Mechanistic Insights for Dry Reforming of Methane on Cu / Ni Bimetallic Catalysts: DFT-Assisted Microkinetic Analysis for Coke Resistance

: Density functional theory (DFT) calculations have been utilized to evaluate the complete reaction mechanism of methane dry reforming (DRM) over Ni 2 Cu (111) bimetallic catalyst. The detailed catalytic cycle on Ni 2 Cu (111) catalyst demonstrated superior coke resistance compared to pure Ni (111) and Ni 2 Fe (111) reported in the literature. Doping Cu in the Ni–Ni network enhanced the competitive CH oxidation by both atomic O and OH species with the latter having only 0.02 eV higher than the 1.06 eV energy barrier required for CH oxidation by atomic O. Among the C / CH oxidation pathways, C* + O* → CO (g) was the most favorable with an energy barrier of 0.72 eV. This was almost half of the energy barrier required for the rate-limiting step of CH decomposition (1.40 eV) and indicated enhanced coke deposition removal. Finally, we investigated the e ﬀ ect of temperature (800~1000 K) on the carbon deposition and elimination mechanism over Ni 2 Cu (111) catalyst. Under those realistic DRM conditions, the calculations showed a periodic cycle of simultaneous carbon deposition and elimination resulting in improved catalyst stability.


Introduction
Dry reforming of methane (DRM) has been regarded as a process to produce syngas (CO and H 2 ), while providing a prospective solution for mitigation of greenhouse gases (CH 4 and CO 2 ). The produced syngas is a valuable precursor for many other downstream applications [1,2]. It can be used directly as fuel or converted to other hydrocarbons to produce valuable ultra-clean fuels and products such as methanol, diesel, gasoline, kerosene and naphtha via Fischer-Tropsch synthesis, and other reactions [3,4]. In addition to syngas, there are ongoing efforts to make the process more economical by producing valuable byproducts such as solid carbon as added value [5,6]. Despite its numerous advantages, DRM is a highly endothermic process (Equation (1)) that requires high temperatures of around 700 • C to achieve equilibrium conversions of CH 4 and CO 2 [7]. Therefore, the reaction proceeds typically with the use of a catalyst.
Catalyst deactivation, commonly caused by a rapid accumulation of carbon or "coking," is one of DRM's major drawbacks. Metal catalysts such as platinum (Pt) [8], rhodium (Rh) [9], ruthenium First, optimal adsorption sites for all DRM reaction species were selected after examining all possible adsorption structures. Then, the adsorption energies of all DRM reaction species from the most stable adsorption configurations were calculated, as shown in Table 1. CH4 species was physically adsorbed at the HCP site with a weak adsorption energy of −0.02 eV.
On the other hand, CH3, CH2, and CH are strongly adsorbed via C atom on the FCC site with corresponding adsorption energies of −2.17 eV, −4.99 eV, and −5.43 eV, respectively. Similarly, the H atom tends to be adsorbed to the FCC site. These results are in good agreement with Ni2Fe overlayer [20,21] with same diagonal arrangement and pure Ni (111) surfaces [28]. In the case of CO, the adsorption is preferable on the Top Ni site with Eads of −1.52 eV, while the O atom is favorably bound to the FCC site with an Eads of −6.34 eV. It indicates that the Cu dopant in Ni (111) network improved atomic O adsorption while reducing CO adsorption compared to both pure Ni (111) and Ni2Fe (111) surfaces, respectively [19]. As a descriptor of coke resistance, the adsorption energy of the C atom indicates that the more strongly the carbon is adsorbed on a specific surface, the lower the coke resistance. The C atom preferentially adsorbed to HCP site with an Eads of −7.04 eV and is less than the Eads of −7.50 eV in a monometallic Ni catalyst [27,29,30]. This means that the Cu dopant on Ni (111) reduces coke deposition, and, as a result, it can increase the coke resistance of the catalyst surface. The adsorption of CO2 on the Ni2Cu (111) surface has been investigated at all possible sites. After geometry optimization, it has been found that CO2 is physically adsorbed towards a vacuum with weak adsorption energy of −0.03 eV in parallel to the surface with C-Cu. This result agrees with Heil and [31], who used both fast ion beam and fast molecular beam techniques to study CO2 dissociation, and found no chemisorbed CO2 on Ni (111). Moreover, it agrees with the computational studies performed on Ni (111) and on Ni2Fe (111) surfaces [19,32]. CO molecules prefer to adsorb at the B 2Ni site with an Eads of −1.52 eV. The COH* intermediate produced by the combination of C* and OH* is First, optimal adsorption sites for all DRM reaction species were selected after examining all possible adsorption structures. Then, the adsorption energies of all DRM reaction species from the most stable adsorption configurations were calculated, as shown in Table 1. CH 4 species was physically adsorbed at the HCP site with a weak adsorption energy of −0.02 eV.
On the other hand, CH 3 , CH 2 , and CH are strongly adsorbed via C atom on the FCC site with corresponding adsorption energies of −2.17 eV, −4.99 eV, and −5.43 eV, respectively. Similarly, the H atom tends to be adsorbed to the FCC site. These results are in good agreement with Ni 2 Fe overlayer [20,21] with same diagonal arrangement and pure Ni (111) surfaces [28]. In the case of CO, the adsorption is preferable on the Top Ni site with E ads of −1.52 eV, while the O atom is favorably bound to the FCC site with an E ads of −6.34 eV. It indicates that the Cu dopant in Ni (111) network improved atomic O adsorption while reducing CO adsorption compared to both pure Ni (111) and Ni 2 Fe (111) surfaces, respectively [19]. As a descriptor of coke resistance, the adsorption energy of the C atom indicates that the more strongly the carbon is adsorbed on a specific surface, the lower the coke resistance. The C atom preferentially adsorbed to HCP site with an E ads of −7.04 eV and is less than the E ads of −7.50 eV in a monometallic Ni catalyst [27,29,30]. This means that the Cu dopant on Ni (111) reduces coke deposition, and, as a result, it can increase the coke resistance of the catalyst surface. The adsorption of CO 2 on the Ni 2 Cu (111) surface has been investigated at all possible sites. After geometry optimization, it has been found that CO 2 is physically adsorbed towards a vacuum with weak adsorption energy of −0.03 eV in parallel to the surface with C-Cu. This result agrees with Heil and [31], who used both fast ion beam and fast molecular beam techniques to study CO 2 dissociation, and found no chemisorbed CO 2 on Ni (111). Moreover, it agrees with the computational studies performed on Ni (111) and on Ni 2 Fe (111) surfaces [19,32]. CO molecules prefer to adsorb at

