Unveiling the Origin of Alkali Metal (Na, K, Rb, and Cs) Promotion in CO2 Dissociation over Mo2C Catalysts

Molybdenum carbide (Mo2C) is a promising and low-cost catalyst for the reverse water−gas shift (RWGS) reaction. Doping the Mo2C surface with alkali metals can improve the activity of CO2 conversion, but the effect of these metals on CO2 conversion to CO remains poorly understood. In this study, the energies of CO2 dissociation and CO desorption on the Mo2C surface in the presence of different alkali metals (Na, K, Rb, and Cs) are calculated using density functional theory (DFT). Alkali metal doping results in increasing electron density on the Mo atoms and promotes the adsorption and activation of CO2 on Mo2C; the dissociation barrier of CO2 is decreased from 12.51 on Mo2C surfaces to 9.51–11.21 Kcal/mol on alkali metal-modified Mo2C surfaces. Energetic and electronic analyses reveal that although the alkali metals directly bond with oxygen atoms of the oxides, the reduction in the energy of CO2 dissociation can be attributed to the increased interaction between CO/O fragments and Mo in the transition states. The abilities of four alkali metals (Na, K, Rb, and Cs) to promote CO2 dissociation increase in the order Na (11.21 Kcal/mol) < Rb (10.54 Kcal/mol) < Cs (10.41 Kcal/mol) < K (9.51 Kcal/mol). Through electronic analysis, it is found that the increased electron density on the Mo atoms is a result of the alkali metal, and a greater negative charge on Mo results in a lower energy barrier for CO2 dissociation.


Introduction
Increasing atmospheric CO 2 concentrations have resulted in global warming [1][2][3]. Therefore, CO 2 capture, storage, and catalytic reduction have drawn attention to reduce this environmental burden [4]. In particular, the reverse water-gas shift (RWGS) reaction, which reduces CO 2 to CO as an intermediate to generate methanol or other hydrocarbons, is promising [3]. The RWGS reaction is endothermic; thus, the RWGS reaction is thermodynamically favorable at high temperatures, as shown in Equation (1) [5].
Noble metal catalysts such as Pt [6,7], Rh [8,9], and Au [10] show reasonable activity and selectivity for the RWGS reaction but are costly. However, supported noble metal catalysts frequently suffer the problem of sintering under high temperature conditions. Moreover, noble metal catalysts are relatively expensive and scarce, which limits their ability to be widely used for CO 2 hydrogenation. Transition metal carbides (TMCs) such as Mo 2 C [11,12], WC [13], and TiC [14] are considered as attractive candidates for the RWGS reaction because of their low cost and similar catalytic activity to platinum-based catalysts. TMCs have good performance in the reaction of CO 2 conversion into CO [15], CH 4 [16],

Computation Detail and Models
All calculations were performed by using the DMol 3 code within the Materials Studio 7.0 program [34]. The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional [35] was selected to calculate the exchange-correlation energy. The wave functions were expanded by the utilization of the double numerical quality basis set with polarization functions (DNP) [36]. The energy, gradient, and displacement convergence criteria were 1 × 10 −5 hartree, 2 × 10 −3 hartree/Å, and 5 × 10 −3 Å, respectively.
LST/QST was used to perform the transition states (TS) search [37,38]. The convergence criterion of the TS search was set to 0.002 Ha/Å on each atom. Only one virtual frequency could be considered as the real transition state.
The adsorption energy (E ads ) of all intermediate species on the surface of catalyst was defined as: E ads = E tot − E cat − E gas (2)  where E tot is the total energy of the adsorbed species on the catalyst, E cat is the total energy of the clean catalyst, and E gas is the energy of the molecules in the gas phase. The activation barrier (E Barrier ) and reaction energy (∆E) were calculated using the formulas: Here, E IS , E TS , and E FS represent the total energies of the initial state (IS), transition state (TS), and the final state (FS), respectively.
By applying geometry optimizations based on the minimization of the total energy of the unit cell, the DFT lattice parameters were found to be a = 6.00 Å, b = 5.78 Å, and c = 4.71 Å, which were in good agreement with the experimental results [39]. The slab model of the β-Mo 2 C (001) surface contained six atomic layers with a total of 24 C atoms and 48 Mo atoms in one unit cell (using a 2 × 2 supercell with size 12.00 × 11.57 × 4.71 Å, with a vacuum space of 20 Å). During the structural optimization, the bottom two layers were constrained in their bulk positions, whereas all the other atoms were allowed to relax. For alkali metal-modified β-Mo 2 C (001), one alkali atom (Na, K, Rb, Cs) was placed at different sites of the top layer of the molybdenum layer. After geometry optimization, the site that exhibited the strongest binding to K atom was selected for further calculations.

