Metal porphyrins (M = Ti, Fe, Co, Ni, Cu, or Zn) as potential catalysts for the oxidation of CO by N₂O: insight from DFT calculations

Abstract

The oxidation of CO by N₂O over M–porphyrin (M = Ti, Fe, Co, Ni, Cu, and Zn) catalysts has been investigated via density functional theory calculations. The whole reaction process is divided into two steps: the catalytic decomposition of N₂O that breaks the N–O bond resulting in O–M active species, and the carbon atoms of the CO molecule reaction with O–M to form CO₂. For the rate-controlled step of the reaction, the porphyrins of different metal centers appear in different positions. The barrier height of N₂O decomposition on Ti–porphyrin is 3.8 kcal mol⁻¹, and the barrier height of CO oxidation is 21.9 kcal mol⁻¹. The rate-controlled step appears in the process of oxidation of CO. However, for Fe–porphyrin, the barrier height of N₂O decomposition is 24.2 kcal mol⁻¹, and the barrier height of CO oxidation is 11.4 kcal mol⁻¹. The rate-controlled step appears in the process of N₂O decomposition. For the catalytic decomposition of N₂O, the Ti–porphyrin has a low activation energy barrier, which may be due to the smaller gap between the highest occupied molecular orbital (HOMO) of the metal porphyrin and the lowest unoccupied molecular orbital (LUMO) of N₂O for Ti–porphyrin compared to Fe–porphyrin.

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Introduction

Nitrous oxide (N₂O) and carbon monoxide (CO) are both potent greenhouse gases that contribute to global warming and damage the ozone layer,¹ and they mainly come from the industrial production and incomplete combustion of automobile fuel. Moreover, carbon monoxide (CO) poisoning is a common disease that endangers people's health. The main mechanism of poisoning is that the binding force of carbon monoxide and hemoglobin is much higher than that of oxygen, resulting in tissue hypoxia, and the aerobic respiratory chain of cells being seriously affected or even blocked.² At present, there is no specific drug for the treatment of carbon monoxide poisoning. Therefore, it is urgent to develop effective CO harmless treatment methods. The accepted method for these two harmful gases is to convert them into less harmful nitrogen (N₂) and carbon dioxide (CO₂),³ and the specific equation involved is N₂O + CO = N₂ + CO₂. However, for this reaction, the high activation energy barrier makes it difficult to carry out at room temperature.⁴ Therefore, it is necessary to develop economic, environmentally friendly, highly reactive, and selective catalysts.

To overcome the reaction energy barrier, numerous catalysts, such as transition metal (TM) cations (Fe⁺, Os⁺, Ir⁺, Pt⁺), have been attempted for activation reactions.⁵ However, the metal ions in the gas phase are mainly used to study the mechanism in the laboratory, which is difficult to be applied in the chemical industry.⁶ Loading TM ions onto oxides is also a widely studied type of catalyst, but this reduces the utilization of TM ions and requires higher reaction temperatures.^3f,7 As a common catalyst, precious metals, such as Pt⁸ and Ag,⁹ have been studied in detail for the reduction treatment of N₂O. However, precious metals are difficult to be applied on a large scale because of their high price, low natural content, and high toxicity.^4a Porphyrins easily form ordered monolayers with two axial coordination through self-assembly, which can be used as catalytic active centers. As a functional site, metal porphyrins can be easily anchored on a variety of carrier bases, so they are used in many applications, such as photovoltaic materials, field-response materials, and catalysts.¹⁰ The coordination between the gas molecules and the metal centers of porphyrins can lead to measurable changes in the electronic properties and color of porphyrins.^10b,11 This phenomenon is due to the interaction between the metal center of porphyrin and some small gas molecules such as NO, CO, and O₂.¹² Therefore, an important application of metal porphyrins is gas sensing. Moreover, metal porphyrins can be fixed as solid phase catalysts and can be widely used to catalyze the reduction of carbon dioxide¹³ and nitrogen oxides¹⁴ as well as the oxidation of hydrocarbons and alcohols.¹⁵

Although metal porphyrins have the excellent performance mentioned above, only the adsorption capacity of N₂O has been reported.^10d,13a Recently, Ehara et al. reported a direct catalytic decomposition of N₂O on Ti–porphyrins and found that it has good catalytic activity and can be used as a potential catalyst for the direct catalytic decomposition of N₂O.¹⁶ However, despite the support of the above outstanding reports, the activation energy of N₂O catalytic decomposition on other transition metal porphyrins has not been studied, which is very important for the direct catalytic decomposition and selective reduction of N₂O. In addition, metal porphyrin is an excellent catalyst for the direct catalytic decomposition of N₂O and other applications. However, using it as a catalyst for N₂O oxidation of CO into CO₂ has not been reported.