DRM Reaction Mechanism
DRM turnover rate is known to be limited only by C-H bond activation, regardless of the concentration of reactants [7]. Consequently, it is expected that the CH 4 is consumed via dissociative adsorption regardless of CO 2 concentration. The resulting CHx species are then oxidized by atomic O and OH species to form CHxO and CHxOH species, respectively, or they undergo further dehydrogenation.
The successive steps of CH 4 dissociation start with the physical adsorption of CH 4 (g) on the Ni 2 Cu (111) surface to form CH 4 *(* denotes an adsorption state). Then, the activation energy in the first step of CH 4 dissociation is found to be 1.30 eV, as shown in Figure 2. The first transition state shows the detached H atom located at the HCP site [33], and the remaining CH 3 fragment settled down at 2.08 Å to achieve maximum C-H-Ni three-center bonding [34,35] After the dissociative adsorption of CH 4 on the Ni 2 Cu (111) surface, the two subsequent dehydrogenation steps of CH 3 * and CH 2 * species are more facile with energy barriers of 0.75 eV and 0.49 eV, respectively. However, CH 3 * dehydrogenation showed endothermicity of 0.33 eV, while CH 2 * exhibited exothermicity by −0.06 eV. On the other hand, oxidations of CH 3 * and CH 2 * by O* or OH* are considerably difficult, due to relatively higher energy barriers than the dehydrogenation pathway mentioned above. After the dissociative adsorption of CH4 on the Ni2Cu (111) surface, the two subsequent dehydrogenation steps of CH3* and CH2* species are more facile with energy barriers of 0.75 eV and 0.49 eV, respectively. However, CH3* dehydrogenation showed endothermicity of 0.33 eV, while CH2* exhibited exothermicity by −0.06 eV. On the other hand, oxidations of CH3* and CH2* by O* or OH* are considerably difficult, due to relatively higher energy barriers than the dehydrogenation pathway mentioned above. Figure 3 shows the activation energy barriers of all possible pathways of CH3*. It confirms that subsequent dissociation to CH2* is dominant over oxidation pathways.CH2* and CH3* oxidation can produce CH3OH* through CH3*, CH3O*, or CH2OH* intermediates. Of these intermediates, CH2OH* was found to be more favorable with a lower activation energy (Ea,r) of 1.10 eV, as shown in Table 2.
In addition, Table 2 shows that the activation energy of the forward reaction (Ea,f) and the activation energy for the reverse reaction (Ea,r). Both of these reaction rates are calculated from Climbing-NEB method considering the enthalpy (Hf) as the energy difference between the final state (F.S) and the initial state (I.S). Next, for the CH dissociation, the activation energy (Ea,f) increases significantly to 1.40 eV, which is higher than that of CH* oxidation by OH* (1.08 eV) and O* species (1.06 eV), as shown in Table 2. The conclusion of this result is that CH dissociation is the rate-limiting step.   Figure 3 shows the activation energy barriers of all possible pathways of CH 3 *. It confirms that subsequent dissociation to CH 2 * is dominant over oxidation pathways.CH 2 * and CH 3 * oxidation can produce CH 3 OH* through CH 3 *, CH 3 O*, or CH 2 OH* intermediates. Of these intermediates, CH 2 OH* was found to be more favorable with a lower activation energy (E a,r ) of 1.10 eV, as shown in Table 2.
In addition, Table 2 shows that the activation energy of the forward reaction (E a,f ) and the activation energy for the reverse reaction (E a,r ). Both of these reaction rates are calculated from Climbing-NEB method considering the enthalpy (H f ) as the energy difference between the final state (F.S) and the initial state (I.S). Next, for the CH dissociation, the activation energy (E a,f ) increases significantly to 1.40 eV, which is higher than that of CH* oxidation by OH* (1.08 eV) and O* species (1.06 eV), as shown in Table 2. The conclusion of this result is that CH dissociation is the rate-limiting step. After the dissociative adsorption of CH4 on the Ni2Cu (111) surface, the two subsequent dehydrogenation steps of CH3* and CH2* species are more facile with energy barriers of 0.75 eV and 0.49 eV, respectively. However, CH3* dehydrogenation showed endothermicity of 0.33 eV, while CH2* exhibited exothermicity by −0.06 eV. On the other hand, oxidations of CH3* and CH2* by O* or OH* are considerably difficult, due to relatively higher energy barriers than the dehydrogenation pathway mentioned above. Figure 3 shows the activation energy barriers of all possible pathways of CH3*. It confirms that subsequent dissociation to CH2* is dominant over oxidation pathways.CH2* and CH3* oxidation can produce CH3OH* through CH3*, CH3O*, or CH2OH* intermediates. Of these intermediates, CH2OH* was found to be more favorable with a lower activation energy (Ea,r) of 1.10 eV, as shown in Table 2.
In addition, Table 2 shows that the activation energy of the forward reaction (Ea,f) and the activation energy for the reverse reaction (Ea,r). Both of these reaction rates are calculated from Climbing-NEB method considering the enthalpy (Hf) as the energy difference between the final state (F.S) and the initial state (I.S). Next, for the CH dissociation, the activation energy (Ea,f) increases significantly to 1.40 eV, which is higher than that of CH* oxidation by OH* (1.08 eV) and O* species (1.06 eV), as shown in Table 2. The conclusion of this result is that CH dissociation is the rate-limiting step.   Table 2. Calculated activation energies of forward (E a,f ), reverse (E a,r ), and enthalpy (H f ) in an elementary reaction of dry reforming of methane (DRM). Consequently, the energy barriers for CHx (x = 1-4) dissociation increase in order of CH 2 < CH 3 < CH 4 < CH [36], which is in line with CH 4 decomposition on pure Ni (111) and Ni 2 Fe (111) systems. In addition, the energy barriers of those subsequent steps are much higher in the case of Ni 2 Cu (111) than Ni (111) and Ni 2 Fe (111) systems, which reduce carbon deposition from CH radical dehydrogenation [19,28,37].

