Thermodynamic and Kinetic Study of Carbon Dioxide Hydrogenation on the Metal-Terminated Tantalum-Carbide (111) Surface: A DFT Calculation

: The need to reduce our reliance on fossil fuels and lessen the environmentally harmful effects of CO 2 have encouraged investigations into CO 2 hydrogenation to produce useful products. Transition metal carbides exhibit a high propensity towards CO 2 activation, which makes them promising candidates as suitable catalysts for CO 2 hydrogenation. Here, we have employed calculations based on the density-functional theory to investigate the reaction network for CO 2 hydrogenation to product molecules on the tantalum-terminated TaC (111) surface, including two routes from either HCOOH* or HOCOH* intermediates. Detailed calculations of the reaction energies and energy barriers along multiple potential catalytic pathways, along with the exploration of all intermediates, have shown that CH 4 is the predominant product yielded through a mechanism involving HCOOH, with a total exothermic reaction energy of − 4.24 eV, and energy barriers between intermediates ranging from 0.126 eV to 2.224 eV. Other favorable products are CO and CH 3 OH, which are also produced via the HCOOH pathway, with total overall reaction energies of − 2.55 and − 2.10 eV, respectively. Our calculated thermodynamic and kinetic mechanisms that have identiﬁed these three predominant products of the CO 2 hydrogenation catalyzed by the TaC (111) surface explain our experimental ﬁndings, in which methane, carbon monoxide, and methanol have been observed as the major reaction products.


Introduction
The Earth's expanding population continues to lead to an increase in the world's energy consumption. However, it is now clear that CO 2 emissions from burning fossil fuels [1] are responsible, to a great extent, for climate change and the resulting environmental consequences. Hence, developments in the production of renewable resources and useful products from CO 2 hydrogenation is a fascinating research area [2][3][4].
Since fossil fuel reserves are finite, hydrogen production and storage as an alternative energy source to balance diminishing oil and gas resources could be feasible in a methanol economy [4,5]. Methanol, an important chemical raw materials, is already in significant demand due to its wide application in power generation and electricity, and it is an excellent alternative fuel [4,6]. Similarly, formic acid is another promising hydrogen storage material, and it is of considerable importance in the chemical and energy industries [2]. Apart from the traditional role of methane (CH 4 ) for power production and heating, this gas is also valuable for industrial processes and for use in the production of important chemicals, e.g., in its conversion to methanol [1,7]. In addition, the low cost, high purity, versatility, and

Method
The computational results are obtained using the Vienna Ab initio simulation package (VASP) [44,45], with the exchange-correlation functional developed by Perdew-Burke-Ernzerhof [46] and used within the generalized gradient approximation (GGA). Moreover, in order to improve the energy description of each system, we have included the DFT-D3 dispersion correction, as proposed by Grimme [47], with a plane wave cut-off energy of 600 eV. We have used a Monkhorst-Pack k-point mesh of 11×11×11 and 4×4×1 for the TaC bulk and (111) surface, respectively. The lattice parameter was calculated at a 0 = 4.450 Å, which is in excellent agreement with the experimental data (a 0 = 4.454 Å) from the inorganic crystal structure database (ICSD) [48] and other DFT studies using different exchange-correlation functionals (4.485 and 4.436 Å) [14]. The convergence force between atoms is set to be smaller than 0.01 eV/Å, and the maximum energy of each atom is converged to 10 −5 eV. In order to avoid the interaction between neighboring unit cells, a vacuum space of more than 20 Å is introduced to create the surface slabs. Transition states were found using the IDM method [49,50], and frequency calculations were carried out to ensure that we have obtained the correct initial, transition, and final states.

Model
The TaC (111) surface and the molecules to be adsorbed at the surface are shown in Figure 1. Two possible planes, terminated by tantalum or carbon atoms, exist for the facecentered cubic (fcc) structure of the TaC (111) surface. In this study the tantalum-terminated TaC (111) surface (see Figure 1a) is investigated. To provide an adequate description of the surface relaxations, the TaC (111) surface is constructed of seven layers, with four bottom layers fixed to mimic the bulk crystal. The simulation cell contains 112 atoms and is the same as the slab used in the study by Vojvodic et al. for the adsorption of atoms and molecules on TMC (111) surfaces [51]. Each adsorbed molecule is located in different initial positions on the surface to calculate the favorable adsorption geometries. We have calculated the adsorption energies of the intermediates relative to CO 2 and four H 2 molecules in the gas phase [52]:

