The mechanism for CO2 reduction over Fe-modified Cu(100) surfaces with thermodynamics and kinetics: a DFT study

The adsorption, activation and reduction of CO2 over Fex/Cu(100) (x = 1–9) surfaces were examined by density functional theory. The most stable structure of CO2 adsorption on the Fex/Cu(100) surface was realized. The electronic structure analysis showed that the doped Fe improved the adsorption, activation and reduction of CO2 on the pure Cu(100) surface. From the perspective of thermodynamics and kinetics, the Fe4/Cu(100) surface acted as a potential catalyst to decompose CO2 into CO with a barrier of 32.8 kJ mol−1. Meanwhile, the first principle molecular dynamics (FPMD) analysis indicated that the decomposition of the C–O1 bond of CO2 on the Fe4/Cu(100) surface was only observed from 350 K to 450 K under a CO2 partial pressure from 0 atm to 10 atm. Furthermore, the results of FPMD analysis revealed that CO2 would rather decompose than hydrogenate when CO2 and H co-adsorbed on the Fe4/Cu(100) surface.


Introduction
Reducing the concentration of CO 2 in the atmosphere has attracted signicant attention, because as the major component of greenhouse gas, excessive emissions of CO 2 have contributed signicantly to environment degradation in the past decades, such as global warming, and melting of glaciers. The conversion of CO 2 as a C resource to synthesize more valuable chemical raw materials not only solves the major crisis of global greenhouse gases and energy shortage, but also provides great opportunities and challenges for exploring novel catalysts and developing a modern catalytic industry. 1 Because CO 2 is a thermodynamically stable molecule, it is difficult to utilize CO 2 as the C resource. 2 Currently, ve ways to reduce CO 2 have been reported: (i) electrocatalytic reduction, [3][4][5][6][7][8] (ii) photocatalytic reduction, 2,[9][10][11] (iii) thermal catalytic reduction, [12][13][14][15] (iv) enzymatic reduction 16,17 and (v) photoelectrocatalytic reduction. 18 In these cases, the catalyst plays a major role in CO 2 activity and reduction.
Numerous experiments and theories have been used to investigate the adsorption, activation and reduction of CO 2 on transition metal-based catalysts. [19][20][21][22][23][24][25][26][27] For instance, Fierro systematically investigated the adsorption of CO 2 on the Co(100), Co(110) and Co(111) surfaces. 19 The results indicated that the adsorption conguration of CO 2 on the substrate was sensitive, especially the Co(110) surface. The experimental results of Rasmussen showed that the Cu(100) surface was able to decompose CO 2 into CO and O 2 . 22 Roberts demonstrated that CO 2 could be decomposed into CO on the Ni(100) surface rather than on the Ni(111) surface. 23 Ding asserted that a weak interaction was formed between CO 2 and the Ni(110) surface. 24 Glezakou investigated the mechanism of adsorption and activation of CO 2 on the Fe fcc(100) surface. 25 Their results indicated that CO 2 on the Fe(100) surface was activated spontaneously. Wilson investigated the reduction of CO 2 into CO on Co(100), Ni(100) and Cu(100) surfaces. 26 The calculated results revealed an interesting trend between reaction energy and the total reaction barrier from Fe to Cu and that reactions tended to be less exergonic. Additionally, Co and Ni were more favorable to decompose CO 2 into CO.
