CO₂ Hydrogenation to Methanol over Cd₄/TiO₂ Catalyst: Insight into Multifunctional Interface

Abstract

Supported metal catalysts have shown to be efficient for CO₂ conversion due to their multifunctionality and high stability. Herein, we have combined density functional theory calculations with microkinetic modeling to investigate the catalytic reaction mechanisms of CO₂ hydrogenation to CH₃OH over a recently reported catalyst of Cd₄/TiO₂. Calculations reveal that the metal‐oxide interface is the active center for CO₂ hydrogenation and methanol formation via the formate pathway dominates over the reverse water‐gas shift (RWGS) pathway. Microkinetic modeling demonstrated that formate species on the surface of Cd₄/TiO₂ is the relevant intermediate for the production of CH₃OH, and CH₂O^# formation is the rate‐determining step. These findings demonstrate the crucial role of the Cd‐TiO₂ interface for controlling the CO₂ reduction reactivity and CH₃OH selectivity.

Multifunctional catalysts: The detailed reaction mechanism of CO₂ hydrogenation to CH₃OH was investigated over the multifunctional catalyst of Cd₄/TiO₂. Benefiting from the cooperation between Lewis acids from the Cd and Ti sites and Lewis bases from TiO₂ surface oxygen atoms, the Cd₄/TiO₂ exhibited high activity and selectivity for the CH₃OH production.

Introduction

The increase of CO₂ concentration in the atmosphere is one of the major factors in global climate change. CO₂ capture and valorization have been considered as promising strategies to mitigate this problem. ^[1] Using CO₂ as a feedstock to produce valuable chemicals not only can help to decrease dramatically the amount of CO₂ emitted into the atmosphere but also provide economic benefits.[ ^1b , ² ] A large number of value‐added chemicals can be produced from CO₂ via platform molecules such as CO, CH₄, and CH₃OH. ^[3] Among these, CH₃OH is highly desirable because it is an important fuel as well as a starting feedstock for the production of more valuable chemical compounds. ^[4] Recently, two different approaches for CO₂ hydrogenation to CH₃OH have received a lot of attention: (1) electrochemical reduction and (2) thermochemical reduction. ^[5] The electrochemical CO₂ reduction offers the advantage that product distribution can be controlled by adjusting electrolyte, electrocatalyst, and applied voltage. ^[6] However, the selectivity, energetic efficiency, electrode lifetime restrict to its large‐scale applications.[ ^6c , ^6d ] Therefore, using the thermochemical approach to synthesize CH₃OH from CO₂ hydrogenation is more practical for potential industrial applications compared to the alternative electrochemical CO₂ reduction. It offers an opportunity for the development of sustainable technologies and environmentally benign chemical processes since H₂ which is a reducing agent can readily be obtained from renewable energy resources.[ ^1a , ² ]

Many studies have been devoted to creating new tailor‐made CO₂ conversion catalysts with improved activity and selectivity to methanol, of which Cu/ZnO/Al₂O₃ catalyst has been industrialized. ^[7] However, the disadvantages of low CH₃OH selectivity and the sintering of Cu and ZnO motivated the development of new Cu‐based catalysts such as Cu/ZnO, ^[8] Cu/ZrO₂, ^[9] and Cu/CeO₂. ^[10] In these catalytic systems, it was found that H₂ molecule is dissociated at the Cu site and CO₂ is activated at the oxide surface, while the interface between Cu and metal oxide supports plays a crucial role for stabilization of the reaction intermediate for CH₃OH formation. ^[9] Besides Cu‐based catalysts, various other materials have also been reported as promising catalysts for CO₂ hydrogenation to CH₃OH. For instance, Au, ^[11] Pd ^[12] , Re, ^[13] ZnO ^[14] and In₂O₃ ^[15] supported on oxides were reported to be active toward the production of CH₃OH under moderate conditions. Although many different types of catalysts have been reported, all of the active sites involved in the reaction have a common feature of multi‐functionality in nature. An efficient cooperation between active sites of different catalytic natures coupled in one heterogeneous catalyst plays a key role for eventual selective CH₃OH formation.

