Electrochemical CO₂ reduction to methanol over Ni@Ti₃CN MXene: a first-principles DFT study

Abstract

Electrochemical carbon dioxide (CO₂) reduction is a promising solution for the conversion of CO₂ to CH₃OH. In this study, we investigated the catalytic activity of nickel-decorated Ti₃CN (Ni@Ti₃CN) using density functional theory combined with a computational hydrogen electrode (CHE) model. This study was completely carried out using an implicit solvation model to understand the impact of the solvent on the production of CH₃OH via electrochemical CO₂ reduction. Using ab initio molecular dynamics (AIMD), Ni@Ti₃CN was found to be thermally stable at T = 300 K. The catalyst activated CO₂ in the side-on orientation, where visible changes in its bond length and angle were observed with an adsorption energy of −0.12 eV. The rate-determining step (RDS) in the overall reaction is the formation of *CO (RDS) with a corresponding free energy change (ΔG) of 0.59 eV. This intermediate plays a crucial role in the CO₂ reduction reaction (CO₂RR). The calculated limiting potential (U_L) for the reaction is −0.59 V, corresponding to a low overpotential of 0.61 V. The faradaic efficiency for CH₃OH production is approximately 99.9%. These results demonstrate that Ni@Ti₃CN is a promising candidate for electrochemical CO₂ reduction, highlighting the potential of carbonitride-based MXenes for future CO₂ reduction applications.

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1. Introduction

The immense use of fossil fuels has led to the release of excess CO₂ into the atmosphere, leading to a wide range of global climate issues. Excessive anthropogenic CO₂ causes an increase in temperature, leading to global warming. Over the past few decades, an increase in environmental temperature due to the increase in global CO₂ has resulted in the melting of glaciers and climate change.¹ These detrimental effects of anthropogenic global CO₂ is expected to cause Earth warming by 4 °C in year 2100; to resolve this problem, a global summit was held in Paris in 2015, where around 192 nations took part in the proposal of different solutions.² As a result, to mitigate these issues, several solutions have been proposed, among which carbon capture, storage, and carbon conversion are anticipated to gradually reduce the negative impact of anthropogenic CO₂. Direct CO₂ conversion to value-added multi-carbon products plays an important role in reducing anthropogenic CO₂ and simultaneously fulfilling the energy needs of various applications. However, CO₂ is a notorious molecule that is extremely stable, has sluggish kinetics, and requires an active catalyst that can break down and activate CO₂, further leading to a reduction reaction. C1, C2, and C3 products (one-, two-, and three-carbon products, respectively) are value-added products, such as formic acid (HCOOH), methanol (CH₃OH), ethanol (C₂H₅OH), propanol (C₃H₇OH), and ethylene (CH₂=CH₂). To date, several methods have been reported for CO₂ reduction, including electrochemical, photochemical, and thermochemical methods.³ Among them, electrochemical CO₂ reduction is attractive because it operates at ambient temperature and pressure under laboratory conditions. It only requires an external electric source from sustainable energy sources, such as solar, wind, and hydro, to drive the reduction, which is another advantage of electrochemical CO₂ reduction.³ Distinct value-added chemical fuels have been obtained based on different electron pathways, such as 2e-, 6e-, and 8e-pathways.⁴ Among the many products, methanol (CH₃OH) is a vital hydrocarbon fuel as it is used in direct methanol fuel cells (DMFC). Owing to its high energy density, it also acts as a hydrogen storage material.^5–7 Accordingly, several cost-effective catalysts have been explored for methanol production via electrochemical CO₂ reduction. However, they suffer from low faradaic efficiencies, high overpotentials, and side reactions.⁷

