Theoretical Study of Ni- and Cu-Doped Molybdenum Ditelluride Electrocatalysts for Carbon Dioxide Reduction to Formic Acid and Carbon Monoxide

Abstract

Under mild conditions, the effective conversion of carbon dioxide (CO₂) into formic acid (HCOOH) and carbon monoxide (CO) represents a promising avenue for mitigating greenhouse gas emissions and addressing energy crises. In this work, we analyzed the electro-catalytic activities of six metals (Ti, Fe, Ni, Cu, Zn, and Cr) anchored on monolayer molybdenum telluride (TM@MoTe₂) for the CO₂ reduction reaction (CO₂RR) from CO₂ to HCOOH and CO. Compared to the reversible hydrogen electrode, the limiting potential for HCOOH production on Ni@MoTe₂ is only about −0.38 V, and it is only about −0.20 V for the CO production on Cu@MoTe₂. The limiting potential is concerned with the free energies of *OCHO and *COOH. Both the CO₂RRs suppress the competing hydrogen evolution reaction (HER) and exhibit good selectivity for the desired reaction products. These features enable the efficient conversion of CO₂ into HCOOH on Ni@MoTe₂ or CO on Cu@MoTe₂. Our calculations could provide valuable insights for the design and synthesis of high-performance catalysts based on MoTe₂.

1. Introduction

In recent years, with the rapid global economic development, the extensive utilization of fossil fuels has given rise to two critical issues. Firstly, the excessive emission of carbon dioxide (CO₂) gas disrupts the equilibrium of global carbon cycling, resulting in the greenhouse effect. Secondly, humanity is confronted with an impending energy crisis [1,2]. To address these challenges, conducting carbon dioxide reduction reactions (CO₂RR) under mild environmental conditions has emerged as a promising approach. This process involves employing suitable catalysts to electrochemically reduce excess atmospheric CO₂ to yield industrially valuable C1 (CH₄, CH₃OH, HCOOH, and CO), C2 (CH₃CH₃, C₂H₅OH, CH₃COOH, and CH₂CH₂), and higher carbon products [3,4,5,6,7,8]. Importantly, CO₂RR occurs under mild conditions and can harness clean energy sources such as solar and wind power; thereby, it will not aggravate the crisis of fossil fuels, and at the same time it will not cause secondary damage to the environment. Since the inception of CO₂RR, substantial efforts have been made by predecessors in this domain. In recent years, a plethora of electro-catalysts encompassing metals, metal oxides, and carbon-based materials have been extensively explored, both experimentally and theoretically, to enhance CO₂RR energy efficiency [9,10,11].

Single-atom catalysts (SACs) can be individually dispersed onto substrates, maximizing atomic utilization and mitigating the cost associated with noble metals. The attributes of SACs, including low metal loading, high catalytic activity, and exceptional selectivity, have rendered them a burgeoning realm within the field of electro-catalysis [12,13,14,15,16]. Moreover, transition metal di-chalcogenides (TMD) have been increasingly reported as electro-catalysts for CO₂RR in recent years [17,18,19,20,21,22,23,24,25]. A single Co atom supported on monolayer MoS₂ demonstrated exceptional CO₂ activation and conversion capabilities [24]. Ru@1T’-MoS₂ and Pt@1T’-MoS₂ catalysts could efficiently reduce CO₂ to CH₄ and CH₃OH at relatively low potentials (−0.56 V and −0.73 V, respectively), thereby presenting potential avenues for highly effective CO₂ conversion [22]. In addition, the single Cu atom embedded in monolayer MoS₂ also exhibited excellent performance in electro-catalytic CO₂RR [20]. It also has been reported that Ni anchored on monolayer WTe₂ may be a promising electro-catalytic material for efficient CO₂ reduction to HCOOH [25]. MoTe₂ is a representative material among transition metal tellurides [26]. Employing chemical vapor deposition, the sub-10-nm thick 2H-phase MoTe₂ (2H-MoTe₂) films can be synthesized in experiments [27]. Theoretically, 2H-MoTe₂ is more stable than the distorted octahedral structure of the 1T’ phase [28]. 2H-MoTe₂ has been utilized to investigate the reaction mechanisms of CO₂RR and the competing HER. It was found that the edges of MoTe₂ show promise as active and selective catalysts for alkaline CO₂RR [29].