Regarding the reaction mechanism, typically, two different reaction pathways have been proposed for the hydrogenation of CO₂ to CH₃OH: (1) the reverse water‐gas shift (RWGS) pathway, and (2) the formate pathway. In the RWGS reaction, CO₂ is hydrogenated to form CO* intermediate which is then further hydrogenated to form CH₃OH. For the formate pathway, CH₃OH is produced via the formate (HCOO*) intermediate. ^[16] Most studies have suggested that the formate pathway is preferred over the RWGS pathway.[ ^7b , ^12a , ¹⁷ ] The main reason is that the binding strength of CO* intermediate on these catalysts is quite weak, leading to the desorption of CO to the gas phase. However, on some other catalysts such as Cu/TiO₂, Cu/ZrO₂, and Cu/CeO_x, CH₃OH was produced through CO* intermediate due to the strong enough interaction between CO* and catalyst.[ ^9b , ¹⁰ ] Therefore, the specific reaction pathway dominating methanol formation is system‐dependent and should be investigated individually.

Recently we have investigated CO₂ conversion to CH₃OH on Cd/TiO₂ and CdTiO₃ catalysts by a combination of experimental and computational studies. ^[18] It was found that Cd/TiO₂ catalyst exhibits a much higher catalytic CO₂ hydrogenation activity than the CdTiO₃ mixed oxide. To further identify the detailed reaction mechanism catalyzed by Cd/TiO₂ and clarify the functionalities of different types of active sites in this system, we constructed a Cd/TiO₂ model catalyst and investigated its catalytic activity towards CO₂ conversion to methanol with H₂ as a reductant. The key objective of this study is to explore the multiple‐site cooperation effects on the catalyst reactivity by combining DFT calculation with microkinetic modeling.

Results and Discussion

Cd₄/TiO₂ Model rationalization

A cluster containing 4 Cd atoms (Cd₄) was selected as representative of the supported Cd nanoparticles on the TiO₂ surface since it was reported as the smallest Cd cluster featuring a magic number of Cd atoms. In order to model the Cd₄/TiO₂ catalyst, two possible configurations of isolated Cd₄ cluster, i. e., a tetrahedron (T_d) and planar rhombus (C_2V) ^[28] were firstly optimized in the vacuum by using a large unit cell of 15×15×15 Å (Figure S1 in the supporting information). Then the so‐obtained Cd₄ clusters were deposited and optimized on the (101) surface of anatase TiO₂. It is found that the most stable configuration of the supported Cd₄ cluster on the (101) TiO₂ surface is a deformed planar geometry even though the tetrahedron is more stable in the gas phase. As shown in Figure 1, the Cd₄ (C_2V) cluster is slightly distorted upon the adsorption with one of the Cd atoms lying above the plane of the other three. The adsorption energy of Cd₄ over the surface is calculated to be −1.05 eV indicating a strong interaction between the metal cluster and the support of TiO₂. Bader charge analysis demonstrates that the entire Cd₄ cluster is +1.48|e| charged, which indicates that the electrons are transferred from Cd₄ cluster to TiO₂ surface through metal‐support interaction.

Figure 1.

(a) Top view and (b) side view of Cd₄/TiO₂(101) slab model. The O_2c and O_3c are twofold coordinated and threefold coordinated oxygen atoms, and the Ti_5c and Ti_6c are fivefold coordinated and sixfold coordinated titanium atoms on the surface of TiO₂, respectively. (c) The electron density different plots upon the adsorption of Cd₄ cluster on TiO₂ surface. The orange and green regions represent electrons depletion and accumulation respectively (isosurface value=0.05 e/Bohr³).

