until the atomic forces are less than 0.03 eV Å−1, while the bottom four layers are held fixed in their bulk position. For metal oxides, the slab contained four layers of the metal and four layers of O. The structures of metals and metal oxides that are used in this work are shown in Figure 1. The slabs are separated by a 10–15 Å vacuum layer. The Monkhorst–Pack meshes of 4×4×1 and 3×3×1 k-point samplings in the surface Brillouin zones are used for metals and metal oxides,23 respectively. The adsorption energy (Eads) and the activation barrier (Ea) are calculated by the following two formulas [Eqs. (1) and (2)]:((2))
((1))
((2))

Figure 1. a–c) Side view of the ideal metal (111) and metal oxide (100) surfaces in 2×2 unit cell. d–f) Different adsorption sites on metal- or O-terminated metal and metal oxide in top view, respectively. top, bri, and hol refer to the top site, bridge site, and hollow site, respectively.
Here EA, EM, EA/M, ETS, and EIS, represent the calculated energy of the adsorbate, substrate, adsorption system, TS, and initial state (IS), respectively.
Results and Discussion
- Top of page
- Abstract
- Introduction
- Calculation Methods and Models
- Results and Discussion
- Conclusions
- Acknowledgements
On the surfaces of IB group metals [M(111), M=Cu, Ag, Au] and the metal-terminated metal oxides [M2O(100)–M, M=Cu, Ag, Au], the reaction path can be assumed to be one in which the adsorbed CO reacts directly with the preadsorbed oxygen atom, namely, CO(a)+O(a)→CO2(g) (Langmuir–Hinshelwood (L–H) reaction mechanism). However, there are three distinct reaction paths on the O-terminated metal oxide surfaces [M2O(100)–O, M=Cu, Ag, Au]: 1) the path in which the molecular CO reacts directly with the lattice oxygen atom (labeled as Os) (Figure 1 d) through a reaction mechanism similar to the Eley–Rideal (E–R) reaction mechanism, 2) the path in which CO first adsorbs on the metal atom of the second layer and then reacts with Os through a reaction mechanism similar to the L–H reaction mechanism, and 3) the path in which CO and oxygen atom both adsorb on the sublayer metal atom and then CO reacts with O(a) and CO2 molecule is formed, which then desorbs spontaneously leaving an oxygen vacancy at the surface. Afterward, the molecular O2 restore the oxygen vacancy. The calculated energies and geometric parameters for the adsorption of oxygen atom, CO, and CO+O are listed in Tables 1–2, 3. The energy profiles for CO oxidation on metal and metal oxide surfaces and the corresponding geometric parameters of the TS are shown in Figure 2, 2a, and the corresponding activation barriers are listed in Table 4.
| Metal | Species | Site | Eads [eV] | RC M [Å−1] | RO M [Å−1] | RC O [Å] |
|---|---|---|---|---|---|---|
| Cu(111) | O | top | −2.91 | – | 1.73 | – |
| bri | −4.82 | – | 1.88 | – | ||
| fcc | −5.15 | – | 1.88 | – | ||
| hcp | −5.01 | – | 1.89 | – | ||
| CO | top | −0.83 | 1.85 | 3.01 | 1.16 | |
| bri | −0.93 | 2.05 | 2.98 | 1.18 | ||
| fcc | −0.97 | 2.05 | 2.98 | 1.18 | ||
| hcp | −0.94 | 2.05 | 2.99 | 1.18 | ||
| CO+O | CO(fcc)+O(fcc) | −5.60 | 2.31 | 1.89 | 2.72 | |
| Ag(111) | O | top | −3.81 | – | 2.14 | – |
| bri | −3.92 | – | 2.14 | – | ||