Adsorption Configurations and Energies on TaC (111) Surface
In this section, the CO2 hydrogenation processes at the TaC (111) surface and the stable adsorption of all possible intermediates are calculated. First, by constructing several initial configurations, the most favorable locations were selected after complete geometric optimization of the TaC (111) surface and adsorbates. The preferred adsorption positions for all intermediates at the TaC (111) surface are presented in Figure 1b, with geometric information and adsorption energies provided in Table 1.
CO binds to the TaC (111) surface through its O atom, which is located exactly on top of a surface Ta atom, with a bond length of 2.27 Å and an adsorption energy of −0.226 eV. In the adsorbed CO2 molecule, two oxygen atoms bond strongly to the surface Ta atoms, while its carbon atom does not bind to the surface atoms; the Ta-O bond lengths are 2.21 Å to both oxygen atoms. Adsorption of the CO2 molecule results in an alteration in the initial structure of the molecule, where the C-O bond length shortens from 1.177 Å to 1.27

Adsorption Configurations and Energies on TaC (111) Surface
In this section, the CO 2 hydrogenation processes at the TaC (111) surface and the stable adsorption of all possible intermediates are calculated. First, by constructing several initial configurations, the most favorable locations were selected after complete geometric optimization of the TaC (111) surface and adsorbates. The preferred adsorption positions for all intermediates at the TaC (111) surface are presented in Figure 1b, with geometric information and adsorption energies provided in Table 1. It should be noted that the bond between the molecules and the surface is indicated by the symbol *, while the chemical bonds in each molecule after adsorption are shown without any sign.
CO binds to the TaC (111) surface through its O atom, which is located exactly on top of a surface Ta atom, with a bond length of 2.27 Å and an adsorption energy of −0.226 eV. In the adsorbed CO 2 molecule, two oxygen atoms bond strongly to the surface Ta atoms, while its carbon atom does not bind to the surface atoms; the Ta-O bond lengths are 2.21 Å to both oxygen atoms. Adsorption of the CO 2 molecule results in an alteration in the initial structure of the molecule, where the C-O bond length shortens from 1.177 Å to 1.27 Å. Besides the bond lengths, the O-C-O bond angle decreases from 180 • to 132 • after adsorption of the molecule, which indicates that the molecule has become activated. These geometric changes have been seen in other studies [53]. For example, the adsorption of CO 2 on the TaC (111) surface without cleavage of the C-O bond agrees with the DFT study of the chemisorption of a CO 2 molecule on the MoC surface, without cleavage of the C-O bonds when the Mo/C ratio is equal to one [54]. The CO 2 adsorption energy (−0.1.891 eV) is also very close to the values found by Kunkel et al. [22,55]  Each oxygen atom of HCOOH bonds to one Ta atom on the surface, with bond lengths of 2.22 Å and 2.23 Å and an adsorption energy of −0.711 eV. The C-O bonds in the HCOOH molecule lengthen by about 9.6% and 11.5% due to adsorption. In the HCO molecule, the oxygen atom is located between three surface Ta atoms, to which it is bound with Ta-O bond lengths of 2.18 Å, 2.18 Å, and 4.18 Å, respectively, causing an adsorption energy of −0.330 eV. Similarly, the O atom of cis-HCOH tends to form a Ta-O bond with a surface Ta atom, with a bond length of 2.21 Å. The c-HCOH molecule is adsorbed immediately above one of the Ta atoms in the surface, with an adsorption energy of −0.458 eV. It is worth mentioning that trans-HCOH on the surface converts to c-HCOH.
Moreover, in the dihydroxycarbene (HOCOH) molecule, the C atom of molecule is located between two surface Ta atoms, but it does not form a bond, whereas two oxygen atoms are bonded with surface Ta atoms with Ta It should be noted that CH 2 prefers to be sited between two surface Ta atoms, but without forming a bond to the TaC (111) surface via its carbon atom. The shortest distance between the C atom and the surface Ta atoms is 2.23 Å, with an adsorption energy of −0.615 eV. CH 3 adsorbs close to the surface in the hollow site of Ta, where it behaves similarly to the CH 2 molecule, at the shortest distance of 2.42 Å between the C atom and the surface Ta atoms and a calculated adsorption energy of −0.998 eV. The CH 4 molecule approaches the surface through its C atom, at a minimum distance of about 2.80 Å and an adsorption energy of −0.095 eV.