H₂ dissociation and H spillover

Many studies have proposed that activation and dissociation of an H₂ molecule take place at the metal‐oxide interface. ^[29] In this work, six possible active sites of Cd₄/TiO₂ catalyst for the activation and dissociation of H₂ molecule were systematically studied. As shown in Figure 2, site A is on top of the supported Cd₄ cluster. Site B, C and D are at the interface of Cd₄/TiO₂ (Cd−O_2c). Site E is located between two nearest O_2c atoms and site F is on top of bridging Ti_5c and O_2c atoms of TiO₂ surface. From Figure 2 it can be seen that that heterolytic H₂ dissociation at the interface of Cd/TiO₂ is more preferable than the other sites. Among all interface sites considered, H₂ dissociation over site C has the lowest activation barrier (0.39 eV). Homolytic dissociation of H₂ molecule over site A needs to overcome an activation barrier of 0.88 eV and generates two hydrides on the supported Cd₄ cluster. On the TiO₂ surface, both homolytic (site E) and heterolytic dissociation pathways (site F) exhibit very high activation barriers (1.74 and 2.25 eV) indicating that TiO₂ surface site is inactive for H₂ activation. This is in agreement with a previous theoretical study of H₂ dissociation on TiO₂ surfaces. ^[30]

Figure 2.

Activation energy (Ea) and reaction energy (ΔE_rxn) for H₂ dissociation at all possible active sites of Cd₄/TiO₂ catalyst.

After we figured out the most favorable active site for H₂ dissociation, the spillover process of the so‐formed H* on the surface of the Cd₄/TiO₂ is further studied. As shown in Figure S2, the migration of the H* generated by H₂ dissociation at the interface (site C) from O_2c site to its neighboring O_3c site has an activation barrier of 0.73 eV. The other H* species on the Cd₄ cluster can also spillover to the surface of TiO₂ with an activation barrier of 0.71 eV. H* on O_3c site can also hoop to another O_2c site next to it by overcoming a barrier of only 0.42 eV. The overall reaction is slightly endothermic. These results indicate that the activated H* on the surface of the Cd₄/TiO₂ catalyst is rather dynamic and hydrogen migrations among different surface sites is thermodynamically and kinetically easy processes.

CO₂ hydrogenation to HCOOH and CO

In this section, the hydrogenation of CO₂ on Cd₄/TiO₂ catalyst will be discussed. Two main reaction pathways of CO₂ hydrogenation which have been intensively debated in the literature were studied: (1) methanol formation via the intermediate of HCOOH*, and (2) methanol formation via the reversed water‐gas shift (RWGS) pathway with CO as an intermediate. Noted that the species with asterisk (*) and hash sign (^#) are species that interact with TiO₂ surface and Cd₄ cluster of the Cd₄/TiO₂ catalyst, respectively.

Formate pathway

The reaction mechanisms of CO₂ hydrogenation to formate (HCOO*) and formic acid (HCOOH*) are shown in Figure 3. After heterolytic dissociation of H₂ at the interface of Cd₄/TiO₂, a hydride coordinated to Cd (H^#) and a proton bonded to O_2c site (H*) are produced. CO₂ is adsorbed over the Ti_5c site nearby both H* and H^# species. The adsorption energy is calculated to be −0.14 eV. Then CO₂ can be hydrogenated by the transfer of H^# from Cd₄ cluster to the C atom of CO₂ forming formate intermediate of HCOO*. The activation barrier for this step is only 0.26 eV. Further protonation of HCOO* to form formic acid (HCOOH*) can be realized via two different reaction routes, either by protonation of monodentate HCOO* intermediate to form cis‐HCOOH* (gray line in Figure 3), or protonation of bidentate HCOO*^# intermediate which can be formed by structure rearrangement to form trans‐HCOOH*^# (orange line in Figure 3). The activation barriers of proton transfer for both routes are relatively low (0.22 and 0.41 eV), however, the configurational transformation of HCOO* from monodentate coordination to bidentate coordination with both Ti_5c and Cd before protonation reaction is dramatically favorable. Another possible pathway for HCOOH* formation is also identified with a small activation barrier of 0.15 eV, the so‐called concerted reaction mechanism with CO₂ hydrogenation by both H* and H^# in one step (green line in Figure 3).