Two Reaction Pathways for CO 2 Dissociation
According to the previous experimental studies [7,38], there are two possible routes for CO 2 dissociation. First, adsorbed CO 2 * is directly dissociated to form CO* and atomic O*. The latter acts as an oxidant for CHx (x = 1-4), ultimately producing CO (g). In the second pathway, CH 4 * is first dehydrogenated to produce atomic H, which subsequently activates the CO 2 * to produce a COOH* intermediate. Then, the decomposition of COOH* produces CO* and an OH* oxidant in the following scheme. CO 2 * + H* → COOH* → CO* + OH* (2) As described above, H* atoms released from the CH 4 dissociation pathway can either contribute towards or activate CO 2 dissociation. The potential energy profile and structure associated with CO 2 hydrogenation (or H-induced CO 2 dissociation) are shown in Figure 4. At the first step, CO 2 and H atoms are co-adsorbed on Ni 2 Cu (111) surface to form a COOH* intermediate with an E a,f of 0.93 eV, and this reaction is exothermic by −0.11 eV. In the final state, CO and OH are co-adsorbed at the B 2Ni site after the breakage of COOH*. For adsorbed CO*, the C-Ni bond length is 1.89 Å, and in OH*, the O-Ni bond length is 1.98 Å. The activation energy (E a,f ) of COOH* dissociation is 0.43 eV, and the reaction is exothermic by 0.59 eV. Previous studies of DRM on pure Ni (111) surfaces have shown that direct CO 2 dissociation has a low energy barrier of 0.67 eV compared to 1.13 eV for the H-induced CO 2 dissociation pathway [28]. Meanwhile, the Ni 2 Cu (111) surface has a lower (E a,f ) of 0.93 eV for H-induced CO 2 dissociation. Thus, doping Cu in Ni (111) network slightly favors the CO 2 hydrogenation process, producing an OH oxidant via COOH * intermediate dissociation. Comparing the direct CO 2 dissociation and the H-induced CO 2 dissociation pathways, the latter is more favorable reaction in Ni 2 Cu (111) bimetallic system than in the case of Ni (111), where both atomic O* and OH* species participate as oxidants of CHx (x = 1-3) intermediates. Similar results have been reported for the Ni 2 Fe (111) surface, where both pathways were found to be competitive [19].

