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

The catalytic removal of C2H2 by Cu2O was studied by investigating the adsorption and partial oxidation mechanism of C2H2 on both perfect (stoichiometric) and CuCUS-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 CuCUS 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.


Introduction
Acetylene (C 2 H 2 ) 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]. C 2 H 2 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-C 2 H 2 -addition (HACA) mechanism [2,3]. The production of C 2 H 2 during combustion could endanger the safety and efficiency of combustors, etc. C 2 H 2 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 C 2 H 2 may cause loss of consciousness or even death, and it is a serious fire and explosion hazard. C 2 H 2 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 C 2 H 2 formation and emission, the efficient removal of C 2 H 2 during combustion and industrial processes is of great interest. To the best of our knowledge, much attention has been paid to the study of C 2 H 2 /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 C 2 H 2 .
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 Cu 2 O thin film catalysts prepared by the pulsed-spray evaporation chemical vapor deposition (PSE-CVD) method are effective for the catalytic removal of C 2 H 2 [8], but the oxidation mechanism of C 2 H 2 on the Cu 2 O 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 C 2 H 2 hydrogenation process have been reported previously. Zhang et al. [27,28] have studied C 2 H 2 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 C 2 H 2 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 C 2 H 2 partial oxidation process on the Cu 2 O surface. The Cu 2 O (111) plane is the most widely used surface model to reveal the heterogeneous reaction mechanism on the Cu 2 O 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 Cu 2 O (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 Cu 2 O (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 Cu 2 O surface chemistry.
To provide a better understanding of the reaction mechanism of C 2 H 2 on the Cu 2 O surface, the adsorption and reaction processes of C 2 H 2 on the Cu 2 O surface models were studied based on DFT calculations in this study. The reaction processes of C 2 H 2 on the Cu 2 O surface models, including the adsorption process, decomposition process, and Habstraction reactions, by a variety of radicals and O 2 have been studied. The effect of the surface defect on the C 2 H 2 elementary reaction steps has been explored by studying the C 2 H 2 conversion on both the stoichiometric perfect Cu 2 O (111) surface model and the Cu 2 O (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.

Computational Details
DFT calculations were performed using the DMol 3 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 Cu 2 O (111) surface from the optimized Cu 2 O 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 ad ) is used to evaluate the interaction between the surface and the adsorbate, which is defined as: where E sys is the energy of the system after adsorption; E ads is the energy of the adsorbate before adsorption; E 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 , 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 ∆G a is the Gibbs free energy of activation. Detailed calculation processes can be found elsewhere [34,40].

Perfect and Defective Cu 2 O (111) Surface Models and C 2 H 2 Adsorption
The (111) surface plane of Cu 2 O 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 Cu 2 O (111) surface models have been established, as shown in Figure 1 The stable adsorption structure of C 2 H 2 on the Cu 2 O (111) surface was explored by comparing the adsorption energies of C 2 H 2 on different surface sites of the Cu 2 O (111) surface models. One C 2 H 2 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 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 CuCUS site, the CuCSS site, the OCUS site, and the OCSS 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 CuCUS 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 OCUS site and its neighboring CuCUS site and one CuCSS 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 OCUS site to form an adsorbed CHCHO* species, which is bonded to three surface CuCSS 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 CuCUS site in activating the C2H2 bond. The adsorption processes of C 2 H 2 on the perfect and defective Cu 2 O (111) surface models are shown in Figure 2. For the adsorption on the perfect Cu 2 O (111) surface model, a C 2 H 2 molecule will first adsorb over the surface unsaturated Cu CUS site with the energy release of 1.13 eV, and the linear structure of C 2 H 2 is slightly distorted with the O-C-C angles decreasing from both 180 • to 162 • and 169 • . The C-C bond length of C 2 H 2 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 C 2 H 2 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 Cu 2 O (111) surface model. One C 2 H 2 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 C 2 H 2 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 Cu 2 O (111) surface model releases 1.26 eV. By comparison, the perfect Cu 2 O (111) surface model is more favorable for the C 2 H 2 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 C 2 H 2 bond.

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,

Decomposition of C 2 H 2 on the Perfect and the Defective Cu 2 O (111) Surface Models
The direct decomposition processes of the chemisorbed C 2 H 2 * molecule undergoing the cleavage of the C-H bond on the Cu 2 O (111) surface models are first investigated, which represents the surface activity toward C 2 H 2 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 Cu 2 O (111) surface model is 1.92 eV, and the reaction is an exothermic process releasing 0.21 eV. The adsorbed C 2 H 2 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 C 2 H 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 C 2 H 2 on the defective Cu 2 O (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 C 2 H 2 on both the perfect and the defective Cu 2 O (111) surface models is hard to happen in terms of the reaction energy barrier, and the perfect Cu 2 O (111) surface model is more favorable than the defective one comparatively, which is due to the existence of the neighboring active Cu CUS site.