Therefore, density functional theory (DFT) was employed to calculate the mechanism of catalytic decomposition of N₂O and oxidation of CO to CO₂ by N₂O on metal porphyrins, as well to study the adsorption, transition state and relative energy. The optimum metal porphyrin catalysts in Ti, Fe, Co, Ni, Cu, and Zn were screened by comparing the barrier height of the N₂O catalytic decomposition. DFT calculation shows that the activation energy barrier of the N₂O decomposition catalyzed by Ti–porphyrin and Fe–porphyrin is lower among these metal porphyrins. Therefore, the whole reaction of CO oxidation by N₂O on these two metal porphyrins were studied. In addition, the molecular frontier orbital, and charge transfer of these two metal porphyrins and N₂O were also analyzed as rate constants using classical transition-state theory (TST), in an attempt to understand the source of the high catalytic activity of these two metal porphyrins. This work elucidates the mechanism of the N₂O oxidation of CO to CO₂ on metal porphyrins, and theoretically identifies suitable catalysts for experiments providing a detailed case for the theoretical design of catalyst.

Fig. 1 The metal porphyrin model used in this study.

Models and method

We chose a metal porphyrin model with 38 atoms as the research object (Fig. 1). All atoms can relax freely, including the metal porphyrins and the small molecules. For the spin state of the metal center, Ehara et al. screened the most stable spin state of each metal porphyrin by investigating the total energies of isolated metal porphyrins.¹⁶ All calculations were performed with the M06-L¹⁷ density functional and the def2-TZVP basis sets¹⁸ for the metal atoms, N atoms and small molecules attached to metal porphyrins. In addition, the 6-31G(d,p) basis set¹⁹ was used for calculatioins for the C and H atoms of metal porphyrins. To verify and confirm the transition states, frequency calculations were performed at the same level of theory to classify the stationary points along the reaction coordinates. In the frequency calculation, zero-point energy (ZPE) was used for energy correction. We also calculated the rate constants using the classical transition-state theory (TST) according to the following equation;
where k is the reaction rate, k_B is Boltzmann's constant, h is Planck's constant, T is the absolute temperature (298.15 K), R is the universal gas constant, ΔG is the free energy difference between the adsorption complex and transition states. Mulliken charge was used because the dispersion function is not involved in the whole calculation. All calculations were carried out using the Gaussian 09 suite of programs, revision D01.²⁰ All 3D images were drawn using CYL-View.²¹

Results and discussion

N₂O Decomposition over M–porphyrin (M = Ti, Fe, Co, Ni, Cu, or Zn)

We first consider the adsorption of reactants N₂O and CO on the M–porphyrin (as shown in Table S1 and Fig. S1, ESI†). The CO molecule can adsorb on the M–porphyrins in two different configurations in which either a C or O atom binds to the metal active site. Regardless of the metal center, the adsorption by the C atom of CO is always stronger than the adsorption by the O atom, which may be due to the negative partial charge located on the C atom. The case of co-adsorption of N₂O and CO on bare Ti and Fe atoms shows that only CO has adsorption behavior on metal atoms, while N₂O does not. By comparing the adsorption energy of N₂O and CO (both ways), we found that CO adsorbs more strongly than N₂O. Subsequently, CO may obstruct the active site of M–porphyrins for N₂O adsorption and N–O bond breaking. Although one possibility proposed by Sombat Ketrat et al.,^3e the N₂O reaction should be allowed to break the N–O bond and form active O, followed by the CO oxidation reaction. However, we suggest that the strong adsorption of CO at the M–porphyrin results in the occupation of the active site, which may block the breaking of the N–O bond in N₂O to form the M–O complex, and this cannot be ignored.