Results and Discussion
The four alkali metal atoms at optimized structures of the X-Mo 2 C (X = Na, K, Rb, Cs) surfaces were all located on the 4F sites on the Mo 2 C surface, that is, between four Mo atoms ( Figure 1). The alkali metal-promoted surfaces are shown in Figure 2a-d, and the key structural parameters of the X-Mo 2 C are listed in Table S1. The distances between alkali metals and Mo atoms increased with the increases in the atomic radii of the alkali metals: 3.26, 3.72, 3.89, and 4.04 Å on average for Na, K, Rb, and Cs, respectively. In addition, after the addition of the alkali metal, the Mo 1 -Mo 3 and Mo 3 -M 4 bonds increased in length by 0.04-0.06 Å, whereas the Mo 1 -Mo 4 bond length was shortened by 0.03 Å for all X-Mo 2 C. The coverage of alkali metals on X-Mo 2 C surfaces was a 0.014 mono layer. where E tot is the total energy of the adsorbed species on the catalyst, E is the total energy of the clean catalyst, and E gas is the energy of the molecules in the gas phase. The activation barrier (E Barrier ) and reaction energy (∆E) were calculated using the formulas: Here, E IS , E TS , and E FS represent the total energies of the initial state (IS), transition state (TS), and the final state (FS), respectively.
By applying geometry optimizations based on the minimization of the total energy of the unit cell, the DFT lattice parameters were found to be a = 6.00 Å, b = 5.78 Å, and c = 4.71 Å, which were in good agreement with the experimental results [39]. The slab model of the β-Mo2C (001) surface contained six atomic layers with a total of 24 C atoms and 48 Mo atoms in one unit cell (using a 2 × 2 supercell with size 12.00 × 11.57 × 4.71 Å, with a vacuum space of 20 Å). During the structural optimization, the bottom two layers were constrained in their bulk positions, whereas all the other atoms were allowed to relax. For alkali metal-modified β-Mo2C (001), one alkali atom (Na, K, Rb, Cs) was placed at different sites of the top layer of the molybdenum layer. After geometry optimization, the site that exhibited the strongest binding to K atom was selected for further calculations.

Optimized Structure of Alkali-Metal-Modified β-Mo2C (001)
The four alkali metal atoms at optimized structures of the X-Mo2C (X = Na, K, Rb, Cs) surfaces were all located on the 4F sites on the Mo2C surface, that is, between four Mo atoms ( Figure 1). The alkali metal-promoted surfaces are shown in Figure 2a-d, and the key structural parameters of the X-Mo2C are listed in Table S1. The distances between alkali metals and Mo atoms increased with the increases in the atomic radii of the alkali metals: 3.26, 3.72, 3.89, and 4.04 Å on average for Na, K, Rb, and Cs, respectively. In addition, after the addition of the alkali metal, the Mo1-Mo3 and Mo3-M4 bonds increased in length by 0.04-0.06 Å, whereas the Mo1-Mo4 bond length was shortened by 0.03 Å for all X-Mo2C. The coverage of alkali metals on X-Mo2C surfaces was a 0.014 mono layer. As shown by the charge analysis in Table 1, the Mulliken charge on Mo atoms in bare Mo2C was positive. In contrast, after the addition of the alkali metal, the charge on the adjacent Mo atoms became negative, suggesting the transfer of electrons from the alkali metal to Mo. Moreover, the closest Mo atoms to the alkali metal gained the most electrons. As shown by the charge analysis in Table 1, the Mulliken charge on Mo atoms in bare Mo 2 C was positive. In contrast, after the addition of the alkali metal, the charge on the adjacent Mo atoms became negative, suggesting the transfer of electrons from the alkali metal to Mo. Moreover, the closest Mo atoms to the alkali metal gained the most electrons. Because Rb and Cs atoms are less electronegative than the other alkali metals, they increased the electron density of the surface Mo atoms and subsurface C atoms. Therefore, in Rb-and Cs-Mo 2 C, the charges on Mo atoms were less negative than those of K and Na-Mo 2 C.
In addition, we calculated the changes in the d-band center [40] as a result of charge transfer between Mo and alkali metal atoms (Figure 2e). The d-band center before and after the addition of the alkali metal remained the same, consistent with previous findings [41,42]. Because Rb and Cs atoms are less electronegative than the other alkali metals, they increased the electron density of the surface Mo atoms and subsurface C atoms. Therefore, in Rb-and Cs-Mo2C, the charges on Mo atoms were less negative than those of K and Na-Mo2C.
In addition, we calculated the changes in the d-band center [40] as a result of charge transfer between Mo and alkali metal atoms ( Figure 2e). The d-band center before and after the addition of the alkali metal remained the same, consistent with previous findings [41,42].

