A Density Functional Theory and Microkinetic Study of Acetylene Partial Oxidation on the Perfect and Defective Cu₂O (111) Surface Models

Abstract

The catalytic removal of C₂H₂ by Cu₂O was studied by investigating the adsorption and partial oxidation mechanism of C₂H₂ on both perfect (stoichiometric) and Cu_CUS-defective Cu₂O (111) surface models using density functional theory calculations. The chemisorption of C₂H₂ on perfect and defective surface models needs to overcome the energy barrier of 0.70 and 0.81 eV at 0 K. The direct decomposition of C₂H₂ on both surface models is energy demanding with the energy barrier of 1.92 and 1.62 eV for the perfect and defective surface models, respectively. The H-abstractions of the chemisorbed C₂H₂ by a series of radicals including H, OH, HO₂, CH₃, O, and O₂ following the Langmuir–Hinshelwood mechanism have been compared. On the perfect Cu₂O (111) surface model, the activity order of the adsorbed radicals toward H-abstraction of C₂H₂ is: OH > O₂ > HO₂ > O > CH₃ > H, while on the defective Cu₂O (111) surface model, the activity follows the sequence: O > OH > O₂ > HO₂ > H > CH₃. The Cu_CUS defect could remarkably facilitate the H-abstraction of C₂H₂ by O₂. The partial oxidation of C₂H₂ on the Cu₂O (111) surface model tends to proceed with the chemisorption process and the following H-abstraction process rather than the direct decomposition process. The reaction of C₂H₂ H-abstraction by O₂ dictates the C₂H₂ overall reaction rate on the perfect Cu₂O (111) surface model and the chemisorption of C₂H₂ is the rate-determining step on the defective Cu₂O (111) surface model. The results of this work could benefit the understanding of the C₂H₂ reaction on the Cu₂O (111) surface and future heterogeneous modeling.

1. Introduction

Acetylene (C₂H₂) is a kind of important industrial raw materials used for various purposes, including oxyacetylene welding, cutting, illuminant, soldering metals, signaling, precipitating metals, particularly copper, manufacture of acetaldehyde, acetic acid, etc. [1]. C₂H₂ is a significant intermediate formed during the combustion of hydrocarbons, especially under fuel-rich conditions, which is responsible for the soot formation during combustion processes via the H-abstraction-C₂H₂-addition (HACA) mechanism [2,3]. The production of C₂H₂ during combustion could endanger the safety and efficiency of combustors, etc. C₂H₂ is also a component of volatile organic compounds (VOCs), and it gains increasing attention due to its toxicity to the environment and human health. Exposure to high concentrations of C₂H₂ may cause loss of consciousness or even death, and it is a serious fire and explosion hazard. C₂H₂ is an undesirable by-product of the petroleum cracking process, and it causes damage to the catalyst for the ethylene polymerization process [4]. To address the problems caused by C₂H₂ formation and emission, the efficient removal of C₂H₂ during combustion and industrial processes is of great interest. To the best of our knowledge, much attention has been paid to the study of C₂H₂/hydrocarbons homogeneous kinetics under pyrolysis [5,6], oxidation [3,7], and flame conditions [2], and kinetic models predicting the reaction characteristics under these conditions have been proposed [3,7], while relatively less attention has been paid to the heterogeneous processes of C₂H₂.