Next, we explored the reaction mechanism of N₂O decomposition over M–porphyrin (M = Ti, Fe, Co, Ni, Cu, or Zn), as shown in Fig. 2. The selection of a suitable catalyst is based on the barrier height of N₂O direct catalytic decomposition. In the adsorption complex formed by each metal porphyrin and N₂O, the structure of N₂O significantly changed, the O–N bonds have an elongation from 0.07 Å to 0.69 Å. This indicates that the coordination action of the metal active center of M–porphyrin can activate the O–N bond in N₂O. Relative to others, adsorption energy of −8.8 kcal mol⁻¹ was provided by Ti–porphyrin (triplet) and −2.0 kcal mol⁻¹ was provided by Fe–porphyrin (triplet), while other M–porphyrin exhibited adsorption energies in the range of 0.3 to 1.9 kcal mol⁻¹. For the activation energy barrier, Ti–porphyrin had an activation energy barrier of 3.7 kcal mol⁻¹ and Fe–porphyrin had an activation energy barrier of 24.2 kcal mol⁻¹, while others exhibited higher activation energy barrier in the range of 38.3 to 58.9 kcal mol⁻¹. This indicates that the catalytic activity of Ti–porphyrin is the best of all and Fe–porphyrin has the lowest barrier height. Therefore, Ti–porphyrin and Fe–porphyrin were selected as the catalysts for the subsequent reactions.

Fig. 2 Energy profile of N₂O decomposition over M–porphyrin.

Reaction mechanism of CO oxidation by N₂O on Ti–porphyrin

Subsequently, we have fully studied the reaction mechanism of CO oxidation by N₂O on Ti–porphyrin and Fe–porphyrin. The reaction energy profile of N₂O direct decomposition over Ti–porphyrin consists of N₂O adsorption, N–O bond scission, and N₂ desorption shown in Fig. 3. AD1_Ti is the complex form of the N₂O adsorbed to the Ti–porphyrin by an O atom. The distance of the Ti–O bond is 2.26 Å, O–N bond has a certain extent of elongation, changing from 1.18 Å to 1.19 Å. The calculated adsorption energy is −8.8 kcal mol⁻¹. The O–N in TS1_Ti further elongates to 1.25 Å, unlike adsorbed complex, N–N length changes from 1.12 Å to 1.14 Å. N₂O is no longer a straight-line molecule, ∠ON1N2 going from a straight angle to 151.4° and having the angle between Ti–O and the porphyrin plane as 90.0°. Moreover, the Ti–O bond changed from 2.26 Å to 2.02 Å where as TS1_Ti has one imaginary frequency of 441.28i cm⁻¹ has an activation energy of 3.8 kcal mol⁻¹ which corresponds to AD1_Ti. The Ti active center extracts an oxygen atom from the adsorbed N₂O to form IM1_Ti, which contains Ti–O active species and N₂. After the TS1_Ti, the dissociation complex in the IM1_Ti formation process was an exothermic process of 67.5 kcal mol⁻¹, where the Ti–O bond was shortened from 2.02 Å to 1.62 Å, and the length of the O–N bond was elongated to 3.29 Å. Compared with the transition state, the Ti–O bond in the decomposition complex has formed, and there is almost no interaction between Ti–O active species and N₂, the desorption of N₂ requires 2.1 kcal mol⁻¹.

Fig. 3 Energy profile and selected geometric parameters of transition states and intermediates involved in the oxidation of CO by N₂O on Ti–porphyrin.

For the oxidation of CO by N₂O on Ti–porphyrin, the adsorption of CO on the Ti–O active material is weaker than N₂O on Ti–porphyrin with the adsorption energy of −2.9 kcal mol⁻¹, which is an exothermic process. In the adsorption complex named AD2_Ti, the distance between the C atom in CO and the O atom of the Ti–O active substance is 2.97 Å, and the CO with O atom forms an angle of 92.0°. The TS2_Ti with a frequency of 982.22i cm⁻¹ has been found. In this transition state, the Ti–O bond was elongated from 1.62 Å to 1.73 Å with the distance between the C atom and the reactive oxygen species reduced from 2.97 Å to 1.77 Å, the C–O bond in CO extends from the original distance of 1.13 Å to 1.15 Å, where the CO with the reactive oxygen species forms an angle of 115.2°. In addition, the Ti–O bond forms a 98.2° angle with the porphyrin plane. This step is required to overcome the activation energy barrier of 21.9 kcal mol⁻¹. In IM2_Ti, the C–O bond of the CO₂ was formed, from 1.77 Å to 1.17 Å, close to CO₂. The desorption energy of CO₂ is 8.8 kcal mol⁻¹, higher than 2.1 kcal mol⁻¹, which is from the desorption of N₂. It is possible that CO₂ is generated in this step, but N₂ escapes much more easily than CO₂. The oxidation of CO by O–Ti–porphyrin has a higher activation energy barrier than the direct catalytic decomposition of N₂O; therefore, the part of oxidation of CO is the rate-controlled step of the whole reaction, with the barrier height of 21.9 kcal mol⁻¹.