Reaction Networks of CO 2 Hydrogenation
Next, we present a detailed investigation of the reaction networks for all possible intermediates involved in the processes of CO 2 hydrogenation at the Ta-terminated TaC (111) surface. It is known that the TaC (111) surface is able to catalyze the following reactions: (2)

Chemical Reactions
In this section, we discuss the feasible reactions underpinning the mechanism of CO2 hydrogenation on the TaC (111) surface. The calculated reaction energies of all intermediates, including the processes of CO2 hydrogenation at the TaC (111) surface, are shown in Table 2. The initial step associated with CO2 hydrogenation is either the formation of a formate (HCOO*) or the generation of a carboxyl species (t-COOH* and/or c-COOH*). The former takes place when hydrogen attacks the carbon atom of CO2 through CO2* + H* → HCOO*, which requires an energy of 0.198 eV. Similarly, the reactions CO2* + H* → (c,t)-COOH* occur when H atoms attach to the O atoms of the CO2 molecule; these are endothermic processes, with energies of 1.056 eV and 0.974 eV for the cis and trans conformer products, respectively. Thus, the first hydrogen atom prefers to attack the carbon atom rather than the oxygen atoms of CO2 to form HCOO*, which agrees with the results of CO2 hydrogenation on the bimetallic MoTiC2 MXenes [56]. Formic acid (HCOOH) is generated from the hydrogenation of HCOO* via the reaction HCOO* + H* → HCOOH*, which is also an endothermic process requiring an energy of 1.580 eV. Moreover, further hydrogenation of the carboxyl species can also result in the formation of HCOOH*. These reactions (c,t-COOH* + H* → HCOOH*) are also endothermic processes, with energies of

Chemical Reactions
In this section, we discuss the feasible reactions underpinning the mechanism of CO 2 hydrogenation on the TaC (111) surface. The calculated reaction energies of all intermediates, including the processes of CO 2 hydrogenation at the TaC (111) surface, are shown in Table 2. The initial step associated with CO 2 hydrogenation is either the formation of a formate (HCOO*) or the generation of a carboxyl species (t-COOH* and/or c-COOH*). The former takes place when hydrogen attacks the carbon atom of CO 2 through CO 2 * + H* → HCOO*, which requires an energy of 0.198 eV. Similarly, the reactions CO 2 * + H* → (c,t)-COOH* occur when H atoms attach to the O atoms of the CO 2 molecule; these are endothermic processes, with energies of 1.056 eV and 0.974 eV for the cis and trans conformer products, respectively. Thus, the first hydrogen atom prefers to attack the carbon atom rather than the oxygen atoms of CO 2 to form HCOO*, which agrees with the results of CO 2 hydrogenation on the bimetallic MoTiC 2 MXenes [56]. Formic acid (HCOOH) is generated from the hydrogenation of HCOO* via the reaction HCOO* + H* → HCOOH*, which is also an endothermic process requiring an energy of 1.580 eV. Moreover, further hydrogenation of the carboxyl species can also result in the formation of HCOOH*. These reactions (c,t-COOH* + H* → HCOOH*) are also endothermic processes, with energies of 0.723 eV and 0.805 for the c-COOH* and t-COOH* reactant species, respectively. In conclusion, the formation of HCOOH* via the carboxyl species is more favorable than via the formate intermediate as a result of the lower reaction energy. The carboxyl species may further hydrogenate to produce dihydroxycarbene (cc-HOCOH*, ct-HOCOH*, and tt-HOCOH*) through the reaction (c,t)-COOH* + H*→ (ct, cc, tt)-HOCOH*. As is clear from Table 2, all of the above reactions are endothermic processes, although the transformation of (cc,ct)-HOCOH* to tt-HOCOH* is exothermic, with reaction energies of −0.261 eV and −0.111 eV, respectively. Therefore, the reaction pathways for CO 2 hydrogenation at the TaC (111) surface include two routes, either from the HCOOH* or HOCOH* intermediates, which can be followed to achieve the formation of other products. Figure 3. Shows the reaction profile for the hydrogenation of CO 2 and subsequent reactions of intermediates to HCOOH, CO, CH 2 O, CH 3 OH, and CH 4 via HCOOH, and HOCOH at the TaC (111) surface. In the next section, these reaction pathways are studied in detail.