Catalytic removal is an important technique in exhaust gas purification, and the activity of catalysts plays a crucial role in the catalytic process. Previous studies have shown that Cu₂O thin film catalysts prepared by the pulsed-spray evaporation chemical vapor deposition (PSE-CVD) method are effective for the catalytic removal of C₂H₂ [8], but the oxidation mechanism of C₂H₂ on the Cu₂O surface remains unclear. Theoretical studies based on density functional theory (DFT) calculations have been widely used as an effective tool in revealing the gas-surface heterogeneous reaction mechanisms on Cu-based oxide surfaces [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. DFT studies regarding the C₂H₂ hydrogenation process have been reported previously. Zhang et al. [27,28] have studied C₂H₂ hydrogenation to ethylene using DFT calculations, and it is found that the valence state of the surface Cu site has an important impact on the surface catalytic ability toward the C₂H₂ hydrogenation to ethylene. Good command of the surface oxidation mechanism could be beneficial for the development of high-performance catalysts. Experiments could provide useful information by studying the dependency of catalysts’ performance on the preparation methods and macroscopic parameters, such as temperature, pressure, PH, etc. Proper characterizing techniques, such as SEM, XPS, XRD, etc., could also throw light upon the surface morphology and surface properties, which could help better understand the nature of the catalytic process. In addition, theoretical studies based on DFT calculations could also reveal the intrinsic surface reaction mechanism, and the effect of surface sites and vacancies on the catalytic performance is still needed. The establishment of a proper surface model is of importance for the theoretical investigation of the C₂H₂ partial oxidation process on the Cu₂O surface. The Cu₂O (111) plane is the most widely used surface model to reveal the heterogeneous reaction mechanism on the Cu₂O surface due to its thermodynamic stability, while many of them used the bulk-terminated models (the stoichiometric surface model or the perfect surface model) [13,16,29,30,31] but not the more stable Cu₂O (111)–Cu_CUS surface model as proposed by Soon et al. [32], and the importance of the Cu_CUS vacancy has also been confirmed by Önsten et al. [33] experimentally. Our previous study also found that the defective Cu₂O (111)–Cu_CUS surface model could improve the surface activity toward CO oxidation [34] than the perfect one. Therefore, it is of significance to consider the surface defects when studying Cu₂O surface chemistry.

To provide a better understanding of the reaction mechanism of C₂H₂ on the Cu₂O surface, the adsorption and reaction processes of C₂H₂ on the Cu₂O surface models were studied based on DFT calculations in this study. The reaction processes of C₂H₂ on the Cu₂O surface models, including the adsorption process, decomposition process, and H-abstraction reactions, by a variety of radicals and O₂ have been studied. The effect of the surface defect on the C₂H₂ elementary reaction steps has been explored by studying the C₂H₂ conversion on both the stoichiometric perfect Cu₂O (111) surface model and the Cu₂O (111)-Cu_CUS defective surface model. The rate constants have been calculated and the parameters are provided in the Arrhenius form, which could be helpful for heterogeneous kinetic modeling studies.

2. Computational Details

DFT calculations were performed using the DMol³ code [35,36]. The generalized gradient approximation (GGA) functional of Perdew–Burke–Ernzerhof (PBE) [37] was used for exchange and correlation potential. The double numerical basis set plus the polarization (DNP) basis set was used for all the calculations. The DFT semi-core pseudopots (DSPP) core treatment was used for inner core pseudopotential treatment, which introduces relativistic correction into the cores. Transition state structures were preliminarily searched by the combination of linear synchronous transit (LST) and quadratic synchronous transit (QST) method and then optimized using the eigenvector following (EF) method to validate only one imaginary vibrational mode, which corresponds to a first-order saddle point on the potential energy surface and correctly connects the reactant and the product of each elementary reaction.

A higher computational accuracy has been used in the current work compared with our previous works [29,34]. The orbital cut-off has increased from 4.0 to 4.4 Å, and the convergence threshold of the self-consistent field (SCF) has increased to 1.0 × 10⁻⁶ from 1.0 × 10⁻⁵. The convergence criteria of energy, maximum force, and maximum displacement are 1.0 × 10⁻⁵ Ha, 0.002 Ha/Å, and 0.005 Å, respectively. For the crystal optimization, a 4 × 4 × 4 Monkhorst–Pack k-point grid was used. The surface planes were built by cleaving the Cu₂O (111) surface from the optimized Cu₂O crystal. A sheet of 10 Å vacuum layer was placed over the surface slab to avoid interference from imaging surface planes due to the periodic boundary conditions. The defective surface model was established by removing the top and bottom layer unsaturated Cu_CUS sites. A 3 × 3 × 1 Monkhorst–Pack k-point grid was used for the energy calculations of the succeeding surface reactions.

Adsorption energy ($E_{\mathrm{ad}}$) is used to evaluate the interaction between the surface and the adsorbate, which is defined as:

$$E_{\mathrm{ad}}=E_{\mathrm{sys}}-E_{\mathrm{ads}}-E_{\mathrm{sur}}$$

(1)

where $E_{\mathrm{sys}}$ is the energy of the system after adsorption; $E_{\mathrm{ads}}$ is the energy of the adsorbate before adsorption; $E_{\mathrm{sur}}$ is the energy of the clean surface before adsorption.