In recent years, single-atom catalysts (SACs) have attracted significant attention from researchers due to their advantages. SACs are a class of heterogeneous catalysts composed of a single atom anchored on a support material (host), where the single atom serves as an active site. The pioneering work by Zhang et al. (2011) led to the synthesis of the first SAC, Pt/FeO_x, for CO oxidation.¹⁰ Typically, SACs feature single transition metals (Sc to Zn, Mo, and Hf), dispersed on various support material (host). These support materials span a wide range of 2D materials including graphene, MoS₂, h-BP, metallenes, metal oxides, metal organic frameworks (MOF), covalent organic frameworks (COF), and MXenes.^8–10 Reducing bulk materials to nanoparticles, and ultimately to single atoms results in a highly unsaturated coordination environment for metal atoms, which increases their surface free energy and enhances their catalytic activity. A major advantage of SACs is their 100% atomic utilization, which not only improves their catalytic performance but also reduces costs compared to traditional bulk catalysts. Beyond the CO₂ reduction reaction (CO₂RR), single-atom catalysts (SACs) are also active in key electrochemical processes such as the oxygen reduction reaction (ORR),^11,12 oxygen evolution reaction (OER),¹³ and nitrogen reduction reaction (NRR).^14,15 Yu et al. investigated transition-metal-doped Ti₂CO₂ (TM = Sc, Ti, Y, Zr, and Hf) MXene as an electrocatalyst for N₂O reduction,¹⁶ and further explored 2D conjugated metal–organic frameworks with 3d metals (Sc–Zn) for cyanide reduction.¹⁷ Baskaran et al. examined TM@Mo₂CS₂ (TM = Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au) MXenes for CO₂RR, leading to CH₄, HCOOH, and CH₃OH formation.¹⁸ Likewise, Cui et al. reported that M@C₂N–graphene SACs (M = Ti, Mn, Fe, Co, Ni, and Ru) exhibit low overpotentials (∼0.58–0.80 V) for CO₂RR.¹⁹

A key challenge in the development of SACs is preventing single-atom aggregation during their synthesis. Methods such as co-precipitation, atomic layer deposition, and wet impregnation have been applied, while the stability and catalytic efficiency of SACs strongly depend on the choice of support, particularly 2D materials.^8,20

The search for 2D materials similar to graphene has attracted considerable research attention. In addition to graphene, the exploration of MXenes for a wide range of applications has increased. MXenes were initially discovered in 2011 when A (Al) from the MAX phase Ti₃AlC₂ was etched, resulting in Ti₃C₂ MXene. The M–A bond in the MAX phase is comparatively weaker than the M–X bond, making it easier to selectively etch A from the MAX phase. MAX phases are layered hexagonal structures with the P6₃/mmc space group, whereas the M_n+1X_n phase is chemically stable with a hexagonal structure.²¹ MXenes are hexagonal layered 2D surfaces with M_n+1X_n [n = 1, 2 or 3], where M represents early transition elements (Ti, Sc, and V) and X represents carbon (C), nitrogen (N), or carbonitride (CN). MXenes have attracted significant attention owing to their exceptional electronic and thermal properties, high electrical conductivity, and large surface area. They have been used in a range of applications such as biomedicine, sensing, and catalysis.^22,23 Titanium (Ti)-based MXenes are nontoxic, environmentally friendly, and abundant in nature.²² Thus far, Ti–MXenes based on carbides and nitrides have been explored; however, carbonitride-based Ti–MXenes have rarely been explored for catalysis.

In this work, using spin-polarized density functional theory and an implicit solvation model (water), Ti-based carbonitride (Ti₃CN) decorated with an Ni atom on the N side of Ti₃CN was investigated for electrochemical CO₂RR to CH₃OH. All studies were performed under an implicit solvent effect (water) only. Initial screening of the catalyst was done based on the binding energy (E_B) and cohesive energy (E_coh) for TM@Ti₃CN (TM = Fe, Co, Ni, and Cu). Among them, Ni@Ti₃CN is found to have the highest E_B and E_coh, and thus further investigated for electrochemical CO₂RR. The initial CO₂ activation was checked, which showed that CO₂ activation occurred owing to the variation in its bond elongation and bond angle. The 6e⁻ (six-electron) pathway (6H⁺ + 6e⁻), which produces CH₃OH (methanol) from the electrochemical reduction reaction, was studied and is given below

*CO₂ → *COOH → *CO → *CHO → *CH₂O → *CH₂OH → *CH₃OH

The high faradaic efficiency and low overpotential towards CH₃OH production indicate that the Ni-decorated Ti-based carbonitride MXene (Ni@Ti₃CN) serves as an efficient catalyst for electrochemical CO₂ reduction to CH₃OH.