| fcc | −3.92 | – | 2.14 | – | ||
| hcp | −3.81 | – | 2.14 | – | ||
| CO | top | −0.27 | 2.18 | 3.33 | 1.15 | |
| bri | −0.18 | 2.03 | 3.27 | 1.16 | ||
| fcc | −0.19 | 2.29 | 3.26 | 1.16 | ||
| hcp | −0.19 | 2.31 | 3.28 | 1.16 | ||
| CO+O | CO(top)+O(fcc) | −3.95 | 2.20 | 2.16 | 3.54 | |
| Au(111) | O | top | −3.08 | – | 2.12 | – |
| bri | −3.37 | – | 2.14 | – | ||
| fcc | −3.38 | – | 2.13 | – | ||
| hcp | −3.10 | – | 2.12 | – | ||
| CO | top | −0.28 | 2.04 | 3.19 | 1.15 | |
| bri | −0.21 | 2.15 | 3.09 | 1.17 | ||
| fcc | −0.18 | 2.24 | 3.11 | 1.18 | ||
| hcp | −0.15 | 2.25 | 3.12 | 1.18 | ||
| CO+O | CO(top)+O(bri) | −3.55 | 2.05 | 2.15 | 3.52 |
| Metal oxide | Species | Site | Eads [eV] | RC M [Å−1] | RO<C-M [Å−1] | RC O [Å] |
|---|---|---|---|---|---|---|
| Cu2O(100) | O | top | −5.48 | – | 1.76 | – |
| –Cu | bri | −4.09 | – | 1.84 | – | |
| CO | top | −1.42 | 1.85 | 2.96 | 1.17 | |
| bri1 | −0.26 | 2.09 | 3.00 | 1.17 | ||
| bri2 | −1.38 | 1.89 | 2.88 | 1.17 | ||
| hol | −1.79 | 1.89 | 2.87 | 1.18 | ||
| CO+O | CO(hol)+O(top) | −7.29 | 1.87 | 1.83 | 3.22 | |
| Ag2O(100) | O | top | −3.77 | – | 1.97 | – |
| –Ag | bri | −2.35 | – | 2.16 | – | |
| CO | top | −0.90 | 2.09 | 3.06 | 1.16 | |
| bri1 | −0.04 | 2.47 | 3.35 | 1.16 | ||
| bri2 | – | – | – | – | ||
| hol | −1.52 | 2.10 | 3.03 | 1.17 | ||
| CO+O | CO(hol)+O(top) | −5.28 | 2.05 | 2.09 | 3.47 | |
| Au2O(100) | O | top | −3.95 | – | 1.96 | – |
| –Au | bri | −4.04 | – | 1.97 | – | |
| CO | top | −0.79 | 1.91 | 3.07 | 1.16 | |
| bri1 | −0.37 | 2.17 | 2.96 | 1.17 | ||
| bri2 | −1.26 | 2.02 | 2.99 | 1.17 | ||
| hol | −1.77 | 2.02 | 2.94 | 1.18 | ||
| CO+O | CO(hol)+O(top) | −5.66 | 2.02 | 1.97 | 4.28 | |
| CO(hol)+O(bri) | −5.68 | 2.00 | 1.97 | 4.77 |
| Metal oxide | Species | Site | Eads [eV] | RC M [Å−1] | RO M [Å−1] | RC O [Å] |
|---|---|---|---|---|---|---|
| Cu2O(100) | O | top (metal ion) | −3.36 | – | 1.81 | – |
| –O | CO | top (lattice oxygen) | −0.15 | – | – | 2.94 |
| bri (metal ion) | −0.85(−0.89)11 | 2.03 | – | 2.90 | ||
| CO+O | CO(top)+Os | −4.99 | – | – | 2.94 | |
| CO(bri)+Os | −5.69 | 2.03 | – | 2.90 | ||
| CO(bri)+O(top) | −4.31 | 2.00 | 1.87 | 3.43 | ||
| Ag2O(100) | O | top (metal ion) | −4.56 | – | 2.21 | – |
| –O | CO | top (lattice oxygen) | −0.22 | – | – | 2.85 |
| bri (metal ion) | −0.85 | 2.29 | – | 3.02 | ||
| CO+O | CO(top)+Os | −3.24 | – | – | 2.85 | |
| CO(bri)+Os | −3.87 | – | – | 3.02 | ||
| CO(bri)+O(top) | −3.91 | 2.26 | 2.74 | 5.21 | ||
| Au2O(100) | O | top (metal ion) | −2.76 | – | 1.99 | – |
| –O | CO | top (lattice oxygen) | −0.26 | – | – | 3.16 |
| bri (metal ion) | −0.75 | 2.14 | – | 2.76 | ||
| CO+O | CO(top)+Os | −3.86 | – | – | 3.16 | |
| CO(bri)+Os | −4.35 | 2.14 | – | 2.76 | ||
| CO(bri)+O(top) | −3.48 | 2.14 | 2.03 | 5.27 |

Figure 2. Reaction energy profiles of CO oxidation and O2 dissociation and corresponding geometric parameters of TSs on IB metal and metal oxide surfaces. a) CO(a)+O(a) on M(111). b) O2 dissociation on M(111). c) O2 dissociation on M2O(100)–M. d) CO(a)+O(a) on M2O(100)–M. e) CO(a)+O2(a) on M2O(100)–M. f) CO(a)+Os on M2O(100)–O. g) CO(a)+O(a) on M2O(100)–O. h) O2 dissociation on M2O(100)–O. Bond length is in Å. Activation barrier is in eV.