Reaction Pathways of CO2 to Possible Products through HCOOH
The Reaction Mechanisms for CO2 Hydrogenation to HCOOH As discussed above, CO2 hydrogenation can lead to the formation of HCOO* or the generation of t-COOH* and/or c-COOH*. These species can further react with hydrogen to yield the HCOOH product. Although all these reactions are endothermic processes, the formation of HCOOH* via a carboxyl species appears to be more favorable than via the HCOO* intermediate because of its lower reaction energy.

The Reaction Paths for CO2 Hydrogenation to CO via HCOOH
There are two paths to CO production: a direct path through the decomposition of (t,c)-COOH* via the reaction (c,t)-COOH* → CO* + OH*, where the reaction is endothermic by 0.702 eV and 0.784 eV for the cis and trans conformers, respectively. Another path is through the decomposition of the HCOOH* intermediate, which leads to the formation of HCO*, with further decomposition of HCO* yielding CO*. The calculated reaction energy of −1.611 eV shows that the decomposition of HCOOH* via HCOOH* → HCO* + OH* is an exothermic process, while the subsequent decomposition of HCO* through HCO* → CO* + H* is an endothermic reaction requiring an energy of 1.590 eV.
The Reaction Paths for the CO2 Hydrogenation to CH2O via HCOOH After formation of HCO*, it can further react with an H atom to form either formaldehyde (CH2O*) or c-HCOH*. As such, the only pathway to obtain the CH2O molecule

Reaction Pathways of CO 2 to Possible Products through HCOOH
The Reaction Mechanisms for CO 2 Hydrogenation to HCOOH As discussed above, CO 2 hydrogenation can lead to the formation of HCOO* or the generation of t-COOH* and/or c-COOH*. These species can further react with hydrogen to yield the HCOOH product. Although all these reactions are endothermic processes, the formation of HCOOH* via a carboxyl species appears to be more favorable than via the HCOO* intermediate because of its lower reaction energy.
The Reaction Paths for CO 2 Hydrogenation to CO via HCOOH There are two paths to CO production: a direct path through the decomposition of (t,c)-COOH* via the reaction (c,t)-COOH* → CO* + OH*, where the reaction is endothermic by 0.702 eV and 0.784 eV for the cis and trans conformers, respectively. Another path is through the decomposition of the HCOOH* intermediate, which leads to the formation of HCO*, with further decomposition of HCO* yielding CO*. The calculated reaction energy of −1.611 eV shows that the decomposition of HCOOH* via HCOOH* → HCO* + OH* is an exothermic process, while the subsequent decomposition of HCO* through HCO* → CO* + H* is an endothermic reaction requiring an energy of 1.590 eV.
The Reaction Paths for the CO 2 Hydrogenation to CH 2 O via HCOOH After formation of HCO*, it can further react with an H atom to form either formaldehyde (CH 2 O*) or c-HCOH*. As such, the only pathway to obtain the CH 2 O molecule from CO 2 takes place through the HCO* + H* → CH 2 O* reaction, with an endothermic energy of 0.809 eV.

The Reaction Paths for CO 2 Hydrogenation to CH 3 OH via HCOOH
The pathway to CH 3 OH includes either CH 2 O* or c-HCOH*, and these routes are explained separately. As mentioned previously, HCO* hydrogenation can result in the formation of c-HCOH* through HCO* + H* → c-HCOH*, with a reaction energy of 1.687eV. Next, c-HCOH* attaches a hydrogen via c-HCOH* + H* → CH 2 OH*, with an energy of 0.520 eV, to form CH 2 OH*. Further hydrogenation of CH 2 OH* leads to CH 3 OH* (CH 2 OH* + H* → CH 3 OH*) which is an endothermic process at an energy of 1.424 eV. The other pathway to CH 3 OH is through the hydrogenation of formaldehyde via CH 2 O* + H* → CH 2 OH*, which is an endothermic reaction requiring an energy of 1.398 eV. For the subsequent reaction, the CH 2 OH* can further react with another H atom to produce CH 3 OH*, which reaction is endothermic by 1.424 eV. Besides CH 2 OH*, further hydrogenation of CH 2 O* may result in the formation of methoxy (CH 3 O*) via the CH 2 O* + H* → CH 3 O* reaction, which process is endothermic and requires 0.504 eV. Once the formed CH 3 O* intermediate reacts further with another H atom, CH 3 OH* will be produced, with the reaction CH 3 O* + H* → CH 3 OH* requiring 2.318 eV.