2. Computational techniques

Structural optimization, electronic structure, and electrochemical CO₂RR were studied in solvent medium (water) by spin-polarized density functional theory (DFT) using the Vienna ab initio simulation package (VASP5.4) software and VaspSol.^24–27 The Perdew–Burke–Ernzerhof (PBE) functional in the generalized gradient approximation (GGA) method was used.^28,29 The interaction of the core valence electrons was considered using projected augmented-wave (PAW) pseudopotentials.^30,31 A plane wave energy cutoff of approximately 500 eV was used in all studies. Ionic optimization was performed using a conjugate gradient algorithm with a convergence threshold of 1 × 10⁻⁰⁴ eV, and the structure was completely relaxed until the Hellmann–Feynman force was less than 0.02 eV Å⁻¹. To account for van der Waals (vdW) long-range interactions throughout this study, the DFT-D3 method accompanied by Becke–Johnson damping correction was implemented in this work.³² Gaussian smearing with a smearing width of 0.05 eV was used for optimization and electronic structure analysis. To sample the Brillouin zone, a Monkhorst–Pack with 2 × 2 × 1 k-points was used, and an even denser k-point of 5 × 5 × 1 was chosen for density of states analysis.³³ To avoid interactions between the periodic slabs, a vacuum of 20 Å was added in the Z-direction.

A computational hydrogen electrode (CHE) model for Gibbs free energy (ΔG) calculations in the electrochemical CO₂RR was used to construct a free energy profile to identify the rate-determining step (RDS) of the reaction.³⁴ The Gibbs free energy (ΔG) for each reaction step was calculated using eqn (1), as follows:³⁵

ΔG = ΔE + ΔE_ZPE − TΔS + ΔG_U + ΔG_pH eV (1)

where ΔE is the reaction energy obtained from DFT and ΔE_ZPE is the zero-point energy obtained by performing the normal-mode vibrational frequency in the harmonic approximation for each adsorbed reaction species. In this case, the vibrational modes of the reaction species were computed by keeping the catalyst static; that is, the contribution of ZPE and entropy towards the free energy from the catalyst was assumed to be negligible.³⁶TΔS denotes the entropy correction, which is also computed from the vibrational frequency analysis at temperature T = 298.15 K, ΔG_U = −enU, where n is the number of proton–electron pairs, e is the transferred electron, U is the applied potential and ΔG_pH represents the free energy correction term due to the H⁺ concentration variation, which is given by G_pH = −k_BT × ln[H⁺] = −k_BT × ln(10) × pH (k_B is the Boltzmann constant and T is temperature).³⁶ This study was carried out in an aqueous environment with the aid of the VASPsol software using an implicit solvation model.

The reaction was studied at an applied potential of ΔG_U = 0 V, and the pH value was considered to be zero for an acidic medium.^18,37 The limiting potential for this reaction was calculated using the equation , with the rate-determining step being the maximum Gibbs free energy change (ΔG_max). Bader charge analysis was used to study the partial charge transfer between the monomers in the complex.³⁸

To verify the binding strength between a single atom and the host surface, the binding energy was calculated using eqn (2), as follows:

where E_complex denotes the total energy of the complexes (single-atom catalyst) and E_monomer describes the total energy of a single isolated transition metal atom (TM = Fe, Co, Ni, and Cu) and the support surface (Ti₃CN).

The stability of a single-atom catalyst is determined by its cohesive energy (E_coh), which is defined as the energy required to break the catalyst surface into its constituent atoms. The equation for calculating the cohesive energy is as follows:³⁹

This equation consists of the total energy of the complex E_X@Ti3CN and total energy of a single isolated titanium (Ti), carbon (C), and nitrogen (N) atom, denoted as E_Ti, E_C and E_N, respectively. The climbing image nudged elastic band (CI-NEB) method was used to determine the diffusion barrier of a single atom decorated on Ti₃CN. The dissolution potential (U_diss) was calculated using eqn (4), as follows:

where U⁰_diss(Ni) represents the standard electrode potential of Ni, n represents the number of electrons involved in dissolution, and E_form represents the formation energy of Ni@Ti₃CN, which was calculated using E_form = E_Ni@Ti3CN − E_Ni − E_@Ti3CN (eV).⁴⁰