Bagger et al. classified metal electrode materials according to different catalytic reduction products (HCOOH, CO, H₂, and hydrocarbons) [30]. We selected the third-period transition metal TM atoms (Ti, Fe, Ni, Cu, and Zn) mentioned in their study for discussion. Additionally, Cr from the same period has been demonstrated as a single-atom catalyst (SAC) with low limiting potential and good selectivity in the CO₂RR process [31]. Therefore, we chose Ti, Cr, Fe, Ni, Cu, and Zn anchored on MoTe₂ as SACs. Through structural stability analysis, free energy pathway calculations, and selectivity screening, Ni and Cu anchored on monolayer MoTe₂ (Ni@MoTe₂ and Cu@MoTe₂) were identified as exhibiting remarkable properties, including low over-potentials (−0.38 V and −0.20 V vs. RHE) and high product selectivity. Finally, the activation mechanism of CO₂ was explored.

2. Results and Discussion

2.1. Structure and Stability

Molybdenum ditelluride exhibits a crystalline configuration with a hexagonal lattice structure consisting of three atomic layers. Figure 1a shows the trigonal prismatic configuration of the 2H-MoTe₂, which is relatively more stable [32]. The central layer is composed of molybdenum atoms, while the upper and lower layers consist of tellurium atoms, collectively forming a three-layer sandwich structure. Within the atomic layers, molybdenum atoms are robustly bound to six tellurium atoms through pronounced covalent bonds. The lattice constant is about 0.353 nm [33]. The anchoring of TM atoms directly above the Mo atom and connected to three Te atoms (referred to as the T1 site) is considered to be more stable [25]. Therefore, we considered the possibility of anchoring Ti, Cr, Fe, Ni, Cu, and Zn atoms at the T1 site in a 4 × 4 2H-MoTe₂ supercell. The top view and side view of the anchored structure are shown in Figure 1b. The binding energy between the TM atoms and MoTe₂ is shown in Figure 1c. The binding energies ($E_b$) of TM atoms on MoTe₂ can be expressed according to following relation,

$$E_b=E_{\mathrm{T}\mathrm{M}@\mathrm{M}\mathrm{o}\mathrm{T}{\mathrm{e}}_2}-E_{\mathrm{M}\mathrm{o}\mathrm{T}{\mathrm{e}}_2}-E_{\mathrm{T}\mathrm{M}-\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}}$$

where $E_{\mathrm{T}\mathrm{M}@\mathrm{M}\mathrm{o}\mathrm{T}{\mathrm{e}}_2}$, $E_{\mathrm{M}\mathrm{o}\mathrm{T}{\mathrm{e}}_2}$, and $E_{\mathrm{T}\mathrm{M}-\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{l}\mathrm{e}}$ represent the total energies of TM@MoTe₂, pure MoTe_2, and the isolated TM atom, respectively. The negative binding energies show that Ti, Cr, Fe, Ni, and Cu atoms adsorbed on the MoTe₂ substrate are stable and unlikely to desorb. In comparison, structural optimization reveals that the Zn atom cannot be adsorbed onto MoTe₂. The optimized structures of TM@MoTe₂ (TM = Ti, Cr, Fe, Ni, Cu, and Zn) can be found in Figure S1 (see Supporting Material). Since Zn@MoTe₂ may be unstable, it will not be considered further. We calculated the Bader charges and atomic radii of TM atoms on TM@MoTe₂ (Table S1 in Supporting Material). The results reveal that TM atoms with larger radii exhibit greater charge transfer, as larger atomic radii lead to less localized electrons. Moreover, TM atoms with larger radii generally possess lower electronegativity, making their electrons more susceptible to attraction by the more electronegative Mo atoms. However, no clear correlation was observed between the Bader charges/atomic radii of TM atoms on TM@MoTe₂ and the binding energy values, suggesting the involvement of more complex interactions. Compared to other systems analyzed in this study, Ni@MoTe₂ is a promising candidate for CO₂RR with the lowest binding energy of Ni anchoring. We investigated the possibility of TM forming clusters on the substrate using Ni as an example. The transition state energy barriers for the formation of clusters with two, three, and four Ni atoms on the substrate are determined to be 1.69 eV, 1.45 eV, and 1.63 eV, respectively, as illustrated in Figure S2. Hence, we conclude that the diffusion and clustering of transition metal atoms on the substrate are hindered.