| Metal | Cu(111) | Ag(111) | Au(111) |
|---|---|---|---|
| Ecoads [eV] | −5.59 | −3.95 | −3.55 |
| Barrier [eV] | 0.71 | 0.16 | 0.28 |
| OC(a)–O(a) distance [Å] | 1.72 | 1.86 | 2.02 |
| Reaction energy [eV] | −0.79 | −2.48 | −2.86 |
| Metal oxide | Cu2O(100)–Cu | Ag2O(100)–Ag | Au2O(100)–Au |
| Ecoads [eV] | −7.29 | −5.28 | −5.66 |
| Barrier [eV] | 1.68 | 1.11 | 1.42 |
OC(a) O(a) distance [Å] | 1.86 | 2.10 | 2.00 |
| Reaction energy [eV] | 0.80 | −1.18 | −0.75 |
| Metal oxide | Cu2O(100)–O | Ag2O(100)–O | Au2O(100)–O |
| Ecoads [eV] | −5.69 | −3.87 | −4.35 |
| Barrier [eV] | 0.36 | 0.19 | 0.59 |
OC(a) Os distance [Å] | 1.89 | 1.94 | 1.93 |
| Reaction energy [eV] | −0.85 | −2.69 | −2.10 |
| Metal oxide | Cu2O(100)–O | Ag2O(100)–O | Au2O(100)–O |
| Ecoads [eV] | −4.31 | −3.91 | −3.48 |
| Barrier [eV] | 1.37 | 0.38 | 0.45 |
OC(a) O(a) distance [Å] | 1.81 | 1.87 | 1.93 |
| Reaction energy [eV] | −2.29 | −3.04 | −3.08 |
CO oxidation on metal surfaces
In the case of the first reaction pathway, to find the most stable IS we first investigate the most stable adsorption configurations for all possible species on different surfaces. The calculated results indicate that the most stable adsorption site of the oxygen atom is face cubic centered (fcc) on all metal surfaces, and the most stable adsorption site of the CO molecule is fcc, top, and top on Cu(111), Ag(111), and Au(111) surfaces, respectively (Table 1). Our calculated results are in good agreement with the results of Lopez and Nørskov.24 They studied the interaction of CO on the pure Cu(111) surface by means of DFT and found that CO prefers to adsorb on the fcc site with the adsorption energy of 0.90 eV. However, these results conflict with the experimental data as regards to which top site is more favorable for CO adsorption.25, 26 The adsorption properties of CO on Ag(111) are consistent with the experimental results obtained by Hansen et al.27 and McElhiney et al.28 They found that CO prefers to adsorb on the top site with the adsorption energy of 0.27 and 0.28 eV, respectively. On the Au(111) surface, the top site is found to be preferred for CO adsorption, and the corresponding adsorption energy is 0.28 eV. This is in good agreement with the results of Gajdoš et al. (0.32 eV on the top site)29 and the experiment results (0.40 eV on the top site).30, 31 The coadsorption of CO+O on metal surfaces is also investigated. Different combinations of adsorption configurations for CO and oxygen atoms are chosen to determine the most stable IS for the reaction. The calculated coadsorption energy results show that the most stable system is CO(fcc)+O(fcc) on the Cu(111) surface, CO(top)+O(fcc) on the Ag(111) surface, and CO(top)+O(fcc) on the Au(111) surface. The corresponding coadsorption energy is −5.60, −3.95, −3.55 eV, and the distance between the C atom and the adsorbed oxygen atom is 2.72, 3.54, and 3.52 Å, respectively. In addition, the different adsorption sites of CO2 on M(111) (M=Cu, Ag, Au) surfaces are studied in order to determine the most stable final state (FS). The most stable adsorption site of CO2 is bridge site on different surfaces. The calculated adsorption energies are very small, and the energy difference between different adsorption sites is only a few meV, and so the physisorption of CO2 is very evident.
For CO oxidation on the Cu(111) surface, initially, the oxygen atom and the CO molecule both adsorb at the fcc site. At the TS, the CO molecule moves to the off-top site from its initial fcc site, whereas the oxygen atom is at the bridge site. The activation barrier of CO oxidation is calculated to be 0.71 eV, and the distance between the C atom and the oxygen atom is 1.72 Å at the TS. This is in good agreement with the results of Gokhale et al.,32 who found that the reaction barrier is 0.82 eV for CO oxidation on the Cu(111) surface. Similarly, for the TS configurations of CO oxidation on Ag(111) and Au(111) surfaces, the CO molecule adsorbs at the off-top site and the oxygen atom adsorbs at the bridge site compared with their initial coadsorption site. The activation barrier of CO oxidation on Ag(111) and Au(111) surfaces is calculated to be 0.16 and 0.28 eV, and the distance between the C atom and the oxygen atom is 1.86 and 2.02 Å at the TS. This is in good agreement with the results of Su et al.,1 who found that the reaction barrier is 0.20 and 0.29 eV for CO oxidation on Ag(111) and Au(111) surfaces. After the TS, the CO2 molecule is formed, which then desorbs from the metal surfaces. The calculated results indicate that CO oxidation reaction is sensitive to the properties of different metals and the order of activation barrier on different metal surfaces for CO oxidation is Ag(111)<Au(111)<Cu(111).
We also studied O2 dissociation on M(111) (M=Cu, Ag, Au) surfaces. The energy profiles for O2 dissociation on M(111) (M=Cu, Ag, Au) surfaces and the corresponding geometric parameters of the TSs are shown in Figure 2. O2 dissociates directly after O2 adsorbs on the Cu(111) surface (i.e., the O2 dissociation is a spontaneous process). This result is in good agreement with the estimated value of 0.08 eV of Habraken et al.33 based on kinetics measurements. On Ag(111) and Au(111) surfaces, O2 initially adsorbs at the bridge site, however, at the TS, two oxygen atoms are located at the nearest fcc sites. The activation barrier for O2 dissociation is 0.84 eV on Ag(111) and 1.16 eV on Au(111) surfaces. The corresponding bond length is 1.97 and 1.84 Å. These results are in good agreement with those of Su et al.34 and Xu and Mavrikakis.35 They found that the activation energy for O2 dissociation is 0.95 eV on Ag(111) and 1.37 eV on Au(111) surfaces. From these calculations, it is clear that although CO oxidation with the oxygen atom is facile on Ag(111) and Au(111) surfaces, a significantly high barrier for O2 dissociation on both surfaces make them less active for CO oxidation.