The adsorption energy (E_ads) used to assess the nature of adsorption between the reaction species and catalyst was calculated using eqn (5), as follows:

E_ads = E_{(catalyst+reaction species)} − E_catalyst − E_{reaction species} eV (5)

where E_{(catalyst+reaction species)} is the total DFT energy of the adsorbed complex (catalyst + reaction species), E_catalyst is the total energy of the catalyst, and E_{reaction species} is the total energy of the reaction species such as reactants, reaction intermediates, and products. The overpotential (η) for the electrochemical CO₂RR was determined using eqn (6), as follows:

η = [U_eq − U_L] V (6)

The above-mentioned equation consists of U_eq, i.e. equilibrium potential (U_eq = 0.02 V for methanol, CH₃OH) and the limiting potential (U_L) obtained using the maximum Gibbs free energy change of the reaction.^18,41

3. Results and discussion

3.1. Structural stability analysis

The Ti₃CN MXene for the electrochemical CO₂RR was constructed using a 4 × 4 × 1 supercell with 48 Ti, 16 C, and 16 N atoms, followed by complete optimization in solvent medium. The optimized Ti₃CN structure is shown in Fig. 1a. The optimized structure exhibits lattice parameters of |a| = |b| = 3.06 Å with a hexagonal crystal system, consistent with previous reports.^42,43 As shown in Fig. 1b, Ti₃CN is a five-layered 2D structure with an alternating Ti layer stacked with nitrogen and carbon layers, and its structural arrangement is in the form of Ti–N–Ti–C–Ti. The average Ti–N bond length ranges from 2.03 to 2.04 Å and the Ti–C bond length is in the range of 2.17–2.20 Å⁴³ (Fig. 1a and b), respectively.

Fig. 1 Optimized structure of pristine Ti₃CN in solvent medium: (a) front view and (b) side view. (c) Phonon dispersion plot, (d) band structure and (e) projected density of states (PDOS) of Ti₃CN.

Experimentally, Ti₃CN was synthesized from the Ti₃AlCN phase by etching a layer of Al (aluminum), resulting in Ti₃CN MXene.⁴⁴ The dynamic stability of Ti₃CN was verified by phonon dispersion, as shown in Fig. 1c. There was no imaginary frequency. Ti₃CN was found to be metallic in the obtained band structure (Fig. 1d), which is in agreement with the results in previous studies.⁴³ Additionally, as shown in Fig. 1e, the projected density of states (PDOS) shows overlapping peaks of the 3d (Ti), 2p (N), and 2p (C) orbitals near the Fermi level, indicating the metallicity of the pristine Ti₃CN. Liu et al. studied the performance of nitrogen-doped graphene for the carbon dioxide reduction reaction and proved that nitrogen atoms improved the catalytic performance.⁴⁵ Wang et al. found that a nitrogen-doped carbon coating enhances the catalytic activity for electrochemical CO₂ reduction.⁴⁶ Moeller et al. demonstrated that metal–nitrogen-doped carbon materials (MNCs) selectively reduced CO₂ to CO at low overpotentials.⁴⁷ Inspired by previous works, we explored electrochemical CO₂ reduction on the nitrogen side of Ti₃CN.

Furthermore, a series of 3d transition metals such as Fe, Co, Ni, and Cu was doped onto the optimized Ti₃CN MXene, and the doped structures were completely relaxed in solvent medium. The resultant optimized doped structures were Fe@Ti₃CN, Co@Ti₃CN, Ni@Ti₃CN, and Cu@Ti₃CN. To determine the most stable catalyst among the aforementioned four structures, the binding energy (E_B) and cohesive energy (E_coh) were calculated using eqn (2) and (3), respectively. The calculated binding energy (E_B) and cohesive energy (E_coh) of the four doped structures are listed in Table 1. The highest binding energy was obtained for Ni@Ti₃CN (E_B = −5.91 eV), while Fe@Ti₃CN exhibited the lowest binding energy of 0.01 eV. The cohesive energy ranges from −6.95 eV to −7.02 eV for TM@Ti₃CN (TM = Fe, Co, Ni, and Cu). Although E_coh lies in the same range, the most suitable catalyst for the electrochemical CO₂RR was chosen from the highest binding energy, accounting for stability.