Oxidation of C and CH
When CH4 dissociates into C and H, CHx (x = 0-3) can combine with atomic O or OH species to produce CHO (H). Table 2 shows that the CH3 and CH2 dehydrogenation reactions are more favorable with relatively lower Ea,f of 0.75 eV and 0.49 eV, respectively. In contrast, CH dehydrogenation has a relatively higher Ea,f of 1.40 eV, while the reverse reaction is energetically favorable with Ea,r of 0.71 eV. Thus, coke formation due to CH decomposition is less desirable for Ni2Cu (111) compared to pure Ni (111) and Ni2Fe (111) surfaces with energy barriers of 1.33 eV [19] and 1.36 eV [28], respectively. Moreover, only CH* and C* are the most stable major intermediates remaining on the surface than the kinetically unstable CH3* and CH2* intermediates, as discussed in Table 1. It turns out that from all possible oxidation reactions of CHx (x = 0-3), C* + O* oxidation is the most favorable reaction.

Carbon elimination by C + O and C + OH
The C* + O* oxidation pathway was found to be more favorable at an Ea,f of 0.72 eV compared to 1.59 eV and 1.58 eV for Ni (111) and Ni2Fe (111), respectively, as shown in Figure 5.

Oxidation of C and CH
When CH 4 dissociates into C and H, CHx (x = 0-3) can combine with atomic O or OH species to produce CHO (H). Table 2 shows that the CH 3 and CH 2 dehydrogenation reactions are more favorable with relatively lower E a,f of 0.75 eV and 0.49 eV, respectively. In contrast, CH dehydrogenation has a relatively higher E a,f of 1.40 eV, while the reverse reaction is energetically favorable with E a,r of 0.71 eV. Thus, coke formation due to CH decomposition is less desirable for Ni 2 Cu (111) compared to pure Ni (111) and Ni 2 Fe (111) surfaces with energy barriers of 1.33 eV [19] and 1.36 eV [28], respectively. Moreover, only CH* and C* are the most stable major intermediates remaining on the surface than the kinetically unstable CH 3 * and CH 2 * intermediates, as discussed in Table 1. It turns out that from all possible oxidation reactions of CHx (x = 0-3), C* + O* oxidation is the most favorable reaction.

Carbon elimination by C + O and C + OH
The C* + O* oxidation pathway was found to be more favorable at an E a,f of 0.72 eV compared to 1.59 eV and 1.58 eV for Ni (111) and Ni 2 Fe (111), respectively, as shown in Figure 5.
The C* + OH* reaction pathway shows an E a,f of 1.13 eV compared to 1.46 eV for Ni (111) and 1.42 eV for Ni 2 Fe (111) surfaces. The reverse reaction of CO* → C* + O* has an E a,r of 2.89 eV, which is clearly in favor of carbon elimination. These results indicate that Cu-rich surfaces can accelerate specific oxidation reactions and change surface properties to improve carbon elimination by both atomic O and even OH species. As will be explained later, temperature plays a crucial role in enhancing these oxidation steps. These results conclude that Cu doped in Ni (111) reduced coke formation by increasing the activation energy barrier of CO* and CH* dissociation, but improved carbon elimination by both atomic O* and OH* species [18,39].
This study shows that the addition of Cu can overcome the limitation of Ni (111) and Ni 2 Fe (111) in terms of coke resistance, which is consistent with the results of previous calculations [26] and experimental studies [37]. The C* + OH* reaction pathway shows an Ea,f of 1.13 eV compared to 1.46 eV for Ni (111) and 1.42 eV for Ni2Fe (111) surfaces. The reverse reaction of CO* → C* + O* has an Ea,r of 2.89 eV, which is clearly in favor of carbon elimination. These results indicate that Cu-rich surfaces can accelerate specific oxidation reactions and change surface properties to improve carbon elimination by both atomic O and even OH species. As will be explained later, temperature plays a crucial role in enhancing these oxidation steps. These results conclude that Cu doped in Ni (111) reduced coke formation by increasing the activation energy barrier of CO* and CH* dissociation, but improved carbon elimination by both atomic O* and OH* species [18,39].
This study shows that the addition of Cu can overcome the limitation of Ni (111) and Ni2Fe (111) in terms of coke resistance, which is consistent with the results of previous calculations [26] and experimental studies [37].

CH + O and CH + OH Reactions
Oxidation of CH* by atomic O* generated from direct CO2 dissociation begins through coadsorption of CH on the FCC site and an O atom on an HCP site via one Cu atom. In the transition state, atomic O moves to the B NiCu site at a Ni-O distance of 1.97 Å and a Cu-O distance of 2.01 Å. CH* settles at the B 2Ni site at a Ni-C distance of 1.86 Å and a Ni-H distance of 1.81 Å. At this step, the energy barrier is 1.06 eV, which is much higher than 0.47 eV for pure Ni (111) and 0.78 eV for the Ni2Fe (111) surface [19,28]. Figure 6 shows that the CHOH* intermediate formed by co-adsorption of CH* and OH* at adjacent FCC and B 2Ni sites easily overcomes the energy barrier of 1.08 eV compared to 1.48 eV and 1.42 eV in pure Ni (111) and Ni2Fe (111), respectively [19,28].