For CO oxidation on Ag(111) and Au(111) surfaces, the demanding activation for O2 dissociation leads to very low activity on these two surfaces. However, Su et al.1 and Liu et al.36 studied that the reaction of CO with molecular O2 involves a four-center OC
O
O intermediate state (labeled as MS) [via CO(a)+O2(a)→[OCOO](a)→CO2(g)+O(a)]36 on Ag(111) and Au(111) surfaces. They found the activation energy to be 0.15 and 0.46 eV for CO oxidized by O2 on Ag(111) and Au(111) surfaces. For the Cu(111) surface, we also considered that CO reacts with molecular O2 through OC
O
O, however, the MS is not found on the Cu(111) surface, possibly due to the spontaneous dissociation of molecular oxygen on Cu(111). The calculated results indicate that the reaction mechanism of CO reacting with molecular O2 is more favorable than that of CO reacting with the adsorbed oxygen atom on Ag(111) and Au(111) surfaces. However, an opposing conclusion is obtained by using the Cu(111) surface; namely, the reaction mechanism of CO reacting with the adsorbed oxygen atom is more favorable than that of CO reacting with molecular O2.
CO oxidation on metal oxide surfaces
M2O(100)–M (M=Cu, Ag, Au)
The preadsorbed oxygen atom results from O2 dissociation, and thus the O2 dissociation on M2O(100)–M (M=Cu, Ag, Au) surfaces is also investigated. The energy profiles for O2 dissociation on M2O(100)–M (M=Cu, Ag, Au) surfaces and the corresponding geometric parameters of the TS are shown in Figure 2. For O2 dissociation on Cu2O(100)–Cu, Ag2O(100)–Ag, and Au2O(100)–Au surfaces, the reaction energy is −3.26, −1.04, and −0.32 eV and the activation barrier is calculated to be 0.14, 0.65, and 1.01 eV, respectively. At the TS, the distance between two oxygen atoms is 1.71, 1.96, and 1.90 Å. On the Cu2O(100)–Cu surface, the O
O bond has already broken at the IS and the distance between two oxygen atoms is 1.47 Å. Moreover, one oxygen atom adsorbs at the off-top site of the surface Cu atom and another oxygen atom adsorbs at the bridge site at both the IS and the TS. However, in the case of Ag2O(100)–Ag and Au2O(100)–Au surfaces, two oxygen atoms are both away from the surface metal atom and the O
O bond does not break at the IS (i.e., the O
O bond length is 1.35 and 1.33 Å, respectively), which is different from that on the Cu2O(100)–Cu surface. On the Ag2O(100)–Ag surface, one oxygen atom adsorbs at the bridge site, with another oxygen atom still at the off-top site of the surface Ag atom at the TS. On the Au2O(100)–Au surface, two oxygen atoms both adsorb at the off-top site of the surface Au atom at the TS. The calculated results show that O2 dissociation reaction is sensitive to the properties of different metal oxides and the order of activation barrier on different metal oxide surfaces for O2 dissociation is Cu2O(100)–Cu<Ag2O(100)–Ag<Au2O(100)–Au, which indeed properly reflects the difference of nobleness among the IB group elements.
In the case of metal-terminated metal oxides, the calculated results indicate that the most stable adsorption site of the oxygen atom and the CO molecule is top and hollow on these surfaces (Table 2). The coadsorption sites of CO+O on metal oxide surfaces are also studied. And the most stable system is found to be CO(hol)+O(top) on all metal oxide surfaces, with the corresponding coadsorption energies, −7.29, −5.28, and −5.66 eV; and the distance between the C atom and the adsorbed oxygen atom, 3.22, 3.47, and 4.28 Å, respectively. The different adsorption sites of CO2 on M2O(100)–M (M=Cu, Ag, Au) surfaces are also considered in order to determine the most stable FS. The calculated results show that the most stable adsorption site of CO2 is all bridge on different surfaces.
On M2O(100)–M (M=Cu, Ag, Au) surfaces, the activation barrier of CO oxidation is calculated to be 1.68, 1.11, and 1.42 eV. The corresponding distance between the C atom and the oxygen atom is 1.86, 2.10, and 2.00 Å at the TS. During the reaction process on Cu2O(100)–Cu and Ag2O(100)–Ag surfaces, the oxygen atom and the CO molecule adsorb at the top and hollow sites at first and then the oxygen atom leans toward the CO fragment with the CO molecule still present at the hollow site at the TS. In the case of Au2O(100)–Au surface, however, at the TS the oxygen atom adsorbs at the bridge site, which moves away from its initial top site, whereas the CO molecule is still at the hollow site. After the TS, the CO2 molecule is formed, which then desorbs from the metal oxide surface.