Adsorption of Intermediate Species on Mo2C and X-Mo2C Surfaces
The schematic mechanism of the redox pathway is shown in Figure 3. We calculated the adsorption energy (Eads) and key parameters of CO2, CO, and O* species on bare and X-Mo2C surfaces involved in the redox pathway (shown in Figure 4 and Table S2).

Adsorption of Intermediate Species on Mo 2 C and X-Mo 2 C Surfaces
The schematic mechanism of the redox pathway is shown in Figure 3. We calculated the adsorption energy (E ads ) and key parameters of CO 2 , CO, and O* species on bare and X-Mo 2 C surfaces involved in the redox pathway (shown in Figure 4 and Table S2).     The most stable adsorption configuration of CO 2 on Mo 2 C is shown in Figure 4, having an adsorption energy of −30.83 Kcal/mol, consistent with the literature value [30]. The C atom in CO 2 was positioned at the bridge site between Mo 3 and Mo 5 , and the two C-Mo bonds were 2.24 Å in length.  [44]. These findings indicate that the electrostatic interaction between O and X was strong and similar to the ionic bonding between O and X in X 2 O. Wang et al. found that for oxygenate species adsorbed on K + -modified Cu (111) and Cu (110) surfaces, when the distance between K and O atoms was 3.00 Å, direct bonding between O δ− and K δ+ ions occurred [22]. Further, a short distance between X and O generated a longer C-O bond, indicating that stronger X-O interactions promote CO 2 activation. Therefore, alkali metals could promote the adsorption and activation of CO 2 , consistent with theoretical and experimental findings [30].
Our charge analysis (Table S3) suggested that electrons are transferred from the alkali metal to Mo atoms and, thus, affect the surface charge of Mo 2 C [28]. Therefore, when CO 2 was adsorbed on Mo 2 C, the Mo atoms lost electrons and CO 2 gained 0.29 e. In contrast, when CO 2 was adsorbed on X-Mo 2 C, the Mo atoms became more positive (lost more electrons); for example, CO 2 gained 0.74 e on Na-Mo 2 C, 0.71 e on K-Mo 2 C, 0.73 e on Rb-Mo 2 C, and 0.69 e on Cs-Mo 2 C. The increase in the charge of CO 2 also indicated enhanced charge transfer via alkali metal promotion. Moreover, in the X-Mo 2 C surfaces, alkali metal atoms lost electrons by 0.72 e for Na, 0.82 e for K, 0.76 e for Rb, and 0.74 e for Cs, respectively. Therefore, on one hand, alkali metal atoms donated electrons to CO 2 , but, on the other hand, they facilitated electron transfer from Mo to CO 2 and thus promoted CO 2 activation.

Adsorption of CO*
When CO adsorbed on the Mo 2 C surface, the carbon atom of CO 2 was adsorbed on the bridge sites between Mo 3 and Mo 5 with an orientation tilted toward  (Table S4) showed that more electrons transferred to CO on X-Mo 2 C than that on bare Mo 2 C. Therefore, the addition of alkali metal atoms increased the adsorption of CO as compared with the clean surface and resulted in longer C-O bonds.