In summary, during the decomposition of N₂O on Ti–porphyrin, the N₂O can be easily attached to the Ti atom, and the reaction needs to overcome a low activation energy barrier of 3.8 kcal mol⁻¹. However, the activation energy barrier for the subsequent oxidation of CO to CO₂ is 21.9 kcal mol⁻¹, which is higher than the direct catalytic decomposition of N₂O. Therefore, the oxidation of CO is the rate-control step of the whole reaction.

Reaction mechanism of CO oxidation by N₂O on Fe–porphyrin

As shown in Fig. 4, for Fe–porphyrin, N₂O is adsorbed to the Fe atom through the O atom to form the adsorption complex AD1_Fe. The adsorption energy of N₂O on Fe–porphyrin is −2.0 kcal mol⁻¹, which is higher than that on Ti–porphyrin. The Fe–O distance is 2.69 Å, and there is no significant change in O–N and N–N distances, which are 1.18 Å and 1.13 Å respectively. Unlike on Ti–porphyrin, the O–N in TS1_Fe elongates to 1.48 Å, with no change in the N–N bond. N₂O is no longer a straight-line molecule, ∠ON1N2 goes from a straight angle to 135.1°and the angle between the Fe–O and the porphyrin plane is 93.9°. Moreover, Fe–O bond has changed from 2.69 Å to 1.86 Å. The TS1_Fe with one imaginary frequency of 708.38i cm⁻¹ has an activation energy of 24.2 kcal mol⁻¹, which is higher than Ti–porphyrin. The Fe active center extracts an O atom from the adsorbed N₂O to form IM1_Fe, which contains Fe–O active species and N₂. The dissociation complex IM1_Fe formation process after the TS1_Fe was an exothermic process of 46.0 kcal mol⁻¹, the Fe–O bond was shortened from 1.86 Å to 1.62 Å, and the length of the O–N bond elongated to 3.18 Å. Compared with the transition state, the Fe–O bond in the decomposition complex has formed, and there is almost no interaction between Fe–O active species and N₂, the desorption of N₂ requires 2.3 kcal mol⁻¹, which is comparable to the desorption of N₂ on Ti–porphyrin.

Fig. 4 Energy profile and selected geometric parameters of transition states and intermediates involved in the oxidation of CO by N₂O on Fe–porphyrin.

Unlike on Ti–porphyrin, for the oxidation of CO by O–Fe–porphyrin, the adsorption of CO on the Fe–O active material is stronger than N₂O on Fe–porphyrin and the adsorption energy is −3.0 kcal mol⁻¹, which is an exothermic process. In the adsorption complex named AD2_Fe, the distance between the C atom in CO and the reactive oxygen species of the Fe–O active substance is 2.89 Å, and the CO and reactive oxygen species form an angle of 92.2°. TS2_Fe with a frequency of 982.22i cm⁻¹ has been found. In the transition state, the Fe–O bond was elongated from 1.62 Å to 1.69 Å. The distance between the C atom and the reactive oxygen species is reduced from 2.89 Å to 1.75 Å, the C–O bond in CO extends from the original 1.13 Å to 1.15 Å and the CO and reactive oxygen species form an angle of 117.7°. Besides these, the Fe–O bond forms a 98.4° angle with the porphyrin plane. This step requires overcoming the activation energy barrier of 11.4 kcal mol⁻¹, which is lower than Ti–porphyrin. In IM2_Fe, the C–O bond of CO₂ has formed, from 1.75 Å to 1.16 Å, close to CO₂. The desorption energy of CO₂ is 4.9 kcal mol⁻¹, higher than 2.3 kcal mol⁻¹, which is from the desorption of N₂. Although the desorption energy of CO₂ is slightly higher than N₂, they both are relatively low, indicating that desorption is not difficult.