Except for the single metal catalysts for CO 2 , Great effort has been devoted to improve the catalytic performance of bimetallic catalysts for CO 2 activation and catalysis. 27, 28 Nerlov pointed out that the performance of Cu-Ni bimetallic catalyst was more than 60 times greater than the pure Cu. [29][30][31] Liu found that the introduction of Pd, Rh, Pt, and Ni metals on the Cu(111) surface promoted the methanol production. 32 Our previous reports revealed that the introduction of a second metal could improve the interaction between CO 2 and the Cu(100) surface. 33,34 Additionally, the results also showed that the interaction between CO 2 and the Co n /Cu(100) surface was structure sensitive for the reduction of CO 2 molecules and the Co 4 /Cu(100) surface was the potential catalyst for the reduction of CO 2 . The results of Song demonstrated that the properties of CO 2 conversion on Fe-Ni and Fe-Co catalysts were similar, and CO* and HCOO* were the preferred intermediates. 35,36 On the basis of these reports, in this work the density functional theory calculations was employed to understand the activation and reduction of CO 2 on the Cu(100) surface with embedded small Fe atoms. The result of a recent STM experiment showed that small Co clusters can be formed in the rst layer of the Cu(100) surface through the vacancy-mediated diffusion of Co atoms. 37 The similarity of the Co/Cu(100) and Fe/Cu(100) epitaxial systems suggests that the diffusion of embedded Fe atoms also leads to the formation of small nanostructures. 38 Firstly, the most stable structure of Fe x / Cu(100) (x ¼ 1-9) was generated using the rst principle molecular dynamics (FPMD) method. Then the adsorption energetics and geometry, vibrational frequencies analysis, charge transfers and d-band center of CO 2 over a series of Fe x / Cu bimetallic surfaces were analyzed. The activation energy barrier for the CO 2 reduction and the Brønsted-Evans-Polanyi (BEP) relationships between the kinetic parameters for CO 2 reduction over the Fe x /Cu(100) systems were investigated. And then the optimal temperature and partial pressure for CO 2 reduction on the Fe 4 /Cu(100) surface was explored in detail. Lastly, the hydrogenation of CO 2 and residual CO or O was considered in the paper.

Method
All of the density functional theory (DFT) calculations using the Vienna ab initio simulation package (VASP) [39][40][41] were according to projector-augmented wave DFT (PAW-DFT). [42][43][44] The Perdew-Burke-Ernzerhof (PBE) functional based on the generalized gradient approximation was employed. 45 The kinetic energy cutoff of 400 eV for the plane-wave expansion was set. In all systems, the effects of dipole correction, spin polarization in the surface normal direction and the van der Waals correction were considered by using DFT-D2 method. 46,47 Geometrical structure was optimized until the energy change and the maximum force were less than 10 À6 eV and 0.02 eVÅ À1 , respectively. The 5 Â 5 Â 1 k-points with Monkhorst-Pack method were used. 48

Surface model
Previous studies reveal that the Cu(100) surface is the most potential value to be reduction of CO 2 molecule among Cu(100), Cu(110) and Cu(111) surfaces. 34 Thus, the Cu(100) surface with a p(3 Â 3) supercell and ve atomic layers was employed. For the Fe x /Cu(100) (x ¼ 1-9) surfaces, Cu atoms on top-layer of the pure Cu(100) surface were substituted by several Fe atoms. In the geometry optimizations, the top three layers were completely relaxed in all directions and the bottom two layers were xed in their bulk position. The vacuum of 15Å between the adjacent slabs was set along the c-axis direction to avoid periodic interactions.
The adsorption energy (E ads ) for the CO 2 molecule on the Fe x / Cu(100) surface was dened eqn (1), as follows: where, E CO 2 , E Slab and E CO 2 /Slab represent the total energy of the free CO 2 molecule in the gas phase, the clean surface and the slab with adsorbed CO 2 , respectively. Therefore, a negative value of E ads indicates an endothermic adsorption and a positive value refers to an exothermic adsorption. The reduction of CO 2 on the Fe x /Cu(100) surface was involved in the formations of CO and HCOO, namely, CO 2 ðgÞ/CO * 2 /CO* þ O* and CO * 2 /H* þ HCOO* (where X* represents X species adsorbed on substrate). The corresponding activation energy barrier was calculated from the relative energy of the transition state (TS) with respect to the sum of the energies of the initial structure (IS) (CO 2 adsorbed on the Fe x / Cu(100) surface), namely, All the transition states were determined using the climbing image nudged elastic band (CI-NEB) 49,50 and DIMER 51,52 methods and performed a vibrational frequency analysis to conrm that the predicted transition state to the rst-order saddle point in the reaction path. Additionally, the Bader charge analysis using the code developed by Henkelman and coworkers was employed to quantify the charge transfer between the substrates and CO 2 molecule. 53-55

Microkinetic model
The rate constants for CO 2 dissociation using the harmonic transition state theory [56][57][58] was analyzed as shown in eqn (3): where, A represents the pre-exponential factor. According to the harmonic transition state theory, the pre-exponential factor (A) can be estimated using the following formula: where f IS i and f TS i were the vibrational frequencies at the IS and the TS. Note that the imaginary frequency in TS was excluded.