The Gibbs free energy of activation was calculated by combining zero-point energy (ZPE), the electronic energies calculated at 0 K, and the thermal corrections at elevated temperatures. For surface species, the translations and rotations were converted into frustrated oscillation modes and were included in the vibration analysis [38]. Reaction rate constants of elementary reaction steps were calculated based on harmonic transition-state theory (HTST) [29,34,38,39], which is $k=\frac{k_{\mathrm{B}}T}{h}\left(\frac{-\mathsf{\Delta }{G}_a}{RT}\right)$, where k is reaction rate constant, k_B is the Boltzmann constant, T is temperature, h is the Planck constant, R is the universal gas constant, and $\mathsf{\Delta }{G}_a$ is the Gibbs free energy of activation. Detailed calculation processes can be found elsewhere [34,40].

3. Results and Discussion

3.1. Perfect and Defective Cu₂O (111) Surface Models and C₂H₂ Adsorption

The (111) surface plane of Cu₂O crystal has been used throughout this study as it is the most thermodynamically stable and, therefore, dominantly exposed low-index surface plane [29,34,41,42]. The perfect and the Cu_CUS-defective Cu₂O (111) surface models have been established, as shown in Figure 1. The lattice constant of the perfect Cu₂O (111) crystal after geometric optimization is 4.33 Å as a result of the improved convergence accuracy, which is close to the previously reported values (4.32 Å [43]) and experimental values (4.27 Å [23]). The perfect Cu₂O (111) surface model is stoichiometric with the Cu/O ratio to be exactly two, and it contains four kinds of surface top-sites on the top layer, including the saturated copper (Cu_CSS) site, the saturated oxygen (O_CSS) site, the unsaturated copper (Cu_CUS), and the unsaturated oxygen (O_CUS) site, while the defective Cu₂O (111) surface model only comprises the Cu_CSS, O_CSS, and O_CUS sites, as the top and bottom Cu_CUS sites are missing. The Cu_CUS sites are active in absorbing the molecules, but the strong covalent bond between the adsorbate and the Cu_CUS sites may hinder the following surface reactions.

The stable adsorption structure of C₂H₂ on the Cu₂O (111) surface was explored by comparing the adsorption energies of C₂H₂ on different surface sites of the Cu₂O (111) surface models. One C₂H₂ molecule was placed on different surface sites, including the surface Cu_CUS site, the Cu_CSS site, the O_CUS site, and the O_CSS site, and the adsorption energies were obtained after the geometric optimization process. Only the most stable adsorption structure corresponding to the largest adsorption energy is presented.

The adsorption processes of C₂H₂ on the perfect and defective Cu₂O (111) surface models are shown in Figure 2. For the adsorption on the perfect Cu₂O (111) surface model, a C₂H₂ molecule will first adsorb over the surface unsaturated Cu_CUS site with the energy release of 1.13 eV, and the linear structure of C₂H₂ is slightly distorted with the O–C–C angles decreasing from both 180° to 162° and 169°. The C–C bond length of C₂H₂ increases to 1.242 from 1.211 Å in the gas phase and the C-H bond length also increases to 1.077 and 1.081 from 1.071 Å. The activated C₂H₂ molecule will then overcome the energy barrier of 0.70 eV and interacts with one surface lattice O_CUS site and its neighboring Cu_CUS site and one Cu_CSS site, forming a chemisorbed structure depicted as FS in Figure 2a with the heat release of 1.78 eV in total. For the same process on the defective Cu₂O (111) surface model. One C₂H₂ molecule will first undergo a physisorption process releasing 0.20 eV. The bond length of the C–H bond close to the surface increases to 1.076 Å, while the bond lengths of the other C–H bond and the C–C bond are almost unchanged after physisorption. The physisorbed C₂H₂ will then overcome the energy barrier of 0.81 eV and react with the surface O_CUS site to form an adsorbed CHCHO* species, which is bonded to three surface Cu_CSS sites. The whole reaction process on the defective Cu₂O (111) surface model releases 1.26 eV. By comparison, the perfect Cu₂O (111) surface model is more favorable for the C₂H₂ adsorption at 0 K with a lower energy barrier and larger energy release, which is due to the existence of the active Cu_CUS site in activating the C₂H₂ bond.