Additionally, we calculated the electronic localization function (ELF) to analyze the bonding characteristics between the transition metal atoms and the substrate. The results for Ni@MoTe₂ are shown in Figure 1d. Similar results for other TM@MoTe₂ can be found in Figure S3 (see Supporting Material). We found that the ELF value around the Ni atom is relatively low, while it is higher around the adjacent Te atoms. The bonding region between Ni and Mo exhibits moderate ELF values, indicating partial electron sharing, consistent with the characteristics of an ionic-covalent bond. The other TM@MoTe₂ structures (TM = Ti, Cr, Fe, and Cu) also exhibit similar phenomena. Combining the Bader charges and atomic radii of TM atoms in TM@MoTe₂ (Table S1 in Supporting Material), we employed the conventional charge density method (ρ = Q_bader/r³) to qualitatively characterize the magnitude of ELF values. The analysis reveals that the degree of electron localization around TM atoms follows the order Ti > Cr > Fe > Cu > Ni, which is consistent with the ELF mapping results. Furthermore, we computed the band structure of pristine MoTe₂, as illustrated in Figure 1e, which shows a band gap width of 1.05 eV, consistent with previous reports [34]. After anchoring Ni on MoTe₂, the band gap of Ni@MoTe₂ decreases to be about 0.41 eV, as shown in Figure 1f, enhancing the metallic character of the substrate material, which is expected to facilitate electron transfer during the electrochemical reduction process. The band structures of other TM@MoTe₂ structures are shown in Figure S4 (see Supporting Material). They also exhibit varying degrees of band gap reduction upon anchoring TM atoms. Therefore, TM@MoTe₂ (TM = Ti, Cr, Fe, Ni, and Cu) demonstrates the potential to serve as an excellent catalyst [35,36,37,38,39].

According to the subsequent calculations, Ni@MoTe₂ and Cu@MoTe₂ are promising candidates for excellent catalysts. Therefore, AIMD simulations were performed on the selected materials with an expanded 2 × 2 × 1 supercell at 300 K for 9 ps to assess the thermal stability of the two structures. As shown in Figure S5 (see Supporting Material), both the temperature (red curve) and energy (purple curve) of the designed catalysts fluctuate around equilibrium. The images inserted in the figure represent the corresponding structures of the studied catalysts after the 9 ps AIMD simulation. Following the AIMD simulations, no significant deformation or fracture of the designed structures was observed. The temperature/energy fluctuations and geometric structures demonstrate good thermodynamic stability. This ensures the feasibility of Ni@MoTe₂ and Cu@MoTe₂ as the electro-catalysts of CO₂RR in experimental studies.

2.2. Free Energy of CO₂ Reduction to HCOOH and CO

For the five TM@MoTe₂ (TM = Ti, Cr, Fe, Ni, and Cu) structures, the CO₂ molecule can successfully adsorb on the metal atoms. The distinct adsorption configurations can be found in Figure S6 (see Supporting Material). For Cr@MoTe₂ and Ti@MoTe₂, the Cr and Ti atoms form bonds with both oxygen atoms within the CO₂ molecule. The linear CO₂ molecule undergoes an inverted V-shaped distortion due to the robust adsorption on the metal atoms. In comparison, Cu@MoTe₂ exclusively establishes a bond with the carbon atom within the CO₂ molecule, while Ni@MoTe₂ and Fe@MoTe₂ concurrently bond with one carbon and one oxygen atom within the CO₂ molecule. The different bonding modes between the substrate and CO₂ molecules in these systems may lead to varying CO₂ electro-catalytic activities.