The actual activation barrier (E act ), including the entropy (DTS), the zero point energy (ZPE) and enthalpy ð Ð C p dTÞ corrections, was calculated as follows: where, S and C p represent the entropy and the heat capacity, respectively. The zero point energy, entropy and enthalpy correction are calculated as follows, 57 respectively: where f i was the vibrational frequency and i represents the different modes of vibration.
To calculate the relative concentrate (q CO ) of CO on the Fe-Cu bimetallic system, the steady state approximation was adopted in this work. 59 The total amount of metal catalytic sites in the reaction was considered as a constant and the sum of the occupied (q x ) and the free metal (q * ) sites were dened as following eqn (9): 60 q CO 2 + 2q CO + q * ¼ 1 (9) where q CO 2 was obtained by q CO 2 Â K CO 2 Â P CO 2 Â q * and . 61 The partial pressure (P CO 2 ) of CO 2 from 0 to 10 atm was set. For the elementary reaction step CO 2 ! kþ kÀ CO þ O (rate constants, K ¼ k þ k À ), according to the steady-state approximation, the equation was as follows: Thus,

Results and discussion
The most stable structure of the different coverage (n) for Fe dopant on the top-layer of the Cu(100) surface was discussed briey. If n > 1/9 ML, more than one possible structure of Fe could be doped in the Cu(100) surface. Optimal doping structure for the different coverage of Fe dopant was predicted aer extensive study of the various arrangements of Fe atoms embedded in the top-layer of the Cu(100) surface. Taking Fe 4 /Cu(100) as an example, four possible congurations for the Fe 4 /Cu(100) surface, namely: M1 $ M4, (see Fig. 1), were considered. In the M1 model, four Fe atoms tended to gather together and form a square nanocluster. For the M2 and M3 structure, the four Fe atoms exhibited the T-and Z-type structure, respectively. In the M4 structure, it was seen as the Fe 3 trimer and an isolated Fe atom. The calculated relative energies ( Fig. 1) indicated that the energetically most favorable conguration among the M1 $ M4 models was the M1. The most stable structure for the Fe x / Cu(100) surfaces was determined by the similar approach and shown in Fig. S1. † Interestingly, from the perspective of thermodynamic, Fe dopant tended to arrange together when the n values increased from 1/9 to 1 ML. Therefore, we focused on the adsorption, activation and reduction of CO 2 molecule on the most stable conguration for the Fe x /Cu(100) surfaces.

Adsorption congurations of CO 2 on Fe x /Cu(100) surfaces
The most stable structure of CO 2 on the Fe x /Cu(100) (x ¼ 1-9) surface was presented in Fig. 2, including CO 2 on the pure Cu(100) and Fe fcc(100) surfaces. It was clearly observed in Fig. 2 that the adsorption behavior of CO 2 on the Fe x /Cu(100) surface was sensitive to the coverage of Fe atoms when the coverage of Fe atoms was less than 4/9 ML ( Aer CO 2 adsorption, some electrons were transferred from the substrate to CO 2 moiety, leading to the bent structure with the O-C-O bond angle from 118 to 135 (Table 1). Furthermore, the C-O1 bond and the C-O2 bond was stretched to about 1.253 to 1.364Å and 1.253 to 1.300Å, respectively. Especially the C-O1 bond, its distance was gradually elongated by 0.2Å compared with the distance of 1.176Å in gas-phase CO 2 molecule when the coverage of the Fe atoms was more than 3/9 ML, which meant that the C-O1 bond was activated aer CO 2 adsorption. Meanwhile, it was also noticed that when the coverage of the Fe atoms was more than 3/9 ML, the extra interaction between the O2 atom in the CO 2 moiety and the Fe atom was established and the corresponding Fe-O2 bond This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 32569-32580 | 32571 length was 2.014Å (Fe 4 /Cu(100)), 2.000Å (Fe 5 /Cu(100)), 1.987Å (Fe 6 /Cu(100)), 1.974Å (Fe 7 /Cu(100)), 1.961Å (Fe 8 /Cu(100)) and 1.965Å (Fe 9 /Cu(100)). Among these Fe-O2 bonds, the distance of the Fe-O2 bond for CO 2 on the Fe 4 /Cu(100) was the longest, requiring the less energy barrier to decompose CO 2 . The calculated adsorption energy (see Table 1) increased monotonously as an increase of the coverage for Fe atoms, suggesting that introducing Fe atoms in the pure Cu(100) surface could improve the bonding strength of CO 2 to the substrate. Compared with the adsorption energy of CO 2 on the pure Cu(100) (E ads ¼ À72.4 kJ mol À1 ) and Fe fcc(100) (E ads ¼ 139.8 kJ mol À1 ) surfaces, 26 the binding strength of CO 2 on the substrate was enhanced while the coverage of Fe atoms was more than 3/9 ML.