Table 1 Calculated binding energy, E_B (eV), and cohesive Energy, E_coh (eV), for TM@Ti₃CN (TM = Fe, Co, Ni, and Cu) in solvent medium

TM@Ti3CN (TM = Fe, Co, Ni, and Cu)	Binding energy (EB) (eV)	Cohesive energy (Ecoh) (eV)
Fe@Ti3CN	0.01	−6.95
Co@Ti3CN	−4.58	−7.00
Ni@Ti3CN	−5.91	−7.02
Cu@Ti3CN	−3.20	−6.99

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According to Table 1, it can be seen that Ni@Ti₃CN has the highest binding energy E_B = −5.91 eV with a cohesive energy of E_coh = −7.02 eV. Based on this, the Ni@Ti₃CN catalyst was selected for the electrochemical CO₂RR. The front and side views of the optimized Ni@Ti₃CN are shown in Fig. 2a and b, respectively. The optimized Ni@Ti₃CN exhibits the Ni–Ti bond distance of 2.37–2.49 Å, and even after doping the average Ti–N bond distance remains the same as that of the pristine Ti–N bond distance of 2.03 Å. The band structure plot (Fig. 2c) of Ni@Ti₃CN, accompanied by the overlap of the 3d and 2p orbital peaks of Ni, Ti, N, and C in the projected density of states (PDOS) (Fig. 2d), reveals the metallic nature of Ni@Ti₃CN.

Fig. 2 Optimized structure of pristine Ni@Ti₃CN in solvent medium: (a) front view and (b) side view. (c) Band structure and (d) projected density of states (PDOS) of Ni@Ti₃CN.

The thermal stability of Ni@Ti₃CN was studied by performing ab initio molecular dynamics (AIMD) in solvent medium at a temperature of T = 300 K using a Nose–Hoover thermostat with an NVT ensemble. The plot is given in Fig. 3a, where it can be observed that the structure is thermally stable, and a single Ni atom remains at the same adsorption site throughout the simulations for a time step of 6 ps. The diffusion barrier of Ni atoms decorated on Ti₃CN was calculated to be 1.01 eV using the climbing image nudged elastic band (CI-NEB) method. This positive diffusion barrier indicates that the migration of a single Ni atom between sites is energetically unfavourable, thereby confirming the stability of the single-atom catalyst. One of the major challenges in synthesizing SACs is the tendency of single atoms to aggregate, which reduces their catalytic efficiency in reduction reactions. To evaluate the possibility of Ni atom aggregation on Ti₃CN, we performed AIMD simulations with two Ni atoms positioned at neighbouring sites on Ti₃CN at T = 300 K over a time step of 5 ps. The results showed that the two Ni atoms retained their respective adsorption sites throughout the simulation without any structural deformation. The corresponding AIMD plot is presented in Fig. 3b.

Fig. 3 (a) AIMD plot of Ni@Ti₃CN and (b) Ni–Ni@Ti₃CN at T = 300 K in solvent medium.

The redistribution of charges between Ni (single atom) and Ti₃CN (support surface in SAC) was observed via the charge density difference (CDD) plot (Fig. 4a), where charge accumulation is represented in yellow and charge depletion is denoted by cyan. The electron localization function plot (ELF) (Fig. 4b) for Ni@Ti₃CN shows a bluish-green region, where the values of ∼0.2–0.5 depict the metallic bond between atoms.

Fig. 4 (a) Charge density difference (CDD) plot of Ni@Ti₃CN and (b) electron localization function (ELF) plot of Ni@Ti₃CN (atom representation: grey-nickel, blue-titanium, bluish grey-nitrogen, and brown-carbon).