Figure 3.

Reaction energy profiles for the CO₂ hydrogenation to HCOOH* on Cd₄/TiO₂ catalyst. Green line is the concerted pathway. Gray line is the stepwise pathway via monodentate HCOO*. Orange line is the stepwise pathway via bidentate HCOO*^#. The species with asterisk (*) and hash sign (^#) are species that interact with TiO₂ surface and Cd₄ cluster of the Cd₄/TiO₂ catalyst, respectively.

RWGS pathway

The RWGS reaction mechanism is initiate by CO₂ hydrogenation to first form carboxylate intermediate (HOCO^#), from which CO is produced and can be further converted into methanol by continuous hydrogenation reactions. As shown in Figure 4, the reaction starts with the adsorption of CO₂ at the perimeter site of Cd₄ cluster after hydrogen spillover process. Then, the CO₂ can be protonated by the H* on TiO₂ surface forming HOCO^#. It is found that this reaction cannot occur directly due to the long distance between CO₂ and H* (4.93 Å). However, it can proceed by the assist of an H₂O molecule which acts as a proton shuttle between H* and CO₂ (blue line in Figure 4). The activation energy in this case is calculated to be 0.42 eV indicating that this process is feasible. Subsequent hydrogenation of the HOCO^# intermediate at its terminal OH group with the breaking of C−O bond produces CO^# and H₂O*. This process requires overcome an activation barrier of 0.35 eV. Finally, CO and H₂O can be desorbed from the catalyst with desorption barriers of 0.13 and 0.19 eV, respectively.

Figure 4.

Reaction energy profiles for the CO₂ hydrogenation to CO on Cd₄/TiO₂ catalyst (RWGS pathway). Blue line is the reaction with the assist of H₂O molecule.

Due to the unfavorable adsorption of CO₂ on the supported Cd₄ cluster, we also explored the CO₂ adsorption on a separate TiO₂ surface site without interaction with the Cd₄ cluster. The mechanisms of RWGS reaction on the TiO₂ surface are shown in Figure 5. In this case this reaction starts with the adsorption of CO₂ on the TiO₂ surface after hydrogen spillover process. The adsorption energy of CO₂ is calculated to be −0.45 eV which is relatively stronger than that on supported Cd₄ cluster. The bent CO₂ geometry can be formed on the TiO₂ surface with an activation barrier of 0.44 eV. Then the adsorbed CO₂* is directly hydrogenated to form HOCO* without the H₂O mediator. The activation energy for this step is calculated to be 0.74 eV. The diffusion of the second H* to the O_3c site close to the OH group of HOCO* needs overcome an activation barrier of 0.76 eV. After that, the cleavage of the C−O bond of HOCO* intermediate to generate CO* and OH* species on the TiO₂ surface is rather difficult with an activation barrier of 1.86 eV. However, the presence of H₂O molecule can again decrease this activation barrier to 0.94 eV with C−O bonding breaking and OH group hydrogenation occurring simultaneously.

Figure 5.

Reaction energy profiles for the CO₂ hydrogenation to CO on clean TiO₂ surface (RWGS pathway). Blue line is the reaction with the assist of H₂O molecule.

It is found that H₂O molecule plays an important role as a proton shuttle to promote the most difficult reaction steps during the RWGS reactions taking place at both interface and TiO₂ surface of Cd₄/TiO₂ catalyst. The hydrogenation reaction of CO₂ is the most difficult step for the reaction occurred at the interface while the C−O bond cleavage of HOCO* carboxylate intermediate is found to be the most difficult step for the reaction occurred at the TiO₂ surface. The highest activation energy of the RWGS reaction that occurs at the interface of Cd₄ and TiO₂ surface (TS‐R1w) is about two times lower than that of the other reaction route on the TiO₂ surface (TS‐r6w). Therefore, it is concluded that the most preferable active site for the RWGS reaction is the interface of Cd₄/TiO₂ catalyst. Therefore, in the next section, the discussion of CH₃OH formation via CO* will only focus on the reaction route at the interface.