Building upon the premise of CO₂ stable adsorption onto the substrate, our subsequent analysis delves into the progressive reduction of CO₂ to CO and HCOOH via proton-electron coupling effects. Figure 2a illustrates the two pathways for CO₂ conversion to CO and HCOOH investigated in this study. Figures S7–S16 (see Supporting Information) present the detailed reaction pathways and structural diagrams for the reduction of CO₂ to CO and HCOOH using Ti, Cu, Cr, Fe, and Ni@MoTe₂. Initially, CO₂ adsorbed on TM@MoTe₂ undergoes protonation through the addition of H, yielding two distinct intermediates: *COOH and *OCHO. In subsequent protonation steps, the intermediates diverge toward distinct reduction products. *COOH advances towards the reduction to CO [40]. After further protonation and loss of a water molecule, *COOH transforms into intermediate *CO. Subsequently, *CO desorbs to form a CO molecule. In contrast, *OCHO proceeds towards the reduction to HCOOH [40]. *OCHO undergoes further protonation to form *HCOOH, which then desorbs to yield an HCOOH molecule.

Figure 2b–f present the Gibbs free energy profiles of various adsorbed intermediates during the protonation of CO₂RR to CO and HCOOH by the aforementioned systems. In Figure 2b, the potential-determining step (PDS) for the reduction of CO₂ to HCOOH on Ti@MoTe₂ is the protonation of *OCHO, with a free energy barrier of 1.47 eV. The PDS for the reduction of CO₂ to CO is the protonation of *COOH to form CO, with a free energy barrier of 0.65 eV. The first protonation steps for the production of both HCOOH and CO exhibit a downward energy trend. However, the free energy barrier of the intermediate *OCHO is lower than that of *COOH, which favors the formation of HCOOH and reduces the efficiency of CO product formation. Similarly, for Cu@MoTe₂, the initial protonation steps in both pathways are not energetically uphill, with *OCHO exhibiting lower energy, as shown in Figure 2c. The key difference lies in the PDS for CO₂ reduction to CO, which is the desorption of *CO with a limiting potential of only −0.20 V, while the limiting potential for HCOOH formation is −1.17 V. For the Fe@MoTe₂ in Figure 2d and Cr@MoTe₂ in Figure 2e, the limiting potentials for the reduction of CO₂ to HCOOH (CO) are −0.74 V (−0.17 V) and −1.29 V (−0.95 V), respectively. Similarly, the first protonation step for HCOOH formation exhibits a lower energy barrier, while the first protonation step for CO formation is energetically uphill, unlike Ti@MoTe₂ and Cu@MoTe₂. Figure 2f indicates that, for Ni@MoTe₂, the PDS for the reduction of CO₂ to HCOOH is the initial protonation of CO₂, with a free energy difference of 0.38 eV. The PDS for CO₂ reduction to CO involves the desorption of CO, with a free energy difference of 1.13 eV. The initial protonation is more likely to proceed through the lower free energy intermediate *OCHO. Therefore, we infer that Ni@MoTe₂ is more favorable for promoting the reduction of CO₂ to HCOOH.

We further investigated the relationship between the Gibbs free energy of key intermediates and the limiting potential of the corresponding products. Figure 3a illustrates the relationship between U_L(CO) and G_*COOH, revealing a volcano plot. Near the zero of G*COOH, Cu@MoTe₂ and Fe@MoTe₂ are positioned at the volcano top, exhibiting lower limiting potential and demonstrating good catalytic activity. In Figure 3b, U_L(HCOOH) and G_*OCHO exhibit a linear relationship. When the G_*OCHO approaches zero, Ni@MoTe₂ shows the optimal limiting potential. The above results indicate that G_*COOH and G_*OCHO can serve as the limiting potential descriptors.