The Reaction Paths for CO 2 Hydrogenation to CH 4 via HCOOH
The route to CH 4 * formation involves the dissociation of CH 2 OH* (CH 2 OH* → CH 2 * + OH*), which leads to CH 2 *. This reaction is exothermic at −1.855 eV. Next, CH 3 * and CH 4 * are produced through the subsequent hydrogenation of CH 2 * and CH 3 * via CH 2 * + H* → CH 3 * and CH 3 * + H* → CH 4 *. Both these reactions are endothermic processes, with reaction energies of 0.431 eV and 1.818 eV, respectively.

The Reaction Paths for CO 2 Hydrogenation to CO via HOCOH
There are two pathways to CO, directly from (c,t)-COOH* decomposition, where (c,t)-COOH* decomposes to CO* and OH* via the (c,t)-COOH* → CO* + OH* reaction. Both processes are endothermic, with energies of 0.702 eV and 0.784 eV for the cis and trans conformers, respectively. Another pathway involves the decomposition of tt-HOCOH* to COH* and OH* through tt-HOCOH* → COH* + OH*, which is an exothermic reaction by −1.375 eV. Next, CO* will form via further decomposition of COH* via the COH* → CO* + H* reaction, which requires 0.493 eV of energy.
The Reaction Paths for CO 2 Hydrogenation to CH 3 OH via HOCOH Once the formed COH* intermediate reacts further with another hydrogen, c-HCOH* will form through the COH* + H* → c-HCOH* reaction, with an endothermic energy of 0.589 eV. Subsequent hydrogenation of c-HCOH* will produce CH 2 OH* through c-HCOH* + H* → CH 2 OH*, which reaction is an endothermic process at 0.520 eV. If CH 2 OH* attaches another hydrogen, CH 3 OH* will finally be produced through the CH 2 OH* + H* → CH 3 OH* reaction, with an endothermic energy of 1.424 eV.
The Reaction Paths for CO 2 Hydrogenation to CH 4

via HOCOH
The dissociation of CH 2 OH* results in CH 2 *, which process takes place through the CH 2 OH* → CH 2 * + OH* reaction with an exothermic reaction energy of −1.855 eV. Further hydrogenation of CH 2 * will produce CH 3 * via CH 2 * + H* → CH 3 *, with an energy of 0.431 eV. Finally, subsequent hydrogenation of CH 3 * leads to CH 4 * via CH 3 * + H* → CH 4 *, which is also endothermic, at 1.818 eV.