CH₃OH formation

In this section, we will discuss the reaction mechanism of CH₃OH formation from HCOOH* as well as CO* intermediates generated from the formate and the RWGS reaction pathways. The results are shown in Figure 6. Totally 4 elementary hydrogenation reaction steps are involved for CH₃OH formation from CO i. e. CO*→HCO*^#, HCO*^#→CH₂O*, CH₂O*→CH₃O* and CH₃O*→CH₃OH. The activation barrier for CO hydrogenation to form HCO*^# is 0.32 eV by H^# on Cd₄ cluster. The next step of dissociative adsorption of H₂ on top of HCO*^# intermediate generating CH₂O* and H^# species has an activation barrier of 1.10 eV. Subsequent CH₃O* formation by CH₂O* hydrogenation is a barrierless process with a reaction energy of −1.40 eV. Finally, the CH₃OH is formed by hydrogenation of CH₃O* intermediate with the activation barrier of 0.48 eV. In addition, CH₃OH can be produced by the hydrogenolysis of CH₃O* (green line in Figure 6). The activation energy of this step is only 0.04 eV lower than that of the CH₃O* hydrogenation step. These results imply that both CH₃O* hydrogenolysis and CH₃O* hydrogenation coexist in the formation of CH₃OH.

Figure 6.

Reaction energy profiles for the production of CH₃OH from CO and HCOOH.

Alternatively, CH₃OH can also be formed from HCOOH* (blue line in Figure 6). The initial step is the hydrogenation of HCOOH* to produce formaldehyde (CH₂O^#) and an OH* species (CH₂O^#+OH*+H*). The activation energy of this step is calculated to be 0.65 eV. Then, the OH* is protonated to form H₂O and regenerate a vacant interfacial active site on the surface. In the next step, after another H₂ molecule is dissociated at the interface, the CH₃OH can be formed by two successive hydrogenation steps from CH₂O*, which is the same process as the reactions via the RWGS pathway.

To summarize, Figure 7 gives a schematical representation of the whole DFT reaction mechanism identified in this work, and the whole reaction pathways of CO₂ hydrogenation to CH₃OH on Cd₄/TiO₂ catalyst is shown in Figure S4. It can be seen that the formate pathway dominates over the RWGS pathway for the production of CH₃OH from CO₂ and H₂. The formation of CH₂O* intermediate is found to be the most difficult reaction step for CH₃OH production from both RWGS and formate reaction routes.

Figure 7.

A schematically representation of the whole reaction mechanism for CO₂ hydrogenation to CH₃OH on Cd₄/TiO₂ catalyst. Numbers in parenthesis represent activation energies in eV. Solid lines and dash lines represent reaction that occurs at the interface and TiO₂ surface, respectively.

Microkinetic modeling

All considered elementary steps of the CO₂ hydrogenation to CH₃OH on Cd₄/TiO₂ catalyst, and corresponding activation energies are listed in Table 1. The MKM is performed using a dual‐site model representing TiO₂ (*) and Cd (^#) sites on Cd₄/TiO₂ catalyst, respectively. The ratio between the number of * and ^# sites is 0.5 : 0.5. The reaction rate, surface coverages, and degree of rate control (DRC) are calculated under the following steady‐state reaction conditions: total pressure=2 MPa., H₂/CO₂=3 : 1, temperature=270–310 °C. The apparent activation energy (E_app) is determined from the slope of the Arrhenius plot, as shown in Figure 8a. The E_app for the CH₃OH formation is calculated to be 1.46 eV (141.0 kJ/mol), while that for the CO formation is much higher, 4.10 eV (395.4 kJ/mol). This agrees with the experiment that the Cd/TiO₂ catalyst exhibits high CH₃OH selectivity (70 %). ^[18] These results also indicate that the reaction rate of products increases with the increasing of reaction temperature.