3.2. Electronic structures of CO 2 on Fe x /Cu(100) surfaces 3.2.1. D-Band center analysis. To interpret a variation in adsorption energy as an increase of coverage for Fe atoms, the position of the d-band center of the Fe x /Cu(100) surface was calculated. As well-known, the d-band center model was used widely to understand the bond formation on a transition metal surface, this is, the higher the d-band center, the stronger the adsorption bond. 33 As shown in Fig. 3(a), the value of the d-band center for the Fe x /Cu(100) surface was in the range of 2.0 to À0.7 eV and tended to increase with an increase of Fe atoms on the Cu(100) surface. Although the coverage exceeded 3/9 ML, the variation of adsorption energy was small as the increase of position of the d-band center because of the same structure of the CO 2 on Fe x /Cu(100) surface. Furthermore, to gain a deeper understanding of the active state of the Fe x /Cu(100) surface, the position of the d-band center for alpha (a) and beta (b) states in 3d-orbitals was extracted from the total position of the d-band center. As shown in Fig. S2 † and 3(b), the trend of the variation of the d-band center for b-states orbitals was consistent with that of the total d-band center, which meant that CO 2 was adsorbed on the Fe x /Cu(100) surface by interaction with the bstates orbitals of the doped Fe atoms. Furthermore, the calculated density of states (DOS) in Fig. 4 conrmed that, aer CO 2 adsorption on Fe x /Cu(100) surface, CO 2 tended to interact with the b-states of the substrates.
3.2.2. Bader charge analysis. As mentioned, the CO 2 on the substrate exhibited the bent structure, indicating that some electrons were transferred to CO 2 from substrate. To verify this conclusion more clearly, the charge density of CO 2 on the Fe x / Cu(100) surface was calculated and shown in Fig. S3-S10. † Taking CO 2 on the Fe 4 /Cu(100) surface as an example, Fig. 5(a) represents the charge density map of CO 2 adsorbed on the Fe 4 / Cu(100) surface (the x-axis represents the distance from the bottom to the top of the Fe 4 /Cu(100) system). Five high-density Table 1 Some optimized bond lengths (Å), O-C-O bond angle (degrees) and the calculated adsorption energies (E ads , in kJ mol À1 ) of CO 2 molecules on pure Fe(100), Cu(100) and different Fe x /Cu(100) bimetallic surfaces  This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 32569-32580 | 32573 peaks in Fig. 5(a) were observed and each peak represented the charge density of one atomic layer in the Fe 4 /Cu(100) surface. Furthermore, a relatively small density peak is observed at $9.0 A along the x-axis, which represented the charge density of the CO 2 moiety. It was noted that an obvious interaction between CO 2 and the Fe 4 /Cu(100) surface was observed at z ¼ 7-9Å. The charge density difference map (Dr) in Fig. 5(b) changed from lightly positive to negative upon crossing the Fe 4 /Cu(100) interface (z ¼ 7.0-8.0Å) and reached a minimum at z ¼ $8.6Å.
Then it changed from negative to positive in the region (z ¼ 8-9 A). This evolution indicated that the electrons owed from the Fe 4 /Cu(100) surface to the CO 2 moiety, forming the CO 2 À anions.