3.2. Decomposition of C₂H₂ on the Perfect and the Defective Cu₂O (111) Surface Models

The direct decomposition processes of the chemisorbed C₂H₂* molecule undergoing the cleavage of the C-H bond on the Cu₂O (111) surface models are first investigated, which represents the surface activity toward C₂H₂ direct decomposition when there are no other adsorbates on the surface. Reaction energy profiles and the structures of the initial states, transition states, and final states are provided in Figure 3. The energy barrier of the reaction process on the perfect Cu₂O (111) surface model is 1.92 eV, and the reaction is an exothermic process releasing 0.21 eV. The adsorbed C₂H₂ molecule will undergo an H-abstraction process, and the H atom will shift to the surface Cu_CUS site after the H-abstraction process. The C₂H part will react with the lattice O_CUS site and form an adsorbed HCCO* species on the surface after the reaction. The H-C-C part of the formed HCCO* species has a nearly linear structure with the H-C-C angle to be 177°. As for the direct decomposition of C₂H₂ on the defective Cu₂O (111) surface model, the energy barrier has increased to 2.46 eV, and the reaction is an endothermic process adsorbing 0.36 eV. Therefore, the decomposition of the chemisorbed C₂H₂ on both the perfect and the defective Cu₂O (111) surface models is hard to happen in terms of the reaction energy barrier, and the perfect Cu₂O (111) surface model is more favorable than the defective one comparatively, which is due to the existence of the neighboring active Cu_CUS site.

3.3. H-Abstraction Reactions of Chemisorbed C₂H₂ by O₂ on the Cu₂O (111) Surface Models

The H-abstraction reactions are important in the consumption of C₂H₂, hence the H-abstraction of the chemisorbed C₂H₂ by O₂ was studied in this section. The Langmuir–Hinshelwood reaction mechanism featuring the reaction between two adsorbed molecules on the perfect and defective Cu₂O (111) surface models is studied. The left part of Figure 4 shows the H-abstraction process on the perfect Cu₂O (111) surface model. The surface unsaturated Cu_CUS site is active for O₂ adsorption, and an O₂ molecule will adsorb on the Cu_CUS site close to the chemisorbed C₂H₂ molecule, releasing 1.09 eV. Then, one H atom of the chemisorbed C₂H₂ will transfer to the adsorbed O₂ forming an adsorbed HO₂ molecule by overcoming the energy barrier of 1.43 eV. The reaction releases 0.23 eV with the formation of an adsorbed HO₂ and an adsorbed HCCO species on the surface.

The energy profile of C₂H₂ H-abstraction by O₂ on the defective Cu₂O (111) surface model is shown in the right part of Figure 4. An O₂ molecule will first adsorb on the surface hollow site, and the chemisorbed C₂H₂ needs to overcome the energy barrier of 0.97 eV to react with the adsorbed O₂ and form an HO₂ on the hollow site with an energy release of 0.86 eV. An adsorbed HCCO species is formed after the reaction on top of three Cu_CSS sites. Compared with the perfect surface model, the H-abstraction of C₂H₂ by O₂ on the defective Cu₂O (111) surface is easier with a lower energy barrier and a larger energy release. The homogeneous H-abstraction of C₂H₂ by O₂ is also calculated for comparison purposes, and the reaction is a strong endothermic process adsorbing 3.59 eV. Therefore, both the perfect and the defective Cu₂O (111) surface models are favorable for the H-abstraction process of C₂H₂ by O₂ from the thermodynamic point of view, and the Cu_CUS defect will be beneficial for the H-abstraction of C₂H₂ by O₂.

3.4. H-Abstraction and H-Addition of Chemisorbed C₂H₂ by Atomic H

The reaction between a chemisorbed C₂H₂ and an adsorbed atomic H via the LH mechanism is further studied in this section. The neighboring adsorbed atomic H, as shown in Figure 5, is bonded to the surface unsaturated Cu_CUS site, and it could attack the chemisorbed C₂H₂ and form an adsorbed H₂ and an adsorbed HCCO species together with a lattice O_CUS. The reaction process is endothermic with energy adsorption of 0.78 eV, and the energy barrier is 2.75 eV. The chemisorbed C₂H₂ could also react with an adsorbed H together with the lattice O to form a CH₂CHO species, as shown in the right part of Figure 5, on the perfect Cu₂O (111) surface model. The energy barrier of the reaction process is 1.78 eV, which is lower than that of the H-abstraction reaction of the adsorbed C₂H₂ with an energy barrier of 2.75 eV. In terms of the reaction energy, the formation of CH₂CHO needs to adsorb 0.67 eV, while the H-abstraction process adsorbs 0.78 eV. Therefore, the adsorbed C₂H₂ is more likely to be converted to CH₂CHO when reacting with an adjacent adsorbed H together with a lattice O_CSS site on the perfect Cu₂O (111) surface model.