Adsorption of O*
Atomic oxygen adsorbed on the 3F sites between the Mo 3 -Mo 4 -Mo 5 atoms, having average Mo-O bond lengths of 2.08 Å and E ads of −80.74 Kcal/mol. The E ads for O* on the surface of X-Mo 2 C (X = Na, K, Rb, and Cs) ranged from −81.64 to −82.10 Kcal/mol, slightly greater than that on bare Mo 2 C. The average distances between O* and Mo 3 atoms were 2.46 Å for Na, 2.85Å for K, 3.03 Å for Rb, and 3.04 Å for Cs. On bare Mo 2 C, the atomic oxygen gained 0.66 e from the surface of Mo atoms, whereas for X-Mo 2 C, the O atom gained more electrons, namely 0.74 e from Na-Mo 2 C, 0.73 e from K-Mo 2 C, 0.72 e from Rb-Mo 2 C, and 0.73 e from Cs-Mo 2 C (see Table S5). Moreover, the Mo atoms in the X-Mo 2 C surfaces were more positive, suggesting that the addition of alkali metals promoted the loss of electrons from the Mo atoms around O*.

Energy Barriers for CO 2 Dissociation on Mo 2 C and Alkali-Metal-Modified Mo 2 C Surfaces
Currently, the RWGS reaction mechanisms are classified into redox-(or direct-), carboxyl-, and formate-mediated routes. Chen et al. [45] performed ambient-pressure X-ray photoelectron spectroscopy (AP-XPS) measurements on the Mo 2 C catalyst, and they did not find intermediate species (carbonate, formate, carbonyl, etc.) under reaction conditions. Furthermore, they proved that CO 2 was directly dissociated on Mo 2 C to produce CO and oxycarbide (Mo 2 C-O). Surface oxygen (Mo 2 C-O) was removed subsequently by hydrogen to produce H 2 O to complete the catalytic cycle [46]. Moreover, the elemental steps for CO 2 dissociation to CO* and O* are known to be the rate limiting steps on both bare Mo 2 C and K-modified Mo 2 C catalysts [30]. Thus, the activation barriers for CO 2 dissociation on the various alkali metal-modified Mo 2 C surfaces were studied and compared.
In Figure 5, we show the activation energy profiles of CO 2 dissociation on the (a) bare, (b) Na-promoted, (c) K-promoted, (d) Rb-promoted, and (e) Cs-promoted Mo 2 C (001) surfaces. The activation barrier for CO 2 dissociation on Mo 2 C surfaces was found to be 12.51 Kcal/mol, and the O-CO bond lengths of the transition states (TSs) were found to be 1.75 Å, indicating the cleavage of a C-O bond. The activation energies for this reaction were remarkably different on the four X-Mo 2 C surfaces, namely 11.21 Kcal/mol for Na-Mo 2 C, 9.51 Kcal/mol for K-Mo 2 C, 10.54 Kcal/mol for Rb-Mo 2 C, and 10.41 Kcal/mol for Cs-Mo 2 C, lower than that on bare Mo 2 C. For CO 2 dissociation on the X-Mo 2 C surfaces, the bond length of C-O b was elongated, ranging from 1.81 to 1.87 Å in the TS, respectively, longer than that on bare Mo 2 C. In addition, the distance between Na, K, Rb, and Cs and O a in CO 2 were 2.14, 2.94, 3.07, and 3.06 Å, respectively, suggesting the interaction between X and O throughout the reaction and suggesting the key role of the alkali metal in CO 2 dissociation, consistent with experimental observations [47][48][49].  Figure 5 suggests that the transition state for CO2 dissociation is a late (product-like) transition state. Therefore, for CO2 dissociation, the stabilization of the final state should also stabilize the transition state, resulting in a lower activation barrier. Figure 5f shows that the CO2 dissociation barrier was strongly influenced by the E ads of CO and O fragments on the catalyst surfaces, and stronger CO or O binding resulted in lower CO2  Figure 5 suggests that the transition state for CO 2 dissociation is a late (product-like) transition state. Therefore, for CO 2 dissociation, the stabilization of the final state should also stabilize the transition state, resulting in a lower activation barrier. Figure 5f shows that the CO 2 dissociation barrier was strongly influenced by the E ads of CO and O fragments on the catalyst surfaces, and stronger CO or O binding resulted in lower CO 2 dissociation barriers. Therefore, the identification of the role of the alkali metal atom on the stability of adsorbed CO and O during the reaction is necessary.