To check whether the distance between the two adsorbed species at the IS has a significant effect on the calculated activation barrier, a different combination of the CO molecule and the oxygen atom is also studied on the Au2O(100)–Au surface [i.e., CO(hol)+O(bri)]. In this IS configuration, the distance between the C atom and the adsorbed oxygen atom is 4.77 Å, which is longer than that in CO(hol)+O(top) (4.28 Å). The corresponding activation barrier is as high as 2.24 eV compared with 1.42 eV, which has been listed above. Thus, it is clear that the activation barrier largely depends on the initial distance between the C atom and the adsorbed oxygen atom at the IS; namely, the activation barrier increases with the increasing distance between the CO molecule and the oxygen atom. Therefore, the appropriate distance between the CO molecule and the adsorbed oxygen atom at the IS plays an important role in searching for the TS. A similar conclusion has also been drawn by Dabbagh et al., who found that the activation barrier for the elimination of a β-hydrogen from the 2-butanol conformers increases with the increasing distance between β-hydrogen and basic sites.37
Except for the reaction mechanism of CO reacting with the precovered oxygen atom, the other reaction mechanism, namely, CO reacting with molecular O2, is also investigated on M2O(100)–M (M=Cu, Ag, Au) surfaces (Figure 2e). The reaction path is that CO oxidized by molecular O2 involves a four-center OC
O
O intermediate state (labeled as MS) [CO(a)+O2(a)→[OCOO](a)→CO2(g)+O(a)].36 The corresponding geometric parameters of the TS are shown in Figure 2. The reaction mechanism of CO reacting with molecular O2 is similar on all M2O(100)–M (M=Cu, Ag, Au) surfaces (i.e., via TS1, MS, and TS2 from the IS to the FS). Initially, CO adsorbs on the hollow site and molecular O2 adsorbs on the top site on different metal oxide surfaces; that is, the most stable system is found to be CO(hol)+O2(top) on all metal oxide surfaces, with the corresponding coadsorption energies, −4.27, −2.74, and −2.71 eV; the distance between two oxygen atoms, 1.48, 1.42, and 1.28 Å; and the distance between one oxygen atom and one carbon atom being 4.76, 3.06, and 3.71 Å, respectively. On M2O(100)–M (M=Cu, Ag, Au) surfaces, the C atom bonds with one oxygen atom of molecular O2 to form MS. At the MS, the corresponding coadsorption energies are −3.86, −3.12, and −2.87 eV, the shortest distances between two oxygen atoms are 1.52, 1.48, and 1.45 Å, and the distances between one oxygen atom and one C atom are 1.38, 1.35, and 1.39 Å, respectively. At the FS, the shortest distance between two oxygen atoms is 3.84, 5.12, and 4.53 Å on M2O(100)M (M=Cu, Ag, Au) surfaces. The reaction energy of CO reacting with molecular O2 is 0.41, −0.32, and −0.15 eV from the IS to the MS on M2O(100)–M (M=Cu, Ag, Au) surfaces. At the TS1, CO moves to the off-top site of the metal atom, with O2 still present at the initial site. The activation barrier of CO oxidation is calculated to be 0.70, 0.33, and 0.26 eV. The corresponding distance between two oxygen atoms is 1.48, 1.42, and 1.33 Å at the TS1. From the MS to the FS on M2O(100)–M (M=Cu, Ag, Au) surfaces, the reaction energy is −3.12, −2.30, and −2.76 eV. The configuration of the TS2 is similar to that of the MS, and the activation barrier of CO oxidation is calculated to be 0.00, 0.29, and 0.13 eV. The shortest distance between two oxygen atoms is 1.91, 1.96, and 1.85 Å at the TS2. After CO reacts with molecular O2, CO2 is formed and leaves an adsorbed oxygen atom on different metal oxides. Additionally, This oxygen atom can also react with CO to form molecular CO2. The calculated results indicate that the activation barrier of the reaction mechanism of CO reacting with molecular O2 is lower than that of CO reacting with the oxygen atom. Therefore, the molecular O2 mechanism is more favorable than the oxygen atom mechanism on M2O(100)–M (M=Cu, Ag, Au) surfaces.
M2O(100)–O (M=Cu, Ag, Au)
In the case of O-terminated metal oxides, three different reaction pathways are proposed: one is the reaction between molecular CO and Os, second is the reaction between adsorbed CO and Os, and third is the reaction between adsorbed CO and adsorbed oxygen atom.