CH + O and CH + OH Reactions
Oxidation of CH* by atomic O* generated from direct CO 2 dissociation begins through co-adsorption of CH on the FCC site and an O atom on an HCP site via one Cu atom. In the transition state, atomic O moves to the B NiCu site at a Ni-O distance of 1.97 Å and a Cu-O distance of 2.01 Å. CH* settles at the B 2Ni site at a Ni-C distance of 1.86 Å and a Ni-H distance of 1.81 Å. At this step, the energy barrier is 1.06 eV, which is much higher than 0.47 eV for pure Ni (111) and 0.78 eV for the Ni 2 Fe (111) surface [19,28]. Figure 6 shows that the CHOH* intermediate formed by co-adsorption of CH* and OH* at adjacent FCC and B 2Ni sites easily overcomes the energy barrier of 1.08 eV compared to 1.48 eV and 1.42 eV in pure Ni (111) and Ni 2 Fe (111), respectively [19,28].
Catalysts 2020, 10, x FOR PEER REVIEW 9 of 17 Figure 6. Activation energy profile of CH oxidation by OH. The OH is an effective oxidant that helps to skip CH dissociation. The transition state (TS) configuration shows where OH is adsorbed on the TopCu site while CH is adsorbed on the TopNi site.

CHOH and COH Decomposition
A stable CHOH* configuration was found at the B 2Ni site with the same C-Ni distance of 1.95 Å. Figure 7 shows two possible pathways for subsequent CHOH*. The first pathway involves CHOH* dissociation (CHOH* → CHO*+H*) with an energy barrier of 0.60 eV. Then, the produced CHO* has a low energy barrier of 0.18 eV, which readily forms CO* and atomic H*. The second pathway follows CHOH* dissociation, which forms COH* and H* with an energy barrier of 0.20 eV, and then the COH* dissociates to CO* and atomic H* with an energy barrier of 1.09 eV.
From the results above, it can be concluded that the CH oxidation by atomic O (1.06 eV) and OH Figure 6. Activation energy profile of CH oxidation by OH. The OH is an effective oxidant that helps to skip CH dissociation. The transition state (TS) configuration shows where OH is adsorbed on the TopCu site while CH is adsorbed on the TopNi site.

CHOH and COH Decomposition
A stable CHOH* configuration was found at the B 2Ni site with the same C-Ni distance of 1.95 Å. Figure 7 shows two possible pathways for subsequent CHOH*. The first pathway involves CHOH* dissociation (CHOH* → CHO* + H*) with an energy barrier of 0.60 eV. Then, the produced CHO* has Catalysts 2020, 10, 1043 9 of 16 a low energy barrier of 0.18 eV, which readily forms CO* and atomic H*. The second pathway follows CHOH* dissociation, which forms COH* and H* with an energy barrier of 0.20 eV, and then the COH* dissociates to CO* and atomic H* with an energy barrier of 1.09 eV.
A stable CHOH* configuration was found at the B 2Ni site with the same C-Ni distance of 1.95 Å. Figure 7 shows two possible pathways for subsequent CHOH*. The first pathway involves CHOH* dissociation (CHOH* → CHO*+H*) with an energy barrier of 0.60 eV. Then, the produced CHO* has a low energy barrier of 0.18 eV, which readily forms CO* and atomic H*. The second pathway follows CHOH* dissociation, which forms COH* and H* with an energy barrier of 0.20 eV, and then the COH* dissociates to CO* and atomic H* with an energy barrier of 1.09 eV.
From the results above, it can be concluded that the CH oxidation by atomic O (1.06 eV) and OH oxidants (1.08 eV) in the Ni2Cu (111) system is very competitive, due to the small difference of 0.02 eV. Moreover, both oxidation pathways have a lower energy barrier than that of Ni (111) and Ni2Fe (111) [19,28]. The energy barrier of CH oxidation by atomic O was slightly lower than that of CH oxidation by OH. Conversely, the oxidation of CH by OH showed a higher reaction rate constant in the temperature range of 800~1000K, which will be described in detail in Section 2.3. From the results above, it can be concluded that the CH oxidation by atomic O (1.06 eV) and OH oxidants (1.08 eV) in the Ni 2 Cu (111) system is very competitive, due to the small difference of 0.02 eV. Moreover, both oxidation pathways have a lower energy barrier than that of Ni (111) and Ni 2 Fe (111) [19,28].
The energy barrier of CH oxidation by atomic O was slightly lower than that of CH oxidation by OH. Conversely, the oxidation of CH by OH showed a higher reaction rate constant in the temperature range of 800~1000K, which will be described in detail in Section 2.3.