To quantify these charges transferred, the Bader charge analysis for all systems was calculated, as shown in Table 2. As expected, CO 2 obtained some electrons from the Fe x /Cu(100) surfaces. In general, as the coverage increased for Fe atoms, the electrons obtained by CO 2 from the surface also increased. In particular, for the Fe 9 /Cu(100) surface, the transferred electrons reached the maximum (1.17e). The atomic charges for C and O atoms of CO 2 moiety were also included in Table 2. It was obviously evident in Table 2 that the transferred electrons were signicantly concentrated on C atom. Fig. 6 displays the charge density difference for CO 2 moiety on Fe x /Cu(100) surface. If the coverage was less than 4/9 ML, the p-bond between C and O1 atoms was weakened slightly, especially the Fe 1 /Cu(100). Although the coverage was more than 3/9 ML, Fig. 6(d)-(i) clearly showed that the degree of activation for the p-bond was quite similar and was more larger than CO 2 on the Fe 1$3 /Cu(100) surface.
3.2.3. Vibrational frequencies analysis. According to the Bader charge analysis, aer CO 2 adsorbed on the Fe x /Cu(100) surface, some electrons were transferred from the substrate to CO 2 moiety and concentrated on the C atom, which weakened the C-O bond and further caused a red shi of the vibrational frequency for C-O bond, especially the C-O1 bond. Table 3 present the stretching vibration frequency of C-O1 and C-O2 bonds in CO 2 moiety on each of the Fe x /Cu(100) surface. Compared with stretching vibration frequency of a free CO 2 molecule, the stretching vibration frequency of the C-O1 and C- Fig. 4 The density of states for the toplayer metallic atoms in clean Fe x /Cu(100) and CO 2 /Fe x /Cu(100) surfaces.
O2 bonds was red-shied when the CO 2 was adsorbed on the Fe x /Cu(100) surface. However, the variation of the stretching vibration frequency for C-O2 bond decreased lightly when the coverage was more than 3/9 ML. Compared with the stretching vibration frequency (1333 cm À1 ) of the gas CO 2 molecule, the reducing value of the stretching vibration frequency for the C-O1 bond was 211 cm À1 (Fe 1 /Cu(100)), 181 cm À1 (Fe 2 /Cu(100)), 216 cm À1 (Fe 3 /Cu(100)), 316 cm À1 (Fe 4 /Cu(100)), 314 cm À1 (Fe 5 / Cu(100)), 308 cm À1 (Fe 6 /Cu(100)), 344 cm À1 (Fe 7 /Cu(100)), 340 cm À1 (Fe 8 /Cu(100)) and 354 cm À1 (Fe 9 /Cu(100)), respectively. Among these frequencies, the variation of the stretching vibration frequency of the C-O1 bond adsorbed on the Fe 9 / Cu(100) surface reached its maximal value, which was consistent with the variation in bond length and the number of transferred charges aer adsorption. Thus, the more electrons were transferred to the CO 2 molecule, the longer the C-O1 bond length was and the easier the stretching vibration frequency for the C-O1 bond was to redshi. 2 on Fe x /Cu(100) surfaces 3.3.1. Transition state analysis. The minimum potential energy map for the decomposition of CO 2 molecules on the Fe x / Cu(100) surfaces was determined using the CI-NEB and DIMER methods and shown in Fig. 7 and S11 † According to the Fe 1 / Cu(100) surface shown in Fig. S11(a), † the O atom bonded to three Cu atoms and one Fe atom (4-fold site), whereas the CO moiety was adsorbed between two adjacent Cu atoms. On all other Fe x /Cu(100) surfaces, the O atom was still bonded to four metal atoms to form the 4-fold site and the C atom of CO moiety was co-adsorbed to the substrate with an incline through the Fe-C adsorption bond. The reaction energy (H) of CO 2 decomposition on the Fe x /Cu(100) surface was calculated, as shown in Fig. 7 and S11. † For the Fe 1 /Cu(100) surface, the highest reaction energy was À4.9 kJ mol À1 , followed by the Fe 3 /Cu(100) surface (À36.1 kJ mol À1 ) and the Fe 2 /Cu(100) surface (À43.1 kJ mol À1 ). When the coverage of Fe atoms was more than 3/9 ML, the reaction energy could be signicantly increased with À65.0 kJ mol À1 for the Fe 4 /Cu(100), À62.3 kJ mol À1 for the Fe 5 /Cu(100) surface, À70.7 kJ mol À1 for the Fe 6 /Cu(100) surface, À121.0 kJ mol À1 for the Fe 7 /Cu(100) surface, À122.5 kJ mol À1 for the Fe 8 /Cu(100) surface and À127.6 kJ mol À1 for the Fe 9 /Cu(100) surface. It was noteworthy that the reaction energy of the Fe x /Cu(100) surface increased with the coverage of the Fe atom increased on the Cu(100) surface, indicating that the introduced Fe atom improved the reaction energy of CO 2 decomposition. It may be reasonable   Fig. 7 and S11. † In addition, the vibration frequencies of all transition states were calculated to ensure that the predicted TS corresponds to the rst-order saddle point in the reaction path and the imaginary frequency (n i ) was also shown in Fig. 7 and S11. † For the Fe 1 /Cu(100) surface, only one TS for the C-O1 bond decomposition was discovered. The activation energy barrier (relative to the energy of the CO 2 adsorption) of CO 2 decomposed on the Fe 1 /Cu(100) surface was 45.6 kJ mol À1 . For the Fe 2 / Cu(100) and Fe 3 /Cu(100) surfaces, the activation energy barrier increased to 59.9 kJ mol À1 and 63.7 kJ mol À1 compared with the Fe 1 /Cu(100) surface, respectively. When the coverage reached 4/ 9 ML, the activation energy barrier reached the minimum value (32.8 kJ mol À1 ). The transition state of CO 2 decomposition on the Fe x /Cu(100) surface was extremely similar to the CO 2 on the Fe 4 /Cu(100) surface when the coverage was greater than 4/9 ML. The corresponding activation energy barrier from the Fe 5 / Cu(100) to Fe 9 /Cu(100) systems was 35.4 kJ mol À1 , 39.7 kJ mol À1 , 34.7 kJ mol À1 , 40.2 kJ mol À1 and 35.0 kJ mol À1 , respectively. The results showed that the activation energy barrier of all systems exhibited an inverted "S" shape, which was Fig. 6 Charge density difference of CO 2 on Fe x /Cu(100) (x ¼ 1-9) surface. Table 3 The stretching vibration of the C-O1 and C-O2 bonds in CO 2 moiety on Fe x /Cu(100) surface and free CO 2  consistent with the variation in the distance between Fe and O2 atoms, that is, the shorter the distance of the Fe-O2 adsorption bond, the larger the activation energy barrier. For instance, the length (2.014Å) of the Fe-O2 adsorption bond formed on the Fe 4 /Cu(100) surface was the largest among the Fe x /Cu(100) system, which indicated that the O2 atom may need to consume less additional energy to "escape" out of the substrate. Therefore the activation energy barrier of CO 2 decomposition on the Fe 4 /Cu(100) surface was minimal. In addition, Fe dopant introduced on the Cu(100) surface signicantly reduced the activation energy barrier of CO 2 decomposition compared with the barrier of CO 2 on the pure Cu(100) surface with the barrier of 92.9 kJ mol À1 and the Fe(100) surface with the barrier of 113.4 kJ mol À1 , especially the Fe 4 /Cu(100) system. 26 Compared to CO 2 on the Co 4 /Cu(100) surface with the barrier of 18.7 kJ mol À1 , 33 the activation energy barrier for CO 2 on the Fe x / Cu(100) is more than 14.1 kJ mol À1 . The main reason is that bond strength of Fe-O (in diatomic molecules: 390.4 kJ mol À1 ) is stronger than that of Co-O (in diatomic molecules: 384.5 kJ mol À1 ), which led to be the extra barrier formed by Fe-O bond to overcome. Moreover, the reaction energy barrier (DE a ¼ E TS À E Slab À E CO 2 ) and the total reaction energy (DE ¼ E ads + H) followed a linear relationship for the C-O bond scission and the BEP relationship was established: DE a ¼ 0.4DE À 2.5 (kJ mol À1 ) (see Fig. 8). This BEP relationship played an important role in estimating the reaction barrier of the C-O bond scission on other metal surfaces. Furthermore, the results in Fig. 3 showed an increasing trend as the number of Fe-dopants increased. It was worth noting that although the Fe 4 /Cu(100) surface did not have the lowest reaction energy barrier and total reaction energy, the Fe 4 /Cu(100) surface had the lowest activation energy barrier for CO 2 decomposition, which facilitated the decomposition of CO 2 .