For the first case, the CO molecule in the gaseous state can react with Os spontaneously to form CO2 on M2O(100)–O (M=Cu, Ag, Au) surfaces (i.e., without activation barrier). For the second case, the CO molecule adsorbs at the sublayer metal atom and then gets oxidized by Os. The calculated results indicate that the most stable combination configuration for CO and Os is found to be CO(bri)+Os on M2O(100)–O (M=Cu, Ag, Au) surfaces, and the distances between the C atom and Os are 2.90, 3.02, and 2.76 Å at the IS (Table 3). And at the TS, the distance between the C atom and Os on these surfaces is 1.89, 1.94, and 1.93 Å. To form a bond with Os, the CO molecule has to overcome an activation barrier of 0.36, 0.19, and 0.59 eV on these metal oxide surfaces (Table 4). The calculated activation barrier is in good agreement with the results of Le et al.,11 who found that the activation barrier of the CO molecule reacting with Os is about 0.40 eV on the Cu2O(100)–O surface. As adsorbed CO reacts with Os, the CO2 molecule is formed, which then desorbs spontaneously leaving an oxygen vacancy at the surface. Therefore, the restoration of the oxygen vacancy by molecular O2 is also calculated. The results show that the activation barrier of the restoration is calculated to be 0.29, 0.38, and 0.62 eV on the reduced surface of M2O(100)–O (M=Cu, Ag, Au). This is in good agreement with the results of Le et al.,11 who found that the activation barrier for the restoration of the oxygen vacancy is 0.30 eV on the Cu2O(100)–O surface. These results suggest that the O-terminated metal oxide surface that gets partially reduced by CO oxidation may be restored by dissociative adsorption of O2 from the surrounding atmosphere. For the third case, the CO molecule adsorbs at the sublayer metal atom and then gets oxidized by the adsorbed oxygen atom, which adsorbs on the top site of the sublayer metal atom on M2O(100)–O (M=Cu, Ag, Au) surfaces. The preadsorbed oxygen atom results from O2 dissociation, and thus the O2 dissociation on M2O(100)–O (M=Cu, Ag, Au) surfaces is also investigated (Figure 2). For O2 dissociation on Cu2O(100)–O, Ag2O (100)–O, and Au2O(100)–O surface, the reaction energy is 1.29, 0.80, and 1.60 eV and the activation barrier is calculated to be 1.56, 1.94, and 2.98 eV, respectively. At the TS, the distance between two oxygen atoms is 2.03, 2.05, and 1.85 Å. Then adsorbed CO reacts with the adsorbed oxygen atom (Table 4). On M2O(100)–O (M=Cu, Ag, Au) surfaces, the activation barrier of CO oxidation is calculated to be 1.37, 0.38, and 0.45 eV. The corresponding distance between the C atom and the oxygen atom is 1.81, 1.87, and 1.93 Å at the TS. The calculated results indicate that the reaction of O2 dissociation on M2O(100)–O (M=Cu, Ag, Au) surfaces is hard to process, although the activation barrier of CO oxidation (CO oxidized by the adsorbed oxygen atom) is low on Ag2O(100)–Ag and Au2O(100)–Au surfaces. Therefore, this reaction mechanism is not favored on oxygen-terminated metal oxide. Our calculated results are in disagreement with the results of Gong et al.,10 who found that the preferred reaction mechanism for CO oxidation is the chemisorbed CO reacting with the adsorbed oxygen atom on platinum metal oxides. The possible reason may arise from the difference in the configuration of the metal oxides; that is, the existence of the surface oxygen on oxygen-terminated IB metal oxides prevents the dissociation of molecular oxygen.
The above DFT results clearly indicate that both the gas phase CO and absorbed CO molecule can react with lattice oxygen on the O-terminated metal oxides, owing to the low activation barrier (especially for the gas phase CO molecule), possibly because the relatively small adsorption energy difference of molecular CO on the metal ion and on the lattice oxygen sites (from 0.70 eV on Cu2O to 0.49 eV on Au2O as shown in Table 3). As the E–R mechanism is a process without barrier, the activity of CO oxidation on IB metal oxides is higher than that on corresponding metals. This is consistent with the experimental results: that the Cu–Cu2O–CuO system for CO oxidation shows higher activity than does the bulk.9 It should be noted that CO oxidation through the reaction path of CO(g)+Os on other metal oxides, such as Co3O4, cannot take place, owing to the large adsorption energy difference of molecular CO on metallic Co and on the lattice oxygen sites (as high as 0.90 eV).38 In addition, the DFT results of Burgel et al. also show that the CO oxidation on Au–O anionic clusters obeys the E–R mechanism whereas the CO oxidation on Au–O cationic clusters can proceed through both E–R and L–H mechanisms.39 The detailed discussion about the influence of the solid structure on the reaction mechanism (E–R versus L–H) will be addressed in a separate paper.
In addition to the above three atomic oxygen mechanisms, the molecular oxygen mechanism (i.e., CO oxidized by molecular O2) is also investigated. However, the four-center intermediate state [OCOO]36 is difficult to find because M2O(100)–O (M=Cu, Ag, Au) surfaces exist on the oxygen atom. Peng et al. proposed another reaction mechanism of CO reacting with adsorbed O2 on the NiO(111) surface.40 Whereas, on M2O(100)–O (M=Cu, Ag, Au) surfaces, it was found that the molecular O2 cannot adsorb on the sublayer metal atom. The possible reason could be that the NiO model used in the work of Peng et al. is the oxygen-defected model, in which O2 can easily adsorb above the Ni atom. However, the M2O(100)–O model adopted in the present work is the ideal one, and thus the surface oxygen would prevent the dissociation of O2. So such an oxygen molecule reaction mechanism is not considered in this work.
Comparison of CO oxidation on IB group metal and metal Oxide surfaces
On the basis of the above calculations, one can know that the adsorption energy of CO/O on metal-terminated metal oxide is higher than that on the metal surface (as seen in Tables 1 and 2). To give a deep insight into the possible reason for such a phenomenon, it is important to analyze its electronic characters. It is well known that the d-band center [Eq. (3)]41–43 and the d-band width [Eq. (4)]44 are the important parameters to characterize the reactivity of a solid metal, but they failed in the case of metal-terminated early-TM carbide surface, owing to the large difference in the electronic properties between metal and carbon atoms.45((3)), ((4))
((3))
((4))
To avoid such problems, a new concept known as “short d-band center” was developed by Chen et al.45 In the short d-band center calculation, the cutoff of 1 Å was used for the surface metal atom. Figure 3 shows the projected density of states onto the metallic d orbital on different surfaces. Clearly, the d-band center of M2O(100)–M is closer to the Fermi energy level as compared with that of pure metals, which results in a larger adsorption energy on the metal-terminated metal oxide. One of the possible reasons could be the strain effect of surface metal caused by the presence of subsurface oxygen in the M2O(100)–M system.45, 46 Interestingly, it is found that the d-band width also correlates well with the d-band center (Figure 4 a), which shows that the wider the d-band width, the further the d-band center away from the Fermi energy level.