3.2. Initial CO₂ activation

The adsorption of CO₂ followed by its activation is considered to be the first step in the electrochemical CO₂ reduction reaction. The activation of CO₂ means the elongation of the linear CO₂ bond length (O=C=O) and bending of its bond angle (∠OCO = 180°) where the injection of an electron in the 2π_u antibonding orbital of CO₂ is required. CO₂, which is thermodynamically stable and inert with a high bond energy (∼806 kJ mol⁻¹), requires additional external sources to break or activate the linear C=O double bonds.^18,48,49 This is achieved by the catalyst in the electrochemical CO₂RR, where the vital role of the catalyst is to activate CO₂ by causing bond elongation, bending, or both. CO₂ was initially maintained in both orientations, end-on and side-on. The adsorption energy (E_ads) for both adsorbed complexes was calculated using eqn (5), and E_ads for the end-on and side-on orientations of CO₂ adsorbed on Ni@Ti₃CN is found to be 2.32 eV and −0.12 eV and its corresponding optimized structures are given in Fig. 5a and b, respectively. It is observed that E_ads is positive for the end-on orientation and endothermic in comparison to the E_ads obtained for the side-on orientation. The negative ΔG_ads for the side-on orientation implies that the initial step of the electrochemical CO₂RR via the side-on orientation is exothermically feasible and spontaneous. Ni@Ti₃CN did not activate CO₂ in the end-on orientation because there was only an infinitesimally small deviation in the bond length and angle of CO₂ (Fig. 5a). However, in the case of the side-on orientation, CO₂ achieved good activation, where both bond elongation and bending were observed, as shown in Fig. 5b. A comparison of the E_ads of CO₂ on Ni@Ti₃CN with that in previous studies is presented in Table 2, which shows that Ni@Ti₃CN activates CO₂ with the optimal E_ads and initiates CO₂ reduction via sequential protonation.

Fig. 5 Optimized structure of (a) end-on and (b) side-on orientation of CO₂ adsorbed on Ni@Ti₃CN (atom representation: red-oxygen, yellow-carbon, violet-nickel, green-titanium, and dark pink-nitrogen).

Table 2 Comparison of adsorption energy, E_ads (eV), of CO₂ on Ni@Ti₃CN with those of previously reported catalysts

Catalyst	E ads (eV)	Ref.
a Represents values in gas phase.
Ni@Ti 3 CN	−0.12 (in solvent)	Present work
Ni/g-C3N4	−0.22^a	50
Ni–Ni@N-doped graphene	−0.14^a	51
Ni@CNT	−0.59^a	52
C2N	−0.31^a	53

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The above-mentioned analysis shows that the electrochemical CO₂RR proceeds via the side-on orientation of CO₂. The overlap of the peaks near the Fermi level for the complex, as shown in the projected density of states (PDOS) plot in Fig. 6a, reveals the covalent nature of CO₂ and Ni@Ti₃CN. The charge density difference (CDD) plot obtained for the complex (Fig. 6b) is in good agreement with the adsorption energy, indicating a strong charge distribution between CO₂ and Ni@Ti₃CN, where yellow indicates the accumulation of charges and cyan denotes charge depletion. Further, Bader charge analysis showed that Ni@Ti₃CN acts as an acceptor (−1.14e), while CO₂ acts as a donor (+3.7e), which explains the charge transfer between the catalyst and CO₂.

Fig. 6 (a) Projected density of states (PDOS) and (b) charge density difference plot of side-on orientation of CO₂ adsorbed on Ni@Ti₃CN (atom representation: red-oxygen, brown-carbon, grey-nickel, blue-titanium, and bluish grey-nitrogen).