Table 1.

Summary of elementary reaction steps and activation energies from DFT calculations used for microkinetic modeling. Ea–f and Ea–b are activation energy for forward and backward reaction, respectively. * and ^# represent TiO₂ and Cd sites on Cd₄/TiO₂ catalyst.

	Elementary reaction step	Ea–f [eV]	Ea–b [eV]
	H2 dissociation
R0:	[H2]+[*]+[#]↔[H2*#]	0.00	0.02
R1:	[H2*#]↔[H*]+[H#]	0.39	0.38
R2:	[H#]+[*]↔[H*]+[#]	0.71	0.78
	Formate pathway 1 (CO2 to HCOOH)
R3:	[CO2]+[H*]+[H#]↔[CO2_H*H#]	0.00	0.01
R4:	[CO2_H*H#]↔[HCOOH*]+[#]	0.15	0.49
R5:	[CO2]+[*]+[H#]↔[CO2*_H#]	0.00	0.14
R6:	[CO2*_H#]↔[HCOO*]+[#]	0.26	0.35
R7:	[HCOO*]+[H*]↔[HCOOH*]+[*]	0.22	0.34
R8:	[HCOO*]+[#]↔[HCOO*#]	0.00	1.04
R9:	[HCOO*#]+[H*]↔[HCOOH*#]+[*]	0.41	0.12
R10:	[HCOOH*#]↔[HCOOH*]+[#]	0.63	0.00
	Formate pathway 2 (HCOOH to CH2O)
R11:	[HCOOH*]+[H#]↔[CH2O#]+[OH*]	0.65	0.33
R12:	[CH2O#]+[*]↔[CH2O*]+[#]	0.00	0.44
R13:	[OH*]+[H*]↔[H2O*]+[*]	0.18	0.63
R14:	[H2O]+[*]↔[H2O*]	0.00	0.57
	CH3OH formation (CH2O to CH3OH)
R15:	[CH2O*]+[H#]↔[CH3O*]+[#]	0.00	1.40
R16:	[CH3O*]+[H*]+[#]↔[CH3OH*#]+[*]	0.48	0.61
R17:	[CH3OH]+[*]+[#]↔[CH3OH*#]	0.00	0.73
	RWGS pathway 1 (CO2 to CO)
R18:	[H2O]+[H*]↔[H2O_H*]	0.00	0.26
R19:	[CO2]+[H2O_H*]↔[CO2_H2O_H*]	0.00	0.06
R20:	[CO2_H2O_H*]+[#]↔[HOCO#]+[HOH*]	0.42	0.37
R21:	[H2O]+[*]↔[HOH*]	0.00	0.19
R22:	[HOCO#]+[H*]↔[CO#]+[HOH*]	0.35	0.20
R23:	[CO]+[#]↔[CO#]	0.00	0.13
	RWGS pathway 2 (CO to CH2O)
R24:	[CO]+[*]↔[CO*]	0.00	0.03
R25:	[CO*]+[H#]↔[HCO*#]	0.32	0.77
R26:	[HCO*#]+[H2]↔[HCO*#_H2]	0.00	0.01
R27:	[HCO*#_H2]↔[CH2O*]+[H#]	1.10	1.67
	CH3O* hydrogenolysis to CH3OH
R28:	[CH3O*]+[H2]+[#]↔[CH3OH*]+[H#]	0.44	0.34
R29:	[CH3OH]+[*]↔[CH3OH*]	0.00	0.46

Figure 8.

Results of the microkinetic modeling for the CO₂ hydrogenation on Cd/TiO₂ catalyst. (a) is product formation rates as a function of temperature (T=270–310 °C) and the calculated apparent activation energy (E_app). (b) is surface coverages of major surface intermediates at 270–310 °C. (c) is degree of rate control analysis at 270–310 °C. (d) is the partial pressure dependence of the CH₃OH formation rate at 290 °C. The partial pressure of another reactant is fixed as 1 MPa.