Energetic Analysis
As discussed earlier, alkali metals enhance the RWGS activity of Mo 2 C by decreasing the energy barriers for CO 2 dissociation. Thus, to elucidate the effects of the alkali metals, the physical origin of the reaction barriers for CO 2 dissociation on both bare and X-Mo 2 C surfaces were assessed using energy decomposition, as proposed by Hammer [50,51] (Equation (4)), and the results are listed in Table 2.
where E CO 2 bond represents the bonding energy of CO 2 in gas. E IS CO 2 , E TS CO , E TS O , and E TS int refer to binding energy of CO 2 * in the IS, binding energy of CO* (O*) in the TS, and the interaction of CO with O in the TS, respectively. In the C-O bond scission of CO 2 on Mo 2 C surfaces, alkali metals stabilize the binding of CO 2 in the IS, which is unfavorable for reducing the energy barrier (Table 2). However, by strengthening CO and O binding in the TS (E TS CO and E TS O ) on X-Mo 2 C relative to those on clean surfaces, the alkali metal reduces the energy barrier and promote CO 2 dissociation. In addition, all alkali metals can enhance the stability of CO or O fragments in the TS on Mo 2 C. However, Na-and K-modified surfaces effectively stabilize adsorbed CO compared to bare Mo 2 C ( ∆E TS CO > ∆E TS O , whereas Rb-and Cs-modified surfaces stabilize adsorbed O ( ∆E TS O > ∆E TS CO . Therefore, Max∆E TS S , i.e., the maximum of ∆E TS CO and ∆E TS O was plotted against the energy barrier for CO 2 dissociation. Figure 6 shows that the energy barrier for CO 2 dissociation on X-Mo 2 C was linearly correlated to Max∆E TS S (R 2 = 0.90), and a greater value of Max∆E TS S indicated a larger decrease of the barrier and a stronger promoting effect of the alkali metal. In other words, increasing the E ads of the CO and O fragments in the TS can effectively reduce the energy barrier, but the extent of the barrier reduction depends on the balance of stabilities of adsorbed CO and O resulting from alkali metal addition.
As displayed in Figure 5, the alkali metals interacted with CO and O on the X-Mo 2 C surfaces throughout the reaction. Hence, apart from the interaction between these adsorbates and surface Mo atoms, the interaction between them and the alkali metal adatom also made up the interaction of them with X-Mo 2 C.The interaction energies of the interactions between adsorbates and alkali metals were calculated with the following formulas, and the results are listed in Table 3.
E TS A/X , E A , and Ex represent the energies of the A−alkali metal complex, isolated A, and alkali metal at Mo 2 C surfaces, respectively; and E TS surf refers to the energy of the clean surface at the TS.
As shown in Table 3, the addition of alkali metal adatoms resulted in interactions between the alkali metal and oxygen species in the TS, but there was little correlation between E CO−X Previous studies have demonstrated that the activation of CO 2 requires electron transfer from the catalyst to CO 2 [52][53][54][55]. The charge analysis in Table 3 shows that the enhancement in the Mo-O and Mo-CO interactions was due to the addition of alkali metals, which induced the accumulation of electron density at Mo and, thus, electron transfer from Mo to CO and O in the TS. Further, we observed a linear increase in the negative charge on the Mo atoms (increase in electron density) in the Na, Rb, Cs, and K-Mo 2 C surfaces, which was consistent with the reduction in E Barrier . This result indicated that the increase in charge at Mo resulted in a lower E Barrier . Additionally, although Rb and Cs are less electronegative than the other alkali metals, they transferred electrons to both Mo and C in the subsurface; thus, fewer electrons accumulated at Mo in Rb/Cs-Mo 2 C than in K-Mo 2 C.
In summary, the CO 2 dissociation energy barrier was in the order of Mo 2 C (12.45 Kcal/mol) > Na (11.21 Kcal/mol) > Rb (10.54 Kcal/mol) > Cs (10.41 Kcal/mol) > K(9.51 Kcal/mol). This is because the K atom promoted the most electrons accumulated at the Mo atom and thereby generated the strongest Mo-CO interactions in the TS. The significantly improved stability of CO fragments in the TS led to the energy barrier of CO 2 dissociation on K-Mo 2 C being the lowest.