3.5. A Comparison of H-Abstraction Reactions of Chemisorbed C₂H₂ by Different Radicals

The energy profile of the interaction between the chemisorbed C₂H₂ species and the pre-adsorbed oxygen molecule and radicals, including H, OH, O, HO₂, and CH₃, on the perfect Cu₂O (111) surface model are compared in Figure 6. The IS state also incorporates the energy release of various radicals on the surface unsaturated Cu_CUS site after adsorption. The interaction between the O radical and the surface releases the largest amount of energy (−4.56 eV after adsorption), followed by HO₂, OH, H, CH₃ radicals, and O₂ with the adsorption energy of −3.79, −3.61, −3.07, −2.21, and −1.09 eV, respectively. The energy barriers have been listed in the left corner of Figure 6. The H-abstraction of the chemisorbed C₂H₂ by OH and O₂ have similar barriers, which are 1.39 and 1.43 eV, while the H-abstraction reactions by adsorbed HO₂, H, CH₃, and O radicals need to overcome higher energy barriers, which are 1.64, 2.75, 2.15, and 2.07 eV. The H-abstraction reactions by all the adsorbed radicals considered are exothermic except for H radical, indicating that the H-abstraction reactions on the perfect Cu₂O (111) surface model is thermodynamically favorable.

The energy profile of the interaction between the chemisorbed C₂H₂ species and the pre-adsorbed oxygen and radicals, including H, OH, O, HO₂, and CH₃ on the defective Cu₂O (111) surface model are compared in Figure 7. In general, the energy release of the radicals on the defective surface is lower than those on the perfect Cu₂O (111) surface model, which is due to the absence of the unsaturated surface Cu_CUS site. The adsorption of an atomic O on the defective Cu₂O (111) surface model releases the highest amount of energy (−3.22 eV), which is located at the bridge site of two surface Cu_CSS sites. The H-abstraction of the chemisorbed C₂H₂ by the adsorbed O radical need to get over the 0.52 eV energy barrier, which is the lowest among all the considered radicals and O₂, and it is also lower than that on the perfect Cu₂O (111) surface model. The bridge site of two neighboring Cu_CSS sites is also the adsorption site for OH radicals, and the energy barrier of the H-abstraction process by OH is 0.91 eV. The energy barriers of the H-abstraction by other adsorbed radicals, including O₂, HO₂, and H radicals are 0.97, 0.98, and 1.17 eV, respectively, which are more active than the same processes on the perfect Cu₂O (111) surface model. Therefore, the Cu_CUS defect could improve the Cu₂O (111) surface activity toward the H-abstraction of C₂H₂ via the LH mechanism.

3.6. Temperature Dependence of Elementary Reaction Rate Constants

The above-mentioned discussions are based on the DFT calculation results at 0 K, and the rate constants at elevated temperatures are more relevant to the real circumstances, and the temperate dependence of elementary reaction rates is discussed in this section. The Gibbs free energy of activation (ΔG) of the elementary reactions, including the C₂H₂ chemisorption, C₂H₂ direct decomposition, and H-abstraction of C₂H₂ by O₂, are shown in Figure 8. ΔG denotes the Gibbs energy difference between the transition state and the initial state, and a larger ΔG corresponds to a smaller reaction rate constant at a given temperature according to the transition state theory. Except for the reaction of H-abstraction by O₂ on the defective Cu₂O (111) surface model, the ΔG of all the considered reactions are positively correlated to the temperature. For the reactions of C₂H₂ chemisorption and the direct decomposition of the chemisorbed C₂H₂ into an adsorbed C₂H and an atomic H species, the perfect Cu₂O (111) surface model shows better performance over the defective Cu₂O (111) surface model, while the H-abstraction process is more favorable on the defective Cu₂O (111) surface model than the perfect one, so the defective surface could facilitate the H-abstraction process of C₂H₂ by O₂.