Figure 8b shows that the HCOO*^# has the highest surface coverage (σ≈0.5), indicating the formation of this intermediate is the resting state of the overall reaction. This results is consistent with the experimental in‐situ IR observation. ^[18] DRC analysis (Figure 8c) shows that the conversion of HCOOH* to CH₂O^# (R11), the most difficult reaction step of the formate pathway, is also the rate‐determining step. This result demonstrates that formate pathway dominates over RWGS pathway for the CO₂ hydrogenation to CH₃OH on the surface of Cd/TiO₂ catalyst. In addition, it was found that the H₂ dissociation reaction step (R1 in Table 1) has only a minor influence on the overall reaction rate. The effect of H₂ and CO₂ partial pressure on the reaction rate is also investigated by MKM, as shown in Figure 8d. These results indicate that increasing H₂ partial pressure can enhance significantly the methanol production rate, which, in turn, is not affected by the CO₂ partial pressure.

Conclusion

In conclusion, the reaction mechanisms of CO₂ hydrogenation to methanol by H₂ have been investigated in this study by comprehensive DFT and MKM. It is proposed that the interface between the Cd₄ cluster and the support of TiO₂ plays a key role for H₂ dissociation as well as preactivation of CO₂. H₂ dissociation and CO₂ activation are energetically more favorable at the Cd‐TiO₂ interface than that at bare TiO₂ surface and Cd cluster. Both CO₂ hydrogenation reactions to formate and CO are remarkably facilitated by the synergy between H⁻ on Cd and H⁺ on TiO₂ surface (Figure 3, formate pathway; Figure 4, RWGS pathway). In contrast, CO₂ conversion to CH₃OH on bare TiO₂ is very difficult compared to the Cd/TiO₂ interface. Cd‐TiO₂ interface is crucial for stabilizing various reaction intermediates and promoting the rate‐determining step of formaldehyde formation identified by DFT and MKM. All these mechanism results indicates that the multifunctionality of Cd/TiO₂ interface including Lewis acids of metals and Lewis base of surface oxygen is of great importance accounting for the outstanding catalytic activity of Cd/TiO₂ material. Water molecules produced from the reaction or present in the reaction system can dramatically facilitate the most difficult reaction steps of RWGS reaction. However, formate is identified to be the relevant intermediate for CO₂ hydrogenation to methanol, with formaldehyde formation being the rate‐limiting reaction step. Our results demonstrate that Cd/TiO₂ can be a promising candidate for valorization of CO₂ to produce methanol and the multifunctionality of the metal‐support interface is a crucial aspect for rational design of CO₂ hydrogenation catalyst.

Experimental Section

All DFT calculations have been performed using the Vienna Ab Initio Simulation Package (VASP). ^[19] The generalized gradient approximation (GGA) with PBE exchange and correlation functional was used to account for the exchange‐correlation energy.[ ^19b , ²⁰ ] The kinetic energy cutoff of the plane wave basis set was set to 400 eV. The threshold for energy convergence for each iteration was set to 10⁻⁵ eV. Geometries were assumed to be converged when forces on each atom were less than 0.05 eV/Å. Gaussian smearing of the population of partial occupancies with a width of 0.10 eV was used during iterative diagonalization of the Kohn‐Sham Hamiltonian. The bulky TiO₂ unit cell in the phase of anatase was firstly fully optimized. The optimized lattice vectors of a=3.799 Å b=3.799 Å c=9.716 Å have a good agreement with the experiment parameters. ^[21] For Cd₄/TiO₂ model, 1x3 and 2×4 supercells of anatase TiO₂ (101) surface with a vacuum space of 15 Å were built for investigation of the reaction mechanism of H₂ dissociation and CO₂ hydrogenation, respectively. These slab models contain six titanium layers with the bottom three layers were fixed while the rest was allowed to relax during the geometry optimization. The lattice parameters were fixed throughout the surface calculations. The nudged‐elastic band method with the improved tangent estimate (CI‐NEB) was used to determine the minimum energy path and to locate the transition state structure for each elementary reaction step. ^[22] The maximum energy geometry along the reaction path generated by the NEB method was further optimized using a quasi‐Newton algorithm. In this procedure, only the extra‐framework atoms were relaxed. Vibrational frequencies were calculated by determining the second derivatives of the Hessian matrix using the density functional perturbation theory as implemented in VASP 5.3.5. Transition state was confirmed by showing a single imaginary frequency corresponding to each reaction coordinate. Bader charge analysis was visualized by VESTA software. ^[23]