3.3. Selectivity between CO₂RR vs. hydrogen evolution reaction (HER)

The hydrogen evolution reaction (HER) is considered to be a parasitic side reaction in the electrochemical CO₂RR occurring in aqueous electrolytes.¹⁸ In most CO₂RR cases, the loss of faradaic efficiency for CO₂RR products is due to the occurrence of competing side reactions (HER).⁴¹ Thus, it is necessary to check the selectivity of the catalyst towards CO₂RR and HER, as both reactions occur with the aid of the H⁺ + e⁻ pair. The first step of CO₂RR occurs with the addition of H⁺ + e⁻ and the initial step for hydrogen evolution reaction requires the binding of the H⁺ + e⁻ pair on the catalyst. Therefore, the Gibbs free energy change (ΔG) for *COOH or *OCHO (CO₂RR intermediate) and *H (HER reaction species) must be evaluated, and the reaction species with a lower ΔG are more selective. The selectivity of CO₂RR vs. HER by Ni@Ti₃CN was found by calculating the ΔG for *COOH and *H. The ΔG_COOH and ΔG_H are 0.06 eV and 1.17 eV, which depict that the catalyst suppresses HER, and its corresponding optimized structures and free energy profile are given in Fig. 7a and b, respectively. According to the obtained results, it can be seen that Ni@Ti₃CN is more selective towards CO₂RR than the HER.

Fig. 7 (a) Adsorption of H (HER intermediate) on Ni@Ti₃CN and (b) free energy profile for HER intermediate adsorption on Ni@Ti₃CN at T = 298.15 K (atom representation: blue-hydrogen, violet-nickel, green-titanium, and dark pink-nitrogen).

3.4. Reaction pathway for electrochemical CO₂RR to CH₃OH

The electrochemical CO₂RR is studied under solvent medium, where water (dielectric constant ε = 78.54) is considered to be the solvent. Electrochemical CO₂RR occurs with the sequential addition of proton–electron pairs (H⁺ + e⁻) (protonation).³⁶ The pathway followed by the Ni@Ti₃CN catalyst for the electrochemical CO₂ reduction to CH₃OH under the solvent effect is shown in Fig. 8. The CO₂RR reaction occurs after the initial activation of CO₂ in the side-on orientation with the addition of H⁺ + e⁻ pairs from the aqueous electrolyte. The first protonation after the initial activation of CO₂ results in two intermediates such as *COOH and *OCHO, where in the case of Ni@Ti₃CN, the catalyst supports the formation of *COOH with the Gibbs free energy change (ΔG) of 0.06 eV. The second protonation step results in the formation of *CO with the desorption of a water (H₂O) molecule with ΔG = 0.59 eV, which serves as the rate-determining step (RDS) for the overall reaction, beyond which the reaction proceeds in the downhill pathway. Further, the third protonation leads to the formation of a *CHO intermediate with a ΔG of −0.15 eV, which is exergonic and spontaneous. The addition of a fourth H⁺ + e⁻ pair to *CHO leads to two possible reaction intermediates, *CHOH and *CH₂O. The optimized reaction intermediates exhibit the Gibbs free energy change (ΔG) of 0.54 eV (CHOH) and −0.72 eV (CH₂O). According to the obtained ΔG, the reaction proceeds via the CH₂O path because it is exergonic and spontaneous, leading to the formation of two more intermediates, CH₂OH and CH₃O, as a result of the fifth protonation step. The calculated ΔG for both intermediates was found to be −1.10 eV and 0.02 eV, where the obtained ΔG shows that the formation of CH₂OH is exergonic and spontaneous in comparison to CH₃O. Therefore, the feasibility of the formation of CH₃OH as a result of the sixth protonation of CH₂OH was analysed. It has been found that the formation of CH₃OH from the CH₂OH intermediate results with the Gibbs free energy change (ΔG) of −0.53 eV. The negative ΔG value for CH₃OH from CH₂OH indicates that the formation of CH₃OH is feasible via CH₂OH, as it is exothermic and spontaneous. The corresponding free energy profile for electrochemical CO₂RR to CH₃OH under the solvent effect is given in Fig. 9. It is observed that the inclusion of the solvent effect in the electrochemical CO₂RR mimics the real environment, which shows that the impact of the solvent on electrochemical CO₂RR is vital.

Fig. 8 Electrochemical CO₂RR pathway on Ni@Ti₃CN catalyst (atom representation: red-oxygen, yellow-carbon, blue-hydrogen, violet-nickel, green-titanium, and dark pink-nitrogen).

Fig. 9 Free energy (ΔG) profile for electrochemical CO₂RR pathway on Ni@Ti₃CN catalyst at T = 298.15 K in solvent medium.