H-Abstraction Reactions of Chemisorbed C2H2 by O2 on the Cu2O (111) Surface Model
The H-abstraction reactions are important in the consumption of C2H2, hence t abstraction of the chemisorbed C2H2 by O2 was studied in this section. The Lang Hinshelwood reaction mechanism featuring the reaction between two adsorbed cules on the perfect and defective Cu2O (111) surface models is studied. The left p Figure 4 shows the H-abstraction process on the perfect Cu2O (111) surface mode surface unsaturated CuCUS site is active for O2 adsorption, and an O2 molecule will a on the CuCUS site close to the chemisorbed C2H2 molecule, releasing 1.09 eV. Then, atom of the chemisorbed C2H2 will transfer to the adsorbed O2 forming an adsorbed molecule by overcoming the energy barrier of 1.43 eV. The reaction releases 0.23 eV 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) s model is shown in the right part of Figure 4. An O2 molecule will first adsorb on th face hollow site, and the chemisorbed C2H2 needs to overcome the energy barrier o eV to react with the adsorbed O2 and form an HO2 on the hollow site with an e release of 0.86 eV. An adsorbed HCCO species is formed after the reaction on top of CuCSS sites. Compared with the perfect surface model, the H-abstraction of C2H2 by the defective Cu2O (111) surface is easier with a lower energy barrier and a larger e release. The homogeneous H-abstraction of C2H2 by O2 is also calculated for comp

H-Abstraction Reactions of Chemisorbed C 2 H 2 by O 2 on the Cu 2 O (111) Surface Models
The H-abstraction reactions are important in the consumption of C 2 H 2 , hence the H-abstraction of the chemisorbed C 2 H 2 by O 2 was studied in this section. The Langmuir-Hinshelwood reaction mechanism featuring the reaction between two adsorbed molecules on the perfect and defective Cu 2 O (111) surface models is studied. The left part of Figure 4 shows the H-abstraction process on the perfect Cu 2 O (111) surface model. The surface unsaturated Cu CUS site is active for O 2 adsorption, and an O 2 molecule will adsorb on the Cu CUS site close to the chemisorbed C 2 H 2 molecule, releasing 1.09 eV. Then, one H atom of the chemisorbed C 2 H 2 will transfer to the adsorbed O 2 forming an adsorbed HO 2 molecule by overcoming the energy barrier of 1.

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 CuCUS site, and it could attack the chemisorbed C2H2 and form an adsorbed H2 and an adsorbed HCCO species together with a lattice OCUS. 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 OCSS site on the perfect Cu2O (111) surface model.  The energy profile of C 2 H 2 H-abstraction by O 2 on the defective Cu 2 O (111) surface model is shown in the right part of Figure 4. An O 2 molecule will first adsorb on the surface hollow site, and the chemisorbed C 2 H 2 needs to overcome the energy barrier of 0.97 eV to react with the adsorbed O 2 and form an HO 2 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 C 2 H 2 by O 2 on the defective Cu 2 O (111) surface is easier with a lower energy barrier and a larger energy release. The homogeneous H-abstraction of C 2 H 2 by O 2 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 Cu 2 O (111) surface models are favorable for the H-abstraction process of C 2 H 2 by O 2 from the thermodynamic point of view, and the Cu CUS defect will be beneficial for the H-abstraction of C 2 H 2 by O 2 .

H-Abstraction and H-Addition of Chemisorbed C 2 H 2 by Atomic H
The reaction between a chemisorbed C 2 H 2 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 C 2 H 2 and form an adsorbed H 2 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 C 2 H 2 could also react with an adsorbed H together with the lattice O to form a CH 2 CHO species, as shown in the right part of Figure 5, on the perfect Cu 2 O (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 C 2 H 2 with an energy barrier of 2.75 eV. In terms of the reaction energy, the formation of CH 2 CHO needs to adsorb 0.67 eV, while the H-abstraction process adsorbs 0.78 eV. Therefore, the adsorbed C 2 H 2 is more likely to be converted to CH 2 CHO when reacting with an adjacent adsorbed H together with a lattice O CSS site on the perfect Cu 2 O (111) surface model. 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 OCSS site on the perfect Cu2O (111) surface model.