2.3. Selectivity Analysis

For an excellent catalyst, high activity alone is insufficient; the selectivity must also be considered. Selectivity primarily considers the competition with the hydrogen evolution reaction (HER). Since both CO₂ reduction and HER involve the activity of hydrogen ions (protons) under reaction conditions, HER might compete with CO₂ electro-catalysis and leads to the decrease of the activity of CO₂RR [41].

Figure 4a presents the free energy diagrams for the HER on the five TM@MoTe₂ (TM = Ti, Cr, Ni, Fe, and Cu) systems. It can be observed that Fe@MoTe₂ and Cr@MoTe₂ exhibit good activity for HER, with limiting potentials of only −0.03 eV and −0.12 eV, respectively, indicating their potential as effective catalysts for HER. On the other hand, Ni@MoTe₂, Cu@MoTe₂, and Ti@MoTe₂ exhibit relatively high limiting potentials, indicating lower activity for HER. Figure 4b provides a visual comparison of the relative selectivity towards the competitive HER for the five systems during CO₂ reduction. In the upper left corner of the diagram (orange region), the reaction favors CO₂ reduction, while the lower right corner (blue region) signifies a preference for HER. Among the ten different CO₂RR processes, only Ni@MoTe₂(HCOOH) and Cu@MoTe₂(CO) exhibit good selectivity towards CO₂RR, while the results of the other materials are located in the blue region. For the CO₂RR of Ni@MoTe₂(HCOOH) and Cu@MoTe₂(CO), the calculated Faradaic efficiency (FE) is about 87.7% and 99.6%, respectively (the calculation formula for the FE can be found in Supporting Material, Note S1).

Due to the excellent selectivity of Ni@MoTe₂ and Cu@MoTe₂, we further analyzed the potential subsequent reactions of their products, *HCOOH and *CO. *HCOOH can undergo subsequent desorption or further protonation to form *HOCHOH, *OCH, or *H₂COOH intermediates. As shown in Figure 4c, the desorption energy of *HCOOH on Ni@MoTe₂ is approximately −0.05 eV. As a comparison, its subsequent protonation to form *HOCHOH, *OCH, and *H₂COOH intermediates is about +1.89 eV, +1.39 eV, and +0.53 eV, respectively. Hence, the protonation of *HCOOH to form *HOCHOH, *OCH, or *H₂COOH requires relatively high energy inputs, while the desorption of HCOOH is an exothermic process that requires no thermodynamic barrier. Consequently, Ni@MoTe₂ tends to desorb HCOOH and suppress the formation of various other products. As shown in Figure 4d, the free energy barrier for *CO desorption on Cu@MoTe₂ is +0.20 eV, while the energy barriers for further protonation to form the *CHO and *COH intermediates are +2.65 eV and +5.03 eV, respectively. Although the desorption of *CO results in an increase in free energy, it is evidently more favorable for *CO to desorb to form the CO product compared to the formation of the *CHO and *COH intermediates. Therefore, both Cu@MoTe₂ and Ni@MoTe₂ not only exhibit high activity and selectivity but also tend to generate target products without introducing unrelated intermediates.

The generation of CO on Cu@MoTe₂ exhibits a low limiting potential (−0.20 V) and good selectivity. However, from the perspective of the free energy difference, Cu@MoTe₂ has lower energy for the *OCHO intermediate in the first hydrogenation step, which may lead to reduced efficiency in the production of CO. We further calculated the energy barriers of transition states using the CI-NEB method to analyze product selectivity from the reaction rate perspective [33]. In Figure 4e,f, we calculated the transition states for the two reaction processes: *CO₂ + H⁺ + e⁻ → *OCHO and *CO₂ + H⁺ + e⁻ → *COOH on Cu@MoTe₂. Although the transition state for the formation of *OCHO has a lower final state energy, it must overcome a higher energy barrier of 2.42 eV, which is greater than the 1.82 eV barrier that the formation of *COOH must surpass. The relatively low energy barrier makes CO generation on Cu@MoTe₂ feasible. Therefore, Cu@MoTe₂ may serve as a reference for the potential candidate catalysts.