Different from Ti–porphyrin, CO oxidation is no longer a rate-controlling step on Fe–porphyrin, and the barrier height of N₂O decomposition is significantly higher than that of CO oxidation. Therefore, in the reaction of Fe–porphyrin, N₂O decomposition is the rate-controlling step of the whole reaction, and the barrier height is 24.2 kcal mol⁻¹.

The energy profile of CO oxidation by N₂O on Ti–porphyrin and Fe–porphyrin are placed over each other in Fig. 5. As shown in the figure, for Ti–porphyrin, CO oxidation is the reaction rate control step, the barrier height is 21.9 kcal mol⁻¹; on the contrary, for Fe–porphyrin, the decomposition of N₂O is the rate-controlling step of the whole reaction, and the barrier height is 24.2 kcal mol⁻¹. The barrier height of N₂O catalyzed decomposition on Ti–porphyrin is 2.3 kcal mol⁻¹, which is lower than Fe–porphyrin (24.2 kcal mol⁻¹), and both are significantly lower than 33.08 kcal mol⁻¹ obtained from Cu-ZSM-5 by Zhang et al.²² The barrier height for CO oxidation on O–Fe–porphyrin is 11.4 kcal mol⁻¹, which is lower than that on O–Ti–porphyrin (21.9 kcal mol⁻¹), and both are lower than 135.5 kcal mol⁻¹ from B₁₁N₁₂Al⁺ and 165.1 kcal mol⁻¹ from B₁₁N₁₂⁺ obtained by Xiufang Hou et al.,^3c and 25.4 kcal mol⁻¹ from Ge–Gr^4a and 25.4 kcal mol⁻¹ from PN₄-Gr obtained by Mehdi D. Esrafili.²³ Furthermore, we studied the direct catalytic decomposition of the second N₂O on O–Ti–porphyrin and O–Fe–porphyrin, and found that for O–Ti–porphyrin, the breaking of the N–O bond of the second N₂O needs to overcome the barrier height of 38.8 kcal mol⁻¹. This is much higher than the 3.8 kcal mol⁻¹ required for the first N₂O decomposition and 21.9 kcal mol⁻¹ required for CO oxidation on O–Ti–porphyrin. For the O–Fe–porphyrin, the breaking of the N–O bond in the second N₂O needs to overcome the barrier height of 74.2 kcal mol⁻¹, which is much higher than the 24.2 kcal mol⁻¹ required for the first N₂O decomposition, and much higher than the 11.4 kcal mol⁻¹ required for CO oxidation in O–Fe–porphyrin. Therefore, the reaction of N₂O on M–porphyrin tends to stay in O–M–porphyrin rather than a further reaction to produce O–O–M–porphyrin (as shown in Fig. S6 and S7, ESI†).

Fig. 5 Energy profile of the catalytic oxidation of CO by N₂O on Ti–porphyrin and Fe–porphyrin.

Table 1 Activation energies and reaction rates of the N–O breaking step of N₂O

M–porphyrin	ΔEact (kcal mol^−1)^a	k 298.15 (s^−1)^b
a From ETS – EAD. b From the transition state theory (TST).
Ti–porphyrin	3.73	1.16 × 10^10
Fe–porphyrin	24.22	1.13 × 10^−5
Co–porphyrin	38.28	5.76 × 10^−16
Ni–porphyrin	52.34	2.91 × 10^−26
Zn–porphyrin	51.83	6.81 × 10^−26
Cu–porphyrin	58.82	5.18 × 10^−31

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Table 2 Activation energies and reaction rates of the C–O forming step of CO₂

O–M–porphyrin	ΔEact (kcal mol^−1)^a	k 298.15 (s^−1)^b
a From ETS – EAD. b From the transition state theory (TST).
O–Ti–porphyrin	21.87	6.00 × 10^−4
O–Fe–porphyrin	11.41	2.72 × 10^4

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Activation energies and reaction rates

Moreover, from the series of activation energies, we can also calculate the reaction rates of the N–O breaking step and C–O forming step (shown in Tables 1 and 2) using simple transition-state theory (TST). These show the reaction rates of the N–O breaking step to be in the order Ti–porphyrin > Fe–porphyrin > Co–porphyrin > Ni–porphyrin > Zn–porphyrin > Cu–porphyrin. The reaction rates of the C–O forming step are in the order O–Fe–porphyrin > O–Ti–porphyrin. The results correlate with the Irving–Williams series.