Figure 4. Relationships a) between d-band width and d-band center, b) between activation energy and coadsorption energy at the IS, and c, d) between activation barrier and d-band center.
Sun et al. studied CO oxidation catalysis on metal-supported ultrathin oxide films, and they found that thin oxygen-terminated oxide layers can be very active in CO oxidation, owing to the special nature of these surface oxygen atoms.47 Therefore, we calculated the electronic properties of the lattice oxygen atom of the O-terminated metal oxide. The calculated results indicate that the p-orbital center [the p-orbital center is −2.72, −1.97, and −2.99 eV on M2O(100)–O (M=Cu, Ag, Au) surfaces] is consistent with the activation barrier (0.39, 0.19, and 0.59 eV) when CO reacts with the lattice oxygen atom (Figure 3).
The present theoretical results reveal that the activation barrier for the CO oxidation follows the order of M2O(100)–O<M(111)<M2O(100)–M (M=Cu, Ag, Au). Naturally, an interesting question arises: Why is there such a large difference in activity? Liu and Hu48 found that the activation barrier is almost a linear function of the total chemisorption energy of reactants on metals [Ecoads(CO+O)] at the IS for CO oxidation on TM surfaces; that is, the larger the total chemisorption energy of reactants at the IS, the more difficult they are to activate. In fact, this rule holds only for the case of M2O(100)–M (Figure 4 b), but it fails for the cases of M(111) and M2O(100)–O (M=Cu, Ag, Au). To further confirm this point, the more open M(100) (M=Cu, Ag, Au) system has also been explored in this work, and the same result is obtained; namely, Ag(100) shows the smallest energy barrier although the order for Ecoads(CO+O) is Cu(100)>Ag(100)>Au(100). In addition, we have examined the influence of exchange-correlation function on the calculated results, and the same conclusion was drawn by using the PAW-PBE function type. It is interesting to note that the d-band center can be correlated well with the energy barrier for M(111) and M2O(100)–M systems (Figure 4 c,d).
To further explore the possible reasons for activation barrier variation, we analyzed the main factors to control the activation barrier. A convenient way to interpret the stability of the TS has been introduced originally by Hammer for NO dissociation on metal surfaces49 and later used by Dupont et al.50 to explain the CO oxidation process. The formula for adsorption energy at the TS is derived as follows [Eq. (5)]: ((5))
((5))
in which
(CO) and
(O) are the bonding energies of CO and oxygen atom fragments at the TS geometry and
is the interaction energy between the CO molecule and the oxygen atom. This formulation can also be used to analyze the IS system, which can be rewritten as follows [Eq. (6)]:
((6))
Hence, the activation barrier Ea is derived easily as a function of the variations of the adsorption energy summed over the fragment Δ(ΣEfrag) and the variations of the interaction energy, ΔEint, between the IS and the TS [Eq. (7)].((7))
((7))
The contribution to the activation barrier Ea of each term is listed in Table 5. From the results, one can see that the variation in the sum of the adsorption energies Δ(ΣEfrag) is small and the variation trend is the same on M(111) and M2O(100)–M/O (M=Cu, Ag, and Au) surfaces (i.e., from 0.26 to 0.51 eV on metals, from 1.00 to 1.11 eV on M-terminated metal oxide surfaces, and from −0.35 to 0.04 eV on O-terminated metal oxide surfaces), which means its contribution to the activation barrier can be neglected. However, on M2O(100)–M surfaces, the value of Δ(ΣEfrag) is larger than that of ΔEint; this may arise from the large adsorption energy difference of CO and the oxygen atom. In contrast, the second energy term ΔEint in the derivation of Ea is stabilizing and is strongly affected by the chemical nature of different catalysts. This interaction energy variation increases from −0.28 to 0.45 eV on M(111), from 0.00 to 0.57 eV on M2O(100)–M (M=Cu, Ag, Au), and from 0.17 to 0.71 eV on M2O(100)–O (M=Cu, Ag, Au). Therefore, the evolution of the activation barrier primarily follows the variation of the interaction energy ΔEint between the CO molecule and the oxygen atom. This is in good agreement with the results of Dupont et al.,50 who found that the variation of the activation energy primarily follows the variation of the interaction energy between CO and oxygen atom fragments.