2.4. Mechanism of CO₂ Activation

To further understand the activation mechanism of CO₂, we present the projected crystal orbital Hamiltonian population (PCOHP) of CO₂ on Ni@MoTe₂ and Cu@MoTe₂ substrates [42], as shown in Figure 5a,b. In the figure, we use -PCOHP. The red curve on the right represents bonding states, with peaks located below the Fermi level (E_F), indicating that they are fully occupied by electrons. The blue curve on the left represents antibonding states, some of which are partially filled with electrons. The integrated crystal orbital Hamilton population (ICOHP) value for the C-O bond awaiting hydrogenation is −14.46 eV on Ni@MoTe₂ and −15.94 eV on Cu@MoTe₂, respectively. The ICOHP values on the remaining three systems, Ti@MoTe₂, Cr@MoTe₂, and Fe@MoTe₂, are −11.79 eV, −14.44 eV, and −15.64 eV, respectively (Figure S17 in Supporting Material). The ICOHP value of the C-O bond in the free CO₂ gas molecule is about −18.45 eV, which indicates that CO₂ adsorbed on these five substrates will be activated to a great extent compared with free CO₂. The C-O bond lengths upon hydrogenation on TM@MoTe₂ (TM = Fe, Cu, Ni, Cr, and Ti) are 1.21 Å, 1.21 Å, 1.24 Å, 1.26 Å, and 1.35 Å, respectively. The higher the ICOHP value, the longer the corresponding C-O bond length upon hydrogenation, indicating more pronounced activation.

Figure 5c–f and Figure S18 show the structures of CO₂ adsorbed on TM@MoTe₂ and the corresponding charge density plots, where blue represents electron depletion and yellow represents electron accumulation. From these figures, we can observe that different amounts of electron exchange occur between CO₂ and the substrates. The transferred charges to CO₂ on TM@MoTe₂ (TM = Cu, Ni, Fe, Cr, and Ti) are calculated to be 0.34 e, 0.36 e, 0.59 e, 0.69 e, and 0.94 e, respectively. Herein, both Ti and Cr exhibit significant electron transfer to CO₂ and form bonds with both oxygen atoms of CO₂. On the MoTe₂ surface, Ti and Cr exist in relatively low oxidation states, enabling more electron donation to the O atoms of CO₂. This partial occupation of CO₂’s π* orbitals facilitates the bent (inverted V-shaped) activation of CO₂. Figure 5g illustrates the relationship between the charge transfer on CO₂ and the center of the d-band. According to the classical d-band center theory, the d-band center of the catalyst surface determines the strength of the interaction between the metal and the reactant [43]. The figure shows that there is a strong linear relationship between the amount of charge transferred on CO₂ and the center of d-band, which is consistent with the d-band theory. By modulating the d-band center, the activation of CO₂ can be effectively controlled. The transferred charge on Fe@MoTe₂ is moderate, and the corresponding generations of HCOOH and CO on Fe@MoTe₂ have relatively low limiting potentials. This is consistent with the Sabatier principle [44], which suggests that optimal catalytic activity is typically achieved when the interaction between the intermediate and the substrate is neither too weak nor too strong.

To better understand the activation mechanism, Figure 5h illustrates the interaction between CO₂ and substrate. Upon CO₂ adsorption, the lone pair electrons in the σ orbital of CO₂ engage in σ donation to the vacant d orbitals of the TM atom, occupying the empty d orbitals of the TM atom [45]. Simultaneously, the occupied d orbitals of the TM atom participate in π* back-donation, populating the π* antibonding orbitals of the CO₂ molecule. These insights shed light on the intricate interplay between CO₂ and the substrate, revealing the mechanistic basis for the diverse adsorption strengths observed in CO₂-derived critical intermediates.