Decomposition of CO
3.3.2. Micro kinetics analysis. To further explore the mechanism of CO 2 decomposition on the Fe x /Cu(100) surfaces from the perspective of dynamics, a microkinetic analysis based on the DFT studies was employed on the most favorable path of CO 2 decomposition. 62,63 In the microkinetic model, the temperatures ranging from 250 to 1000 K was adopted to investigate its impact.
The zero point energy, entropy and enthalpy corrections for the activation energy barrier (E a ) were considered to accurately describe the reaction at high temperatures (from 250 to 1000 K) in this section. The obtained results were presented in Tables S2-S19. † The forward and reverse rate constants of the elementary reaction steps for CO 2 decomposition on the Fe x /Cu(100) surfaces at temperature ranging from 250 to 1000 K were displayed in Fig. 9. The Fig. 9 showed that the forward rate constants and inverse rate constants for the CO 2 decomposition on the Fe x /Cu(100) surfaces increased as the temperature increased. At the same temperature, the rate constants for CO 2 dissociation increased with an increase in the coverage of dopant Fe atom, indicating that the doped Fe signicantly improved the rate constants. Moreover, it was further noting that the both forward rate constants and inverse rate constants for CO 2 decomposition was not only increased as the increase of temperature, but the forward rate constants in all Fe x /Cu(100) surface were much larger than the inverse rate constants. In addition, the equilibrium constants (K ¼ k + /k À ) of CO 2 decomposition on the Fe x /Cu(100) surfaces were also considered as a critical parameter. As shown in Fig. 10 and in Tables S11-S19, † the K decreased as the temperature increased, which meant that the increase in the inverse rate constants was greater than the positive rate constants as the temperature increased. The nine curves for K (equilibrium constants) were divided into four groups, i.e. G1 (Fe 1 / Cu system), G2 (Fe 2 /Cu and Fe 3 /Cu systems), G3 (Fe 4 /Cu, Fe 5 /Cu and Fe 6 /Cu systems), G4 (Fe 7 /Cu, Fe 8 /Cu and Fe 9 /Cu systems). In each group the equilibrium constants were close to each other, which was agreement with the variation in the BEP relationship. According to the K, the order of the four group was G4 > G3 > G2 > G1 at the same temperature. Thus, the doped Fe atom was favorable to be activation and decomposition of CO 2 molecule and the K of CO 2 decomposition increased as the coverage of the Fe atom increased. Moreover, although increasing temperature was favorable to the increases of the forward rate constants and invers rate constants, it was unfavorable to the increase of the equilibrium constants. From  This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 32569-32580 | 32577 the perspective of dynamics, this results indicated that the lower the temperature for CO 2 decomposition, the more favorable the decomposition of CO 2 on the Fe x /Cu(100) surface.
3.3.3. Effects of partial pressure of CO 2 . Fig. 11 illustrated the impact of partial pressure of CO 2 towards the decomposition of CO 2 . The results in Fig. 11(a) showed that the decomposition of CO 2 into CO at partial pressure from 0 to 10 atm was not obviously observed when the temperature was less than 300 K. While the concentration of CO reached 50% at the partial pressure of 0.5 atm when the temperature is higher than or equal to 300 K. To further explore the decomposition of CO 2 at the low partial pressure of CO 2 , the partial pressure of CO 2 from 0 atom to 0.01 atm was studied and the results were shown in Fig. 11(b). It was seen in Fig. 11(b) that when the temperature is below 300 K, the decomposition reaction of CO 2 was not observed at the partial pressure from 0 atm to 0.01 atm; The relative concentration of CO increased with the partial pressure of CO 2 increased when the temperature was at 350 K; if the temperature was greater than 350 K, the concentration of CO reached 49% at the partial pressure of 0.0003 atm (in general, the partial pressure of CO 2 in the atmosphere is less than 0.03%). Therefore, when the temperature was greater than 350 K, CO 2 could be decomposed into CO on Fe 4 /Cu(100) surface under the normal partial pressure of CO 2 in the atmosphere.   