H 2 and H 2 O Formation
The reaction of H* + H* → H 2 (g) requires an E a,f of 0.73 eV, and is an endothermic reaction at a H f of 0.57 eV, as shown in Table 2. The H 2 (g) is physically adsorbed on the catalyst surface with an E ads of −0.016 eV, which prefers the product formation in a higher reaction temperature. Hence, H 2 (g) formation in Ni 2 Cu (111) catalyst is more facile than in pure Ni (111) and Ni 2 Fe (111), which have relatively higher energy barriers of 0.92 eV and 1.18 eV, respectively. In the first step of H 2 O* formation, the adsorbed H* and O* react to produce OH* with an E a,f of 0.94 eV and exothermic reaction energy (H f ) of −0.24 eV, as shown in Table 2. Figure 8, which describes the next step, shows that the formed OH* undergoes an exothermic reaction with H* with an energy barrier of 0.91 eV. These two steps are energetically preferred over pure Ni (111) and Ni 2 Fe (111) surfaces [19,28]. At high temperatures in DRM, H 2 O (or steam) facilitates the physical removal of coke deposition from the catalyst surface. formation, the adsorbed H* and O* react to produce OH* with an Ea,f of 0.94 eV and exothermic reaction energy (Hf) of −0.24 eV, as shown in Table 2. Figure 8, which describes the next step, shows that the formed OH* undergoes an exothermic reaction with H* with an energy barrier of 0.91 eV. These two steps are energetically preferred over pure Ni (111) and Ni2Fe (111) surfaces [19,28]. At high temperatures in DRM, H2O (or steam) facilitates the physical removal of coke deposition from the catalyst surface.

Effect of Temperature on Carbon Deposition Resistance
One drawback of the DFT calculations used to investigate the DRM reaction is that all atoms are localized to the "minimum energy" position at zero temperature (0 K). A complete vibrational analysis is performed on the elementary reaction to overcome this problem. The analysis has two advantages; the first is that the transition state configuration as well as the activation energy barrier can be verified with a single imaginary frequency. The second advantage is that the rate constants can be calculated through the Vineyard formula [38], a crucial step in developing microkinetic models and identifying atomic models [40,41].
In this regard, the calculated vibrational frequencies are used to evaluate the rate constant at the confirmed transition states, focusing on the effect of Cu doping and temperature on coke deposition resistance. The calculations of the vibrational frequency and rate constant are described in more detail in the supplementary information. Coke deposition can come from two primary sources: CH4 and CO2.Inthe CH4 dissociation pathway, the ratio of the rate constant of the CH oxidation pathway to the C oxidation pathway determines the carbon deposition. According to a previous study, increasing this ratio reduces carbon formation [29]. Coke can be also formed during the dissociation of CO into C* and O* in the CO2 reaction pathway. Table 3 shows the rate constants k (s −1 ) of carbon elimination and deposition on the Ni2Cu (111) surface over various temperature ranges. We found that k of C* + O* (or + OH*) or CH* + O* (or + OH*) oxidation reactions increases with the increasing temperature, and the carbon deposition from CO* is negligible due to the very small k value. In addition, the rate constant of CH dissociation was lower than that of carbon oxidation (kC(O) and kC(OH)) by atomic O or OH species, respectively. As the temperature increases, kCH/kC(O) increases while kCH/kC(OH) decreases.

Effect of Temperature on Carbon Deposition Resistance
One drawback of the DFT calculations used to investigate the DRM reaction is that all atoms are localized to the "minimum energy" position at zero temperature (0 K). A complete vibrational analysis is performed on the elementary reaction to overcome this problem. The analysis has two advantages; the first is that the transition state configuration as well as the activation energy barrier can be verified with a single imaginary frequency. The second advantage is that the rate constants can be calculated through the Vineyard formula [38], a crucial step in developing microkinetic models and identifying atomic models [40,41].
In this regard, the calculated vibrational frequencies are used to evaluate the rate constant at the confirmed transition states, focusing on the effect of Cu doping and temperature on coke deposition resistance. The calculations of the vibrational frequency and rate constant are described in more detail in the supplementary information. Coke deposition can come from two primary sources: CH 4 and CO 2 .Inthe CH 4 dissociation pathway, the ratio of the rate constant of the CH oxidation pathway to the C oxidation pathway determines the carbon deposition. According to a previous study, increasing this ratio reduces carbon formation [29]. Coke can be also formed during the dissociation of CO into C* and O* in the CO 2 reaction pathway. Table 3 shows the rate constants k (s −1 ) of carbon elimination and deposition on the Ni 2 Cu (111) surface over various temperature ranges. We found that k of C* + O* (or + OH*) or CH* + O* (or + OH*) oxidation reactions increases with the increasing temperature, and the carbon deposition from CO* is negligible due to the very small k value. In addition, the rate constant of CH dissociation was lower than that of carbon oxidation (k C(O) and k C(OH) ) by atomic O or OH species, respectively. As the temperature increases, k CH /k C(O) increases while k CH /k C(OH) decreases.  Figure 9 shows the temperature effect on carbon elimination reactions. The reaction of C* + O* has the highest rate constant in all carbon elimination reactions, followed by CH* + OH*. C* + OH* and CH* + O* reactions have similarly low rate constants as a function of temperature. OH* is the primary oxidizing agent for CH*, whereas atomic O is dominant in coke removal at different temperatures. It indicates that coke deposition by atomic O is easily removed at higher temperature ranges. On the other hand, it also reveals the importance of OH species in bypassing the coke formation step from CH dissociation where k CH /k C(OH) >> k CH /k C(O) , as shown in Figure 10. Comparing these results with previous studies [42,43], we can conclude that carbon elimination via C* + O* is enhanced in Ni 2 Cu (111) system over the Ni 2 Fe (111) and pure Ni (111) systems [19,25,28]. It suggests that the incorporation of Cu to Ni-Ni surface can simultaneously improve carbon elimination by C* + O* reaction, while reducing carbon deposition via CH dissociation. The higher the Cu/Ni ratio, the more it is expected to suppress catalyst activity when occupying the Ni active site. This result is consistent with the experimental results [22,24].  Figure 9 shows the temperature effect on carbon elimination reactions. The reaction of C* + O* has the highest rate constant in all carbon elimination reactions, followed by CH* + OH*. C* + OH* and CH* + O* reactions have similarly low rate constants as a function of temperature. OH* is the primary oxidizing agent for CH*, whereas atomic O is dominant in coke removal at different temperatures. It indicates that coke deposition by atomic O is easily removed at higher temperature ranges. On the other hand, it also reveals the importance of OH species in bypassing the coke formation step from CH dissociation where kCH/kC(OH) >> kCH/kC(O), as shown in Figure 10. Comparing these results with previous studies [42,43], we can conclude that carbon elimination via C*+O* is enhanced in Ni2Cu (111) system over the Ni2Fe (111) and pure Ni (111) systems [19,25,28]. It suggests that the incorporation of Cu to Ni-Ni surface can simultaneously improve carbon elimination by C*+O* reaction, while reducing carbon deposition via CH dissociation. The higher the Cu/Ni ratio, the more it is expected to suppress catalyst activity when occupying the Ni active site. This result is consistent with the experimental results [22,24]. Since the carbon elimination rate by both OH and atomic O is much higher than that of carbon deposition through CH dissociation, the Ni2Cu (111) surface is expected to exhibit higher catalytic activity. In addition, this periodic cycle of carbon deposition and elimination will result in catalyst stability.