Mean‐field microkinetic modeling (MKM) is applied based on the DFT calculations of all elementary reaction steps. The rate constant of the adsorption reaction is calculated by the Hertz‐Knudsen equation [Eq. 1]: ^[24]

$${\displaystyle k_{ads}=\frac{PA}{\sqrt{2\pi m{k}_{b}T}}S}$$ (1)

where $k_{ads}$ is the rate constant of adsorption reaction, $P$ is the partial pressure of the adsorbate in the gas phase, $A$ is the surface area of the adsorption site, $m$ is the mass of adsorbate, $k_b$ is the Boltzmann constant, $T$ is the temperature, and $S$ is the sticking coefficient.

The desorption reaction is calculated by Equation 2:

$${\displaystyle k_{des}=\frac{k_b{T}^3}{h^3}\frac{A\left(2\pi m{k}_b\right)}{\sigma {\theta }_{rot}}{e}^{\left(\frac{-E_{des}}{k_{b}T}\right)}}$$ (2)

whare $k_{des}$ is the rate constant of desorption reaction, $h$ is the Plank's constant, $\sigma$ is the symmetry number of a molecule, ${\theta }_{rot}$ is the rotational temperature of a molecule, and $E_{des}$ is the desorption energy.

For the surface reaction, it is calculated by the Eyring equation [Eq. 3]: ^[25]

$${\displaystyle k=\frac{k_{b}T}{h}{e}^{-\frac{E_a}{RT}}}$$ (3)

where $k$ is the rate constant of surface reaction, $E_a$ is the activation energy, and R is the gas constant.

The approach to MKM has been presented in detail elsewhere. ^[26] The differential equations are constructed using the rate constants and the set of elementary reaction steps. For each of the M components in the kinetic network, a single differential equation is in the form [Eq. 4]:

$${\displaystyle r_i=\sum _{j=1}^N\left(k_j{v}_i^j{\prod }_{k=1}^M{c}_k^{v_k^j}\right)}$$ (4)

where $r_i$ is the rate reaction, $k_j$ is the elementary reaction constant, $v_i^j$ is the stoichiometric coefficient of component $i$ in elementary reaction step $k$ and $c_k$ is the concentration of component $k$ on the catalytic surface.

The degree of rate control (DRC) was performed to investigate the elementary steps that contribute to the rate control over the overall reaction ref: [21–23[. ^[27] For elementary step $i$ , the degree of rate control $X_{RC,i}$ is defined as [Eq. 5]

$${\displaystyle X_{RC,i}=\frac{k_i}{r}{\left(\frac{\partial r}{\partial k_i}\right)}_{k_{j\ne i,K_i}}={\left(\frac{\partial lnr}{\partial ln{k}_i}\right)}_{k_{j\ne i,K_i}}}$$ (5)

where $k_i,K_i$ and $r$ are the rate constants, the equilibrium constant for step $i$ and the reaction rate, respectively. All MKM results are simulated by a homemade script.

Conflict of interest

The authors declare no conflict of interest.

Supporting information

As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re‐organized for online delivery, but are not copy‐edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.

Supporting Information

G. Li, J. Meeprasert, J. Wang, C. Li, E. A. Pidko, ChemCatChem 2022, 14, e202101646.

Data Availability Statement

The data that support the findings of this study are available in the supplementary material of this article.