CO Desorption on Mo 2 C and Alkali-Metal-Modified Mo 2 C Surfaces
Next, we calculated the energies of CO desorption on the surfaces of bare Mo 2 C and X-Mo 2 C (Figure 7). The CO desorption energy on bare Mo 2 C was endothermic by 63.65 Kcal/mol. The addition of alkali metals on Mo 2 C slightly increased the difficulty of CO desorption. Mpourmpakis et al. found that by pre-adsorption of low-coverage oxygen (<0.50 ML), the desorption of CO on K-modified Mo 2 C could be effectively promoted [56].

Conclusions
The activity of CO2 dissociation into CO on bare Mo2C and those on promoted surfaces of X-Mo2C (X = Na, K, Rb, and Cs) were studied using DFT calculations. The addition of alkali metal elements induced the accumulation of negative charges on the Mo atoms and thus promoted the adsorption and activation of CO2 on Mo2C. The CO2 dissociation energy barrier was in the order of Mo2C (12.45 Kcal/mol) > Na (11.21 Kcal/mol) > Rb (10.54 Kcal/mol) > Cs (10.41 Kcal/mol) > K (9.51 Kcal/mol). On the basis of energetic and electronic analysis, although the alkali metals directly bonded with oxygen atoms in the adsorbed oxygen species, the main reason for the reduction in the energy of CO2 dissociation was the stronger interaction between CO/O fragments and Mo in the TS. Through electronic analysis, the promoting effects of alkali metals were influenced by the difference in the increase of electron density at the Mo atoms. Specifically, the greater the negative charge on the Mo site, the lower the energy barrier for CO2 dissociation. In comparison, the K atom promoted the most electrons accumulated at the Mo atom and thereby generated the strongest Mo-CO interactions in the TS. The significantly improved stability of CO fragments in the TS led to the energy barrier of CO2 dissociation on K-Mo2C being the lowest.
Supplementary Materials: The following supporting information can be downloaded at: www.mdpi.com/xxx/s1, Table S1: The key structural parameters of Mo2C and X-Mo2C; Table S2: Adsorption energies (Kcal/mol) and bond length (Å) of all possible intermediates on the X (Na, K,

Conclusions
The activity of CO 2 dissociation into CO on bare Mo 2 C and those on promoted surfaces of X-Mo 2 C (X = Na, K, Rb, and Cs) were studied using DFT calculations. The addition of alkali metal elements induced the accumulation of negative charges on the Mo atoms and thus promoted the adsorption and activation of CO 2 on Mo 2 C. The CO 2 dissociation energy barrier was in the order of Mo 2 C (12.45 Kcal/mol) > Na (11.21 Kcal/mol) > Rb (10.54 Kcal/mol) > Cs (10.41 Kcal/mol) > K (9.51 Kcal/mol). On the basis of energetic and electronic analysis, although the alkali metals directly bonded with oxygen atoms in the adsorbed oxygen species, the main reason for the reduction in the energy of CO 2 dissociation was the stronger interaction between CO/O fragments and Mo in the TS. Through electronic analysis, the promoting effects of alkali metals were influenced by the difference in the increase of electron density at the Mo atoms. Specifically, the greater the negative charge on the Mo site, the lower the energy barrier for CO 2 dissociation. In comparison, the K atom promoted the most electrons accumulated at the Mo atom and thereby generated the strongest Mo-CO interactions in the TS. The significantly improved stability of CO fragments in the TS led to the energy barrier of CO 2 dissociation on K-Mo 2 C being the lowest.
Author Contributions: Investigation, formal analysis and writing-original draft preparation, R.L.; Resources, software, C.C.; Formal analysis, investigation, writing-review-editing, W.C. Formal analysis, investigation, writing-review-editing, W.S. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement:
The data presented in this study are available from the corresponding author, upon reasonable request.

Conflicts of Interest:
The authors declare no conflict of interest.