Dominant Reaction Pathways and Rate-Limiting Steps
After determining the initial and final state of each elementary reaction of DRM, transition states are identified and confirmed by vibrational analysis. Then, zero-point energy corrections and rate  Since the carbon elimination rate by both OH and atomic O is much higher than that of carbon deposition through CH dissociation, the Ni 2 Cu (111) surface is expected to exhibit higher catalytic activity. In addition, this periodic cycle of carbon deposition and elimination will result in catalyst stability.

Dominant Reaction Pathways and Rate-Limiting Steps
After determining the initial and final state of each elementary reaction of DRM, transition states are identified and confirmed by vibrational analysis. Then, zero-point energy corrections and rate constants are evaluated. As a result, the dominant reaction pathway and rate-limiting step are determined. CH 4 undergoes successive dehydrogenation steps, of which CH 3 and CH 2 dissociation more readily occur with lower energy barriers of 0.75 eV and 0.49 eV, respectively. However, CH 3 and CH 2 oxidation by atomic O or OH are energetically unfavorable due to the high energy barriers. To illustrate, CH 3 requires energy barriers of 1.37 eV and 1.6 eV while CH 2 needs 0.76 eV and 0.78 eV for oxidation by O and OH, respectively.
Consequently, CH 4 is dissociated to CH, C, and H intermediates. The main intermediate of CH 4 dissociation, CH, follows three primary pathways: (a) CH* → C* + H*, (b) CH* + O* → CHO* → CO* + H*, and (c) CH* + OH* → CHOH*. The CH dissociation, as a significant source of coke formation, is energetically and kinetically unfavorable. Therefore, CH dissociation is the rate-limiting step of CH 4 dissociation and determines the overall reaction rate. In the case of CH* oxidation pathways, both (b) and (c) are very competitive, with only a 0.02 eV difference and (b) slightly preferred with a lower energy barrier of 1.06eV. However, the kinetic data shown in Table 3 indicate that CHOH* formation is more favorable reaction than CHO* at the temperature range 800~1000 K. Concerning CHOH*, the most preferred pathway goes through COH* formation with an energy barrier of 0.20 eV, which further dissociates into CO* and H*. From the standpoint of coke elimination, C oxidation by atomic O is a more favorable reaction with an energy barrier of 0.72 eV, which is lower than all other C and CH oxidation pathways. As for H* intermediate, H* + H* → H 2 * is the most preferred pathway. In the CO 2 activation pathway, we investigated the direct CO 2 dissociation to form CO and O, and the H-induced CO 2 formation pathway to form CO* and OH*. Unlike pure Ni (111) system, the H-induced CO 2 formation pathway is the more favorable than the direct CO 2 dissociation with a lower energy barrier of 0.93 eV. Eventually, this result suggests that the doped Cu atoms promote the H-induced CO 2 formation pathway and form O and OH oxidants that remove CH and C from the Ni 2 Cu (111) surface, as shown in Figure 10.