3. Computational Methodology

All computations were carried out utilizing the spin-polarized density functional theory (DFT) methodology implemented in the Vienna Ab-initio Simulation Package (VASP 5.4.4) [46]. The electron–ion interactions were modeled using the projector-augmented wave (PAW) approach, while the electronic exchange and correlation effects were described using the Perdew–Burke–Ernzerhof (PBE) functional within the framework of the generalized gradient approximation (GGA) [47,48]. To account for van der Waals (vdW) interactions between reactants, intermediates, and catalysts, the empirical correction scheme based on the Grimme method (DFT + D3) was employed [49]. The transition states involved were systematically explored by employing the climbing-image nudged elastic band (CI-NEB) method [50]. A plane wave energy cutoff of 400 eV was employed for structural optimizations, while a value of 500 eV was chosen for electronic structure calculations. The k-point grids were set to 1 × 1 × 1 for geometry optimization and 5 × 5 × 1 for electronic structure calculations. Convergence criteria for electronic energy and forces were established at 10⁻⁵ eV and 0.05 eV/Å, respectively. Additionally, an 18 Å vacuum layer was introduced to mitigate interlayer interactions. Catalyst thermal stability was assessed through ab initio molecular dynamics (AIMD) simulations using VASP, with a Nose–Hoover thermostat employed. The selected materials were expanded to a 2 × 2 × 1 supercell. A time step of 3 fs and a total simulation duration of 9 ps were selected to verify the thermal stability of catalysts.

To ascertain the Gibbs free energy during proton transfer in CO₂RR, computations were conducted utilizing a computational hydrogen electrode (CHE) model [51,52]. The Gibbs free energies (G) for all intermediate steps were determined using the following equation: $G=E+\Delta ZPE-T\Delta S+G_{pH}$; here, E corresponds to the energy of surface and intermediate species obtained from DFT calculations, ΔZPE represents the variation in zero-point energy, and ΔS accounts for the entropy change of free molecules and adsorbates at 298.15 K. The pH-dependent G_pH was calculated using the formula $G_{pH}=k_{B}T\times ln10\times pH$; here, k_B stands for the Boltzmann constant, and pH was set to zero. The limiting potential (U_L) was determined as U_L = −ΔG_max/|e|, where ΔG_max denotes the difference in free energy of the highest energy step on the reaction pathway, and e represents the unit of charge. Smaller |U_L| corresponds to higher activity level.

4. Conclusions

This study primarily presents a theoretical and computational investigation. In this work, using MoTe₂ as the substrate material, we considered six transition metals (TM = Ti, Cr, Fe, Ni, Cu, and Zn) anchored to the surface of MoTe₂ as candidates for novel CO₂RR catalysts. After the stability analysis of the substrate material, the Zn atom was excluded from further consideration due to the inability to anchor effectively on MoTe₂. Through comprehensive study, Cu@MoTe₂ and Fe@MoTe₂ exhibit low limiting potentials for CO₂ reduction to CO, with values of 0.20 eV and 0.17 eV, respectively. In addition, Ni@MoTe₂ exhibits excellent activity for CO₂ reduction to HCOOH, with a limiting potential of 0.38 eV. The key intermediates *COOH and *OCHO can serve as descriptors to predict the limiting potentials for the formation of CO and HCOOH. After selective screening, Ni@MoTe₂ exhibits excellent selectivity for CO₂ reduction to HCOOH, with a Faradaic efficiency (FE) of 88.7%. The CO₂RR on Cu@MoTe₂ may be influenced by the hydrogenation free energy in the first step, where the free energy of the *COOH intermediate is higher than that of *OCHO. The formation of CO on Cu@MoTe₂ may be affected. However, transition state analysis reveals that the lower energy barrier for *COOH makes CO generation on Cu@MoTe₂ possible. The FE for the CO₂RR on Cu@MoTe₂ is as high as 99.6%. Since the results of this study primarily rely on computational simulations, these findings are model-based. We hope that our calculations will contribute to the design and synthesis of high-performance catalysts based on MoTe₂.