The reaction rate constants of elementary reaction steps are further calculated based on transition state theory, and the rate constants including C₂H₂ chemisorption, C₂H₂ direct decomposition, and the H-abstraction of C₂H₂ by O₂ are presented in Figure 9. The C₂H₂ chemisorption process is more active on the perfect Cu₂O (111) surface model than on the defective Cu₂O (111) surface model, and the reaction rate is about one order of magnitude higher. The C₂H₂ direct decomposition rate constants are the slowest regardless of the perfect or the defective Cu₂O (111) surface models compared with other elementary reaction steps considered in Figure 9, and the rate on the defective surface model is slower than on the perfect surface. The rate constant of H-abstraction by O₂ on the defective surface model is remarkably higher than on the perfect one, and the rate constant is faster by about 4.4 orders of magnitudes at 1000 K. Therefore, the perfect Cu₂O (111) surface model is more favorable for the C₂H₂ chemisorption process, while the defective surface model could be beneficial for the H-abstraction reaction of C₂H₂ by O₂ over the considered temperature range from room temperature to 1000 K. In terms of the reaction rate constants, the direct decomposition of C₂H₂ is less likely to proceed compared with the H-abstraction process. Therefore, the chemisorption and the succeeding H-abstraction process by O₂ could be the possible partial oxidation reaction pathway of C₂H₂ on the Cu₂O (111) surface model. The chemisorption of C₂H₂ is the rate-determining step on the defective Cu₂O (111) surface model, and the H-abstraction by the O₂ process is the rate-determining step on the perfect Cu₂O (111) surface model.

The calculated rate constants are then converted into the Arrhenius form with the A, n, and E parameters provided in

Table 1. Calculated rate constants of C₂H₂ elementary reactions on the perfect and defective Cu₂O (111) surface models, units are in K, kcal, mol, s, and cm.

No.	Elementary Reactions	A	n	E
R1	C2H2 chemisorption on the perfect Cu2O (111) surface	5.11 × 1013	−0.687	15.117
R2	C2H2 decomposition on the perfect Cu2O (111) surface	1.15 × 1010	0.906	40.193
R3	C2H2 H-abstraction on the perfect Cu2O (111) surface by O2	3.16 × 1010	0.689	29.443
R4	C2H2 chemisorption on the defective Cu2O (111) surface	1.98 × 1011	−0.021	18.130
R5	C2H2 decomposition on the defective Cu2O (111) surface	5.13 × 107	1.656	51.245
R6	C2H2 H-abstraction on the defective Cu2O (111) surface by O2	8.15 × 1012	0.588	18.679

for future heterogeneous kinetic modeling works.

4. Conclusions

The adsorption and oxidation of C₂H₂ on the perfect stoichiometric and Cu_CUS-defective Cu₂O (111) surface models are studied using DFT calculations. The perfect Cu₂O (111) surface model is active in adsorbing the C₂H₂ molecule with 1.13 eV adsorption energy and an energy barrier of 0.70 eV to form the chemisorption, while the adsorption of C₂H₂ on the defective Cu₂O (111) surface model only releases 0.20 eV. The energy barrier of the C₂H₂ chemisorption on the defective surface model is 0.81 eV which is close to that of the perfect model. The reaction rate of H-abstraction of the chemisorbed C₂H₂ on the defective surface model is much faster than on the perfect surface model with the energy barrier decreasing from 1.43 to 0.97 eV at 0 K. The H-abstraction of C₂H₂ by O₂ is about 4.4 orders of magnitudes faster at 1000 K on the defective Cu₂O (111) surface model than on the defective Cu₂O (111) model. Therefore, the surface defect featuring the absence of surface unsaturated Cu_CUS sites significantly facilitates the H-abstraction of C₂H₂ by O₂ process. The partial oxidation of C₂H₂ on the Cu₂O (111) surface model is likely to proceed by the chemisorption of C₂H₂ and a succeeding H-abstraction process by O₂. C₂H₂ chemisorption is the rate-determining step on the defective Cu₂O (111) surface model and the H-abstraction process is the rate-determining step on the perfect Cu₂O (111) surface model. The activity of H-abstractions of C₂H₂ via the LH mechanism by various radicals follows the order of OH > O₂ > HO₂ > O > CH₃ > H from high to low on the perfect Cu₂O (111) surface model. On the defective Cu₂O (111) surface model, the activity follows the order: O > OH > O₂ > HO₂ > H > CH₃.