Energy levels and shapes of the frontier molecular orbitals

We further studied the HOMO orbital distribution and the energy levels of Ti–porphyrin and Fe–porphyrin, and the LUMO orbital distribution of N₂O molecules, as shown in Fig. 6. The results show that the HOMO energy of Ti–porphyrin is −82.8 kcal mol⁻¹ and that of Fe–porphyrin is −113.3 kcal mol⁻¹. The energy difference between HOMO of Ti–porphyrin and LUMO of N₂O is 60.6 kcal mol⁻¹; however, the energy difference between the HOMO of Fe–porphyrin and LUMO of N₂O is 91.1 kcal mol⁻¹; Ti–porphyrin and N₂O have a small energy gap, but the energy gap of Fe–porphyrin and N₂O is bigger than Ti–porphyrin. This could explain why Ti–porphyrin is more active than Fe–porphyrin in the catalytic decomposition of N₂O into N₂ and O–M active substances. Moreover, we did the same analysis for the oxidation process of CO and found that the energy difference between the HOMO of O–Fe–porphyrin and LUMO of CO was 7.8 kcal mol⁻¹ lower than O–Ti–porphyrin.

Fig. 6 (a) Energy levels and shapes of the frontier molecular orbitals of M–porphyrin and N₂O; (b) energy levels and shapes of the frontier molecular orbitals of O–M–porphyrin and CO (energies in kcal mol⁻¹).

Conclusions

In conclusion, DFT calculations have been performed to investigate the mechanism of CO oxidation by N₂O on M–porphyrin (M = Ti, Fe, Co, Ni, Cu, and Zn). The reaction mechanism began with the breaking of the N–O bond in adsorbed N₂O to form the M–O active species intermediate. The O atom of M–O active species then reacts with the CO molecule via the C–O bond formation to produce CO₂. For the reaction on Ti–porphyrin, the activation energy barrier height of N₂O decomposition is 3.8 kcal mol⁻¹, and the energy barrier of CO oxidation by Ti–O active species to CO₂ is 21.9 kcal mol⁻¹, so the CO oxidation process is the rate-control step of the whole reaction. For the reaction on Fe–porphyrin, the activation energy barrier height of N₂O decomposition is 24.2 kcal mol⁻¹, and the energy barrier of CO oxidation by O–Fe active species to CO₂ is 11.4 kcal mol⁻¹, so the N₂O decomposition process is the speed control step for the whole reaction. The rate constant between the adsorbed complex and the transition state of the N–O bond fracture and C–O bond formation processes is extracted (by transition state theory). Finally, the distribution and energy levels of the HOMO of M–porphyrin and LUMO of N₂O were studied. It is found that the low energy gap corresponds to the low activation energy barrier, which could explainmore active Ti–porphyrin being more active than Fe–porphyrin in the catalytic decomposition of N₂O into N₂ and O–M active substances. A harmless catalyst for the treatment of N₂O and CO has been screened in theory, which will provide valuable guidance for experimental research.

Author contributions

S.-T. Wang conceived the scientific research project. S.-T. Wang and Z. Liu completed the main content of this study. Y.-J. Ye performed the drawing of pictures in this paper. Y.-J. Ye, X. Meng and P.-C. Yang completed data collation and proofreading. Z.-Z. Zhang is responsible for maintaining the computing cluster. S.-T. Wang, Z. Liu, Y.-F. Qiu and J.-Q. Lei wrote the original manuscript. Y.-F. Qiu and J.-Q. Lei completed review and proofreading of the manuscript. J.-Q. Lei revised the manuscript.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

We gratefully acknowledge the National Natural Science Foundation of China (No. 81960323). This work was carried out in Shanxi Supercomputing Center of China, and the calculations were performed in Tianhe-2. We thank associate professor Hong Gao (Lanzhou University) for helpful discussion.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d2nj04440d

‡ These authors contributed equally to this work.

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