The mechanism of CO 2 hydrogenation on the Fe 4 /Cu(100) surface was also examined in this section. There were three reaction pathways for CO 2 hydrogenation: the C atom was attacked by H atom and the O1 and O2 atom was attacked, respectively. However, our previous works reveal that the hydrogenation of the C atom in CO 2 moiety is more favorable than that of the O atom. 16,33,34 Thus, the C atom hydrogenation was considered as an important reaction pathway while CO 2 moiety was dissociated. The initial structure (IS), translation structure (TS) and nally structure (FS) was presented in Fig. 12. In Fig. 12, the distance between C and H atoms was changed from 2.464Å in the IS to 1.570Å in the TS, and then to 1.111Å in the FS. The translation structure had been conrmed by the single imaginary frequency with 686 cm À1 . It was worth noted that the calculated activation energy barrier of CO 2 hydrogenation to HCOO* was 31.8 kJ mol À1 , which was less 1.0 kJ mol À1 than that of decomposition for CO 2 on the Fe 4 /Cu(100) surface. Such the small difference suggests that CO 2 hydrogenation could also be performed during the CO 2 decomposition. To understand the relationship between hydrogenation and dissociation of CO 2 , the FPMD was carried to the system with CO 2 and H co-adsorption on Fe 4 /Cu(100) surface at temperature from 250 to 450 K. The radial distribution function of C-O suggests that the broad peak was observed from 2.5 to 3.5Å in Fig. S15(a) † and it was not found for the peak of C-H in Fig. S15( Fig. S15(c) † from 1.0 to 1.5Å at 400 K. This means that CO 2 would rather decompose than hydrogenate at 400 K.

Conclusions
The adsorption, activation and reduction of CO 2 molecule on the Fe x /Cu(100) (x ¼ 1-9) had been investigated by the density functional theory based on the rst principle. The results indicated that the introduction of dopant Fe atom could enhance the adsorption and activation of CO 2 molecule on the Cu(100) surface. The most stable structure for CO 2 on the Fe x / Cu(100) surface was sensitive to the coverage of the Fe dopant. The electronic structural analysis, including d-band center, Bader charge, vibrational frequencies, showed that CO 2 molecule interacted with the b-state orbitals of the Fe x /Cu(100) surface. Aer CO 2 adsorption, some electrons were transferred from substrate to CO 2 moiety and the electrons transferred to CO 2 moiety increased with the coverage of Fe atoms increased, leading to formation of CO 2 À anion. Additionally, the mechanism of CO 2 moiety decomposition on Fe x /Cu(100) surfaces had been studied in detail. The results indicated that the activation energy barrier (E a ¼ 32.8 kJ mol À1 ) of CO 2 decomposition on Fe 4 /Cu(100) was the smallest among the Fe x /Cu(100) surfaces.
The major reason was that, if coverage was more than 4/9 ML, the extra formed Fe-O2 bond played an handle role for CO 2 decomposition. From the viewer of kinetic, the rate constants of CO 2 on Fe 4 /Cu(100) surface were close to that of the Fe 9 /Cu(100) surface and the equilibrium constants analysis revealed that the servers of the equilibrium constants were divided into the four group, and the order of the four groups was G1 (Fe 1 /Cu) > G2 (Fe 2 /Cu and Fe 3 /Cu) > G3 (Fe 4 /Cu, Fe 5 /Cu and Fe 6 /Cu) > G4 (Fe 7 / Cu, Fe 8 /Cu and Fe 9 /Cu). Furthermore, our results conrmed that the lower the temperature, the more favorable it was to decompose the CO 2 molecule into CO. When the simulated temperature was in range from 350 K and 450 K, the decomposition of C-O1 bond in CO 2 moiety was only observed. The results of partial pressure for CO 2 revealed that when the temperature was in range from 350 K to 450 K, the concentrate of CO on the Fe 4 /Cu(100) surface reached 49% under the partial pressure of 3 Â 10 À4 atm. Lastly, the mechanism of CO 2 hydrogenation on the Fe 4 /Cu(100) surface was also investigated. The activation energy barrier of 31.8 kJ mol À1 was slightly less than that of CO 2 decomposition. However, the results of the FPMD analysis revealed that CO 2 was decomposed to form CO*, instead of hydrogenated. Our results provide insight into the mechanism for CO 2 decomposition and hydrogenation on bimetallic surfaces from the perspective of thermodynamics and kinetics, which was important for the design and optimization of novel Cu-based bimetallic catalysts.

Conflicts of interest
The authors declare that they have no known competing nancial interests or personal relationships that could have appeared to inuence the work reported in this paper.