A Comparison of H-Abstraction Reactions of Chemisorbed C 2 H 2 by Different Radicals
The energy profile of the interaction between the chemisorbed C 2 H 2 species and the pre-adsorbed oxygen molecule and radicals, including H, OH, O, HO 2 , and CH 3 , on the perfect Cu 2 O (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 HO 2 , OH, H, CH 3

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 CuCUS 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  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 CuCUS site. The adsorption of an atomic O on the defective Cu2O (111) surface model releases the highest amount of  Figure 7. In general, the energy release of the radicals on the defective surface is lower than those on the perfect Cu 2 O (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 Cu 2 O (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 C 2 H 2 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 O 2 , and it is also lower than that on the perfect Cu 2 O (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 O 2 , HO 2 , and H radicals are 0.97, 0.98, and 1.17 eV, respectively, which are more active than the same processes on the perfect Cu 2 O (111) surface model. Therefore, the Cu CUS defect could improve the Cu 2 O (111) surface activity toward the H-abstraction of C 2 H 2 via the LH mechanism.

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 Habstraction 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.

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 (∆G) of the elementary reactions, including the C 2 H 2 chemisorption, C 2 H 2 direct decomposition, and H-abstraction of C 2 H 2 by O 2 , are shown in Figure 8. ∆G denotes the Gibbs energy difference between the transition state and the initial state, and a larger ∆G 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 O 2 on the defective Cu 2 O (111) surface model, the ∆G of all the considered reactions are positively correlated to the temperature. For the reactions of C 2 H 2 chemisorption and the direct decomposition of the chemisorbed C 2 H 2 into an adsorbed C 2 H and an atomic H species, the perfect Cu 2 O (111) surface model shows better performance over the defective Cu 2 O (111) surface model, while the H-abstraction process is more favorable on the defective Cu 2 O (111) surface model than the perfect one, so the defective surface could facilitate the H-abstraction process of C 2 H 2 by O 2 . 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 The reaction rate constants of elementary reaction steps are further calculated based on transition state theory, and the rate constants including C 2 H 2 chemisorption, C 2 H 2 direct decomposition, and the H-abstraction of C 2 H 2 by O 2 are presented in Figure 9. The C 2 H 2 chemisorption process is more active on the perfect Cu 2 O (111) surface model than on the defective Cu 2 O (111) surface model, and the reaction rate is about one order of magnitude higher. The C 2 H 2 direct decomposition rate constants are the slowest regardless of the perfect or the defective Cu 2 O (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 O 2 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 Cu 2 O (111) surface model is more favorable for the C 2 H 2 chemisorption process, while the defective surface model could be beneficial for the H-abstraction reaction of C 2 H 2 by O 2 over the considered temperature range from room temperature to 1000 K. In terms of the reaction rate constants, the direct decomposition of C 2 H 2 is less likely to proceed compared with the H-abstraction process. Therefore, the chemisorption and the succeeding H-abstraction process by O 2 could be the possible partial oxidation reaction pathway of C 2 H 2 on the Cu 2 O (111) surface model. The chemisorption of C 2 H 2 is the rate-determining step on the defective Cu 2 O (111) surface model, and the H-abstraction by the O 2 process is the rate-determining step on the perfect Cu 2 O (111) surface model. 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 for future heterogeneous kinetic modeling works. The calculated rate constants are then converted into the Arrhenius form with the A, n, and E parameters provided in Table 1 for future heterogeneous kinetic modeling works.

Conclusions
The adsorption and oxidation of C 2 H 2 on the perfect stoichiometric and Cu CUSdefective Cu 2 O (111) surface models are studied using DFT calculations. The perfect Cu 2 O (111) surface model is active in adsorbing the C 2 H 2 molecule with 1.13 eV adsorption energy and an energy barrier of 0.70 eV to form the chemisorption, while the adsorption of C 2 H 2 on the defective Cu 2 O (111) surface model only releases 0.20 eV. The energy barrier of the C 2 H 2 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 C 2 H 2 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 C 2 H 2 by O 2 is about 4.4 orders of magnitudes faster at 1000 K on the defective Cu 2 O (111) surface model than on the defective Cu 2 O (111) model. Therefore, the surface defect featuring the absence of surface unsaturated Cu CUS sites significantly facilitates the H-abstraction of C 2 H 2 by O 2 process. The partial oxidation of C 2 H 2 on the Cu 2 O (111) surface model is likely to proceed by the chemisorption of C 2 H 2 and a succeeding H-abstraction process by O 2 . C 2 H 2 chemisorption is the rate-determining step on the defective Cu 2 O (111) surface model and the H-abstraction process is the rate-determining step on the perfect Cu 2 O (111) surface model. The activity of H-abstractions of C 2 H 2 via the LH mechanism by various radicals follows the order of OH > O 2 > HO 2 > O > CH 3