Activation Energies
In order to gain further insight, activation barriers of a number of selected elementary reactions (listed in Table 3) in the CO 2 hydrogenation process over the TaC (111) surface have been calculated and compared, using the E b = E TS − E IS relationship, where E IS and E TS represent the total energy of the initial and transition states, respectively. The calculated activation barriers for the selected steps are summarized in Table 3, and in the following section, we will discuss these reactions in more detail, with the initial, transition and final states of the reactions depicted in Figure 4.  As discussed above, CH2 can be produced from CH2OH* → CH2* + OH* and then can react further with adsorbed hydrogen to produce CH4 within two continuous reaction steps. A first pathway to CH3* (CH2* + H* → CH3*) has an activation barrier of 1.210 eV, whereas in the subsequent reaction, the adsorbed CH3 can further react with another H atom to produce CH4, but with a much higher activation barrier of 2.224 eV. The formed As previously mentioned, in the formation of HCOO (CO 2 * + H* → HCOO*) H approaches the C atom of CO 2 to form a C-H bond, where the distance between the C and H atoms decreases from 3.29 Å in the initial state (IS) to 1.95 Å in the transition state (TS), and then to 1.10 Å in the final state (FS). The calculated activation barrier is 0.808 eV. The generation of formic acid through formate hydrogenation (HCOO* + H* → HCOOH*) must overcome an activation barrier of 1.828 eV, where H bonds with the O of formate to form an O-H bond, which shortens from an initial distance of 2.55 Å to 1.27 Å and finally, to 0.98 Å in the IS, TS, and FS, respectively. The dissociation of HCOOH* via HCOOH* → HCO* + OH* has a rather small activation barrier of 0.264 eV, which is therefore kinetically favorable. The increase in the C-O bond length in HCOOH* weakens the C-O bond, resulting in the decomposition of HCOOH* to HCO* and OH*, with the C-O bond lengthening from 1.49 Å to 1.91 Å and finally, to 3.2 Å in the IS, TS, and FS, respectively. HCO* can further hydrogenate to formaldehyde or dissociate to carbon monoxide. In the former reaction (HCO* + H* → CH 2 O*), formaldehyde can be produced when the distance between the H* and C atom of HCO* decreases from 1.61 Å in the TS to 1.15 Å in the FS to form an H-C bond. This reaction must overcome an activation barrier of 1.304 eV. The latter reaction (HCO* → CO* + H*) takes place over an energy barrier of 0.614 eV, which shows that kinetic CO formation occurs preferentially. The hydrogenation of CH 2 O* generates either CH 2 OH* through CH 2 O* + H* → CH 2 OH* or CH 3 O* via CH 2 O* + H* → CH 3 O*. The formation of CH 3 O* (1.282 eV) is slightly more favorable than CH 2 OH* production (1.480 eV), owing to the lower energy barrier.
In the next step, CH 3 OH* can be produced via CH 3 O* hydrogenation (CH 3 O* + H* → CH 3 OH*), with an energy barrier of E b = 1.429 eV. The H atom approaches the O atom of the methoxide, leading to O-H bond formation. In the IS, the distance between H and O is 3.8 Å, decreasing to 1.88 Å and 0.98 Å in the TS and FS, respectively. However, hydroxymethyl (CH 2 OH) can dissociate to CH 2 * (CH 2 OH* → CH 2 * + OH*), with a small activation barrier of 0.126 eV that is kinetically favorable. The C-O bond in CH 2 OH weakens as the bond length increases, from a C-O distance of 1.52 Å to 1.81 Å and 3.18 Å in the IS, TS, and FS, respectively.
As discussed above, CH 2 can be produced from CH 2 OH* → CH 2 * + OH* and then can react further with adsorbed hydrogen to produce CH 4 within two continuous reaction steps. A first pathway to CH 3 * (CH 2 * + H* → CH 3 *) has an activation barrier of 1.210 eV, whereas in the subsequent reaction, the adsorbed CH 3 can further react with another H atom to produce CH 4 , but with a much higher activation barrier of 2.224 eV. The formed CH 4 species can be assumed to bind only weakly with the surface, from which it may easily desorb.
From the above detailed insight, we can conclude that the mechanism of CO 2 *→ HCOO*→ HCOOH*→ HCO*→ CH 2 O*→ CH 2 OH*→ CH 2 *→ CH 3 *→ CH 4 * is the preferred overall exothermic pathway, passing thorough HCOO* and HCOOH* species, which releases a total energy of 4.24 eV (Figure 3), indicating that CH 4 is the predominant product of CO 2 hydrogenation over the TaC (111) surface. These results agree well with other studies, showing that all TMCs form CH 4 as the primary product, except for WC and NbC, which produce a significant amount of CO [12]. The rate-determining step (RDS) in this pathway is the hydrogenation reaction of CH 3 to CH 4 , with a barrier of 2.224 eV and the largest endothermic reaction energy of 1.818 eV. The smallest barrier, at 0.126 eV, belongs to the reaction of CH 2 OH*→ CH 2 * + OH*, with the largest exothermic reaction energy of −1.855 eV. The present mechanism resulting in CH 4 formation is also similar to that in the DFT study by Qi et al. [57] on CO hydrogenation over molybdenum carbide, in which they found the same mechanism for the favorable pathway with the reaction of CH 3 to CH 4 as in the RDS reaction. The preferred reaction mechanism is also consistent with previous work studying CO hydrogenation over MoS 2 , where the reaction product is CH 4 , progressing through the intermediate of CH 2 OH prior to C-O bond breaking [58].
The reaction pathway of CO 2 *→HCOO*→HCOOH*→HCO*→ CO* producing CO as the second favored product releases a total energy of 2.55 eV overall. CH 3 OH as the next product was formed by the reaction series CO 2 *→HCOO*→HCOOH*→HCO*→CH 2 O*→ CH 3 O*→CH 3 OH*, with a total exothermic energy of −2.10 eV. The RDS for the reaction mechanisms resulting in CO and CH 3 OH is the hydrogenation step of HCOO*, with a barrier of 1.828 eV, while the reaction of HCOOH*→ HCO* + OH* contains the smallest barrier of 0.264 eV.