| Metal/metal oxide | Ea | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | Δ(ΣEfrag) | ΔEint |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Cu(111) | 0.71 | −4.88 | −0.56 | −4.40 | 0.08 | −5.59 | −0.44 | −4.78 | −0.37 | 0.26 | 0.45 |
| Ag(111) | 0.16 | −3.79 | −0.02 | −3.26 | −0.50 | −3.95 | −0.19 | −3.53 | −0.22 | 0.44 | −0.28 |
| Au(111) | 0.28 | −3.27 | −0.05 | −2.60 | −0.62 | −3.55 | −0.10 | −3.06 | −0.39 | 0.51 | −0.23 |
| Cu2O(100)–Cu | 1.68 | −5.61 | −1.28 | −4.19 | −0.14 | −7.29 | −1.24 | −5.34 | −0.71 | 1.11 | 0.57 |
| Ag2O(100)–Ag | 1.11 | −4.17 | −0.45 | −3.15 | −0.57 | −5.28 | −0.74 | −3.97 | −0.57 | 1.11 | 0.00 |
| Au2O(100)–Au | 1.42 | −4.24 | 0.00 | −3.48 | −0.77 | −5.66 | −0.84 | −3.64 | −1.19 | 1.00 | 0.42 |
| Cu2O(100)–O | 0.36 | −5.33 | −1.04 | −4.75 | 0.46 | −5.69 | −0.64 | −4.80 | −0.25 | −0.35 | 0.71 |
| Ag2O(100)–O | 0.19 | −3.68 | −0.63 | −3.31 | 0.26 | −3.87 | −0.56 | −3.40 | 0.09 | 0.02 | 0.17 |
| Au2O(100)–O | 0.59 | −3.76 | −0.10 | −3.40 | −0.25 | −4.35 | −0.09 | −3.45 | −0.80 | 0.04 | 0.55 |
A careful examination of the IS and TS structures reveals that there is an additional reason (maybe more fundamental) for the different reaction activity of metals and metal oxides, which is the geometrical factor. The process of CO oxidation on metals and metal oxide surfaces can be decomposed into two steps: 1) the oxygen atom movement on metals and metal oxide surfaces and 2) the CO and the oxygen atom move together to achieve the TS. For the adsorbed CO reacting with Os on M2O(100)–O (M=Cu, Ag, Au) surfaces, CO adsorbs on the bridge site of the sublayer metal atom on all metal oxide surfaces at the IS. At the TS, CO moves to the off-top site of the sublayer metal atom, with the Os still being at the initial site. So the activation barrier would mainly be ascribed to the CO movement (0.01–0.40 eV as seen in Table 5), whereas for the reaction on both Ag(111) and Au(111) surfaces, initially CO adsorbs at the top site and the oxygen atom adsorbs at the fcc site. At the TS, the adsorbed oxygen atom is at the bridge site of the surface metal atom, with the CO molecule being at the off-top site. Hence, the activation barrier would mainly be ascribed to the oxygen atom movement [−0.27 and −0.46 eV on Ag(111) and Au(111) surfaces]. In the case of the Cu(111) surface, however, the CO molecule and the oxygen atom are both at the fcc site at the IS whereas the CO molecule moves to the off-top site, with the oxygen atom still being near the fcc site at the TS. The oxygen atom movement is very similar to that on Ag(111) and Au(111) surfaces, whereas the CO movement is quite different. Therefore, the activation barrier would mainly be ascribed to the CO molecule and the oxygen atom movement (0.12 and −0.38 eV). For Ag2O(100)–Ag and Cu2O(100)-u surfaces, at the TS the oxygen atom moves to the off-top site, with CO still being near the hollow site. Therefore, the activation barrier would mainly be ascribed to the oxygen atom movement (−0.82 and −1.15 eV on Ag2O(100)–Ag and Cu2O(100)–Cu surfaces). For the Au2O(100)–Au surface, initially the CO molecule is at the hollow site and the oxygen atom is at the near bridge site at the IS and CO moves to the off-top site and the oxygen atom moves to the bridge site at the TS. Hence, the activation barrier would mainly be ascribed to the CO molecule and the oxygen atom movement (−0.84 and −0.16 eV). In particular, from Table 5, one can see that the adsorption energy difference between the IS and the TS of the CO molecule and the oxygen atom is about −0.12–0.46 eV on metals and −0.84 and 1.15 eV of metal oxides. So the energy difference cost on metal oxides is larger than that on metals for the CO molecule and the oxygen atom movement from the IS to the TS, which results in a high activation barrier on metal oxide surfaces.
Conclusions
- Top of page
- Abstract
- Introduction
- Calculation Methods and Models
- Results and Discussion
- Conclusions
- Acknowledgements
CO adsorption and oxidation on the IB group metals [M(111) (M=Cu, Ag, Au)] and metal oxides [M2O(100) (M=Cu, Ag, Au)] are studied by performing the DFT calculations. The calculated results show that the order of activation barrier for CO oxidation on metal surfaces is Ag(111)<Au(111)<Cu(111); CO oxidation on the Ag2O(100) surface exhibits higher activity than that on Cu2O(100) and Au2O(100) surfaces. Interestingly, we find that gas phase CO and adsorbed CO molecule can react with lattices oxygen easily on the oxygen-terminated metal oxides. In addition, it is found that the activation barrier follows the order of M2O(100)–O<M(111)<M2O(100)–M (M=Cu, Ag, Au), which indicates that the activity of CO oxidation on IB group metal oxides is favored compared with that on the corresponding metals. This is in agreement with the available experimental observations. The detailed analysis of the calculated results indicates that the interaction energy between two adsorbed species at the TS plays an important role in determining the trend in the barrier.
Acknowledgements
- Top of page
- Abstract
- Introduction
- Calculation Methods and Models
- Results and Discussion
- Conclusions
- Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grants No. 20273034 and 20673063) and the TianHe-1 supercomputer.
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