Computational Details
The first-principles calculations performed in this study are based on spin-polarized DFT implemented in the Vienna Ab initio Simulation Package (VASP) [28,44]. Blöchl's all-electron-like projector augmented wave (PAW) method [45] was employed to explain the interactions between the ion cores and the valence electrons. The exchange-correlation of the Kohn-Sham theory are treated by the generalized gradient approximation (GGA) [46] with Revised Perdew-Burke-Ernzerhof (RPBE), which gives more accurate chemisorption energies than the PW91 and PBE functional [47,48]. A plane-wave basis set with a kinetic energy cut-off of 400 eV is used for DFT calculations. All geometries were optimized using a force-based conjugate gradient algorithm until the forces acting on each atom converge better than 0.01 eV/Å. The optimized lattice constant for Ni is 3.523 Å, which is consistent with the experimental value of 3.524 Å [19]. Brillouin zone samplings are defined using Monkhorst-Pack scheme [39] and electronic occupancies are determined in a Methfessel-Paxton smearing method [49] with smearing energy of 0.2 eV.
Previous DFT studies on Ni catalysts considered the spin polarization of the surface magnetism to obtain more accurate total energies [50]. The Ni 2 Cu (111) surface is represented as a four-layer slab with a p(3 × 3) supercell where only the bottom layer of the slab is constrained. The neighboring slabs are separated by a vacuum region of 12 Å. The first Brillouin zone of the supercell is sampled Catalysts 2020, 10, 1043 13 of 16 with a 3 × 3 × 1 k-point grid, which is sufficient for this cell structure. The climbing nudged elastic band [51,52] and dimer methods [53] are used to locate the transition state (TS). Total energy and band structure energy are converged to obtain accurate forces within 1 × 10 −7 eV/atom during the electronic optimization. The adsorption energy (Eads) is calculated as follows: where E (adsorbate/slab) is the total energy of the slab model with an adsorbate, E slab is the total energy of the bare slab model, E adsorbate is the total energy of the isolated adsorbate. As agreed in the literature [54], the more negative adsorption energy indicates that the gas species is more strongly adsorbed on the surface. The Ni structure is crystallized in a face-centered cubic (FCC) crystal lattice. We selected the (111) orientation of this lattice due to their abundance in nickel-based alloys [50]. The Cu/Ni (111) surface alloy was then constructed by replacing three nickel atoms in the topmost layer of Ni (111) by copper atoms (i.e., at the dopant coverage of 1/3 ML). The ratio (1/3 ML) was chosen from the experimental results [27] as having better carbon gasification and suitable activation energies for the CH4 dehydrogenations, compared to high Cu loading (1.0 ML) and low Cu loading (1/9ML). The slab model surface is shown in Figure 1. Unless otherwise specified, the bottom-most layer in the slab models was constrained at the bulk position, and the top three layers, as well as the adsorbates, were allowed to relax during geometry optimization and transition state (TS) search [55]. The TS and minimum energy paths are obtained using the climbing-image nudged elastic band (Climbing-NEB) method, and confirmed by a single imaginary frequency from the vibrational analysis [56].

Conclusions
In this study, density functional theory (DFT) calculations were used to understand the mechanism of DRM over a Ni 2 Cu (111) catalyst. In addition, carbon deposition and elimination for have been investigated at the molecular level and under realistic reaction conditions. All elementary reaction steps, including CH 4 dehydrogenation, CO 2 activation, CH and C oxidations, were comprehensively described. The results showed a significant improvement in inhibiting carbon deposition compared to similar reactions on the Ni (111) and Ni 2 Fe (111) surfaces. First, the energy barriers in CH 4 dissociation steps were found to be relatively increased to Ni (111) and Ni 2 Fe (111) catalysts. Specifically, the CH dissociation was found to be the rate-limiting step with the highest energy barrier of 1.41 eV when compared to 1.33 eV for Ni (111) and 1.36 eV for Ni 2 Fe (111) catalysts. Moreover, the source of coke had been confirmed to be from CH 4 dissociation rather than CO 2 , which agrees with previous studies on Ni-based catalysts. The coke elimination through oxidation is remarkably improved by both OH and atomic O species as competitive oxidants. From the C/CH oxidation pathways, C* + O* → CO (g) was found to be the most favorable reaction with an energy barrier of 0.72 eV. This value is less than half of similar oxidation reaction on Ni (111) and Ni 2 Fe (111) catalysts. In addition, coke deposition is physically prevented by H 2 O (g), which is easily formed in a Ni 2 Cu (111) system. Combining the above results showed that the Ni-Ni surface with Cu atoms could improve carbon elimination (by C* + O* reaction), while simultaneously reducing carbon deposition from CH dissociation.
The vibrational frequencies were used to evaluate the rate constant k of coke deposition and elimination reactions at typical DRM reaction temperatures. The rate constant of CH dissociation was lower than those of carbon oxidation (k C(O) and k C(OH) ) by atomic O or OH species, respectively. Their calculated values revealed the importance of OH species in bypassing the coke formation step from CH dissociation. Last, when carbon deposition occurs on the Ni 2 Cu (111) surface, coke could be instantaneously removed by various oxidation reactions. In conclusion, this efficient periodic cycle of carbon deposition and carbon elimination results in a more stable catalytic performance and excellent carbon deposition resistance in DRM.
Funding: This paper was made possible by an NPRP exceptional grant award [NPRP-EP X-100-2-024] from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the authors.