Conclusions
We have performed a series of DFT calculations to shed light on the reaction network of CO 2 hydrogenation to CO, HCOOH, H 2 CO, CH 4, and CH 3 OH products over the Taterminated TaC (111) surface, first identifying the optimal adsorption sites for all of the reactants, intermediates, and products on the TaC (111) surface. The adsorption of the CO 2 molecule results in its activation, shown by the alteration of the initial structure, where the C-O bond lengths increase from 1.17 to 1.27 Å and the O-C-O bond angle decreases to 132 • . The two oxygen atoms of the CO 2 molecule strongly bond to the Ta atoms on the surface.
The results from the reaction energy calculations of the hydrogenation reaction sequences showed that the largest exothermic reaction energy value of −1.891 eV is related to the adsorption of CO 2 *, which could therefore release sufficient energy to overcome some of the energy barriers in the hydrogenation reactions. The range of exothermic reactions is wide, with the smallest energy of only −0.111eV, produced during the conversion of ct-HOCOH* to tt-HOCOH*. The sequence of reactions, in order of the largest exothermic reaction energies to the least energetically favorable, is as follows: CO 2 (g) → CO 2 *, CH 2 OH* → CH 2 * + OH*, cc-HOCOH* → COH* + OH*, HCOOH* → HCO* + OH*, ct-HOCOH* → COH* + OH*, tt-HOCOH* → COH* + OH*, cc-HOCOH* + H* → tt-HOCOH*, ct-HOCOH* + H* → tt-HOCOH* The results revealed that the thermodynamically preferred CO 2 hydrogenation mechanism, including two routes from either HCOOH* or HOCOH* intermediates, progresses via CO 2 *→ HCOO*→ HCOOH*→ HCO*, which results in CH 4 , CO, and CH 3 OH formation.
The results from the energy barrier and reaction energy calculations show that the mechanism of CO 2 * + H*→ HCOO*, HCOO* + H*→ HCOOH*, HCOOH*→ HCO* + OH*, HCO* + H*→ CH 2 O*, CH 2 O* + H*→ CH 2 OH*, CH 2 OH*→ CH 2 * + OH*, CH 2 * + H*→ CH 3 *, and CH 3 * + H*→ CH 4 * resulting in methane production is the most exothermic mechanism, releasing a total energy of 4.24 eV, indicating that CH 4 will be the predominant product, which is in good agreement with the results in the available literature. The RDS along this pathway is the hydrogenation reaction of CH 3 * + H*→ CH 4 *, with a barrier of 2.224 eV and the largest endothermic reaction energy of 1.818 eV, while the dissociation reaction of CH 2 OH*→ CH 2 * + OH* has the smallest barrier and largest exothermic reaction energies of 0.126 eV and−1.855 eV, respectively.
Methanol production as the third-preferred product occurs via the reactions of CO 2 * + H*→ HCOO*, HCOO* + H*→ HCOOH*, HCOOH*→ HCO* + OH*, HCO* + H*→ CH 2 O*, CH 2 O* + H*→ CH 3 O*, and CH 3 O* + H*→ CH 3 OH* by releasing a total exothermic reaction energy of 2.10 eV. Along this pathway, HCOO* hydrogenation and HCOOH* dissociation require the largest and smallest barriers of 1.828 and 0.264 eV, respectively, to be overcome, whereas HCOOH* dissociation and CH 3 O* hydrogenation have the largest exothermic and endothermic reaction energies of −1.611 eV and 2.318 eV, respectively. The chemical picture and molecular level insights derived from this work suggest that TaC (111) surfaces should have high activity towards CO 2 activation, which along with their other favorable properties, makes them promising candidates for the catalytic hydrogenation of CO 2 to beneficial products.