3.5. Descriptors of catalytic efficiency

3.5.1. Limiting potential and overpotential. The limiting potential was obtained from the ΔG of the rate-determining step (RDS), which was denoted as the maximum Gibbs free energy change in the entire reaction pathway. Generally, the rate-determining step is the uphill part of the entire reaction pathway, which determines the speed of the overall reaction. Hence, the limiting potential is a vital parameter that determines the efficiency of a catalyst. The limiting potential (U_L) for electrochemical CO₂ reduction is calculated using eqn (7), as follows:where ΔG_max represents the maximum Gibbs free energy change in the overall reaction.

The formation of the *CO intermediate was found to be RDS and its corresponding ΔG = 0.59 eV with respect to the limiting potential is calculated to be U_L = −0.59 V. It is seen that the obtained limiting potential is comparatively lower than that in the previous literature. A comparison of the limiting potential obtained in the present study with that in previous studies is presented in Table 3.

Table 3 Comparison of the limiting potential (U_L) (V) for electrochemical CO₂ reduction to CH₃OH of the present work with those of previously reported works

Catalyst	Limiting potential UL (V)	Ref.
a Represents values in the gas phase.
Ni@Ti 3 CN	−0.59 (in solvent)	Present work
Nitrogen doped graphdiyne	−0.46^a	54
Ni@g-C3N4	−0.72^a	50
Cu3Ir	−0.47^a	55
α-Fe2O3 (0001)	−0.81^a	56

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The overpotential is defined as the additional potential required to drive a chemical reaction beyond thermodynamic requirements at a faster rate. A catalyst is considered to be efficient if it drives the reaction at a low overpotential. Therefore, an efficient catalyst must exhibit a low overpotential. The overpotential was calculated using the equation η = [U_eq − U_L] V. In this study, the overpotential for Ni@Ti₃CN is found to be η = [0.02 − (−0.59)] V = 0.61 V. Although the overpotential under solvent influence is 0.61 V for the electrochemical reduction of CO₂ to CH₃OH, it is well below 1 V. A comparison of the overpotential in the present work with that in previous studies is presented in Table 4.

Table 4 Comparison of the overpotential (η) for electrochemical CO₂ reduction to CH₃OH by various catalysts

Catalyst	Overpotential (η) (V)	Ref.
a Represents values in the gas phase.
Ni@Ti3CN	0.61 (in solvent)	Present work
Cu3Pd and Cu3Pt	∼0.70^a	55
Zn–SiNT	0.84^a	57
Hexagonal Cu(111) ML	0.46^a	58
α-Fe2O3 (0001)	0.8^a	56

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3.5.2. Faradaic efficiency. The faradaic efficiency is a measure of how efficiently the amount of charge passed in the electrochemical reaction is used to produce the desired product. The faradaic efficiency or current efficiency for the electrochemical CO₂RR was calculated using the Boltzmann distribution, as shown in eqn (8) below:³⁷where ΔG is the difference between the free energies of the rate-determining steps for the CO₂RR and HER. T is the ambient temperature, which is 298.15 K, and k_B is the Boltzmann constant. Saha et al. studied the electrochemical reduction of CO₂ to CH₃OH with the aid of an iron porphyrinoid catalyst and obtained a faradaic yield for CH₃OH of ∼50%.⁵ Lee et al. studied the eCO₂RR to CH₃OH on a cuprous oxide electrode, which showed a faradaic efficiency of approximately 38% towards CH₃OH.⁵⁹ In a work on CO₂ reduction to methanol using a nonmetal electrocatalyst, boron phosphide nanoparticles achieved a faradaic efficiency for CH₃OH of 92.0%.⁶⁰ Lei et al. designed an Fe₂P₂S₆ nanosheet for the electrocatalytic reduction of CO₂ to CH₃OH, resulting in a faradaic yield of CH₃OH of up to 65.2%.⁶¹ In the present study, the Ni@Ti₃CN catalyst exhibited a faradaic efficiency of ∼99% for the production of CH₃OH.

4. Conclusion

In conclusion, Ni@Ti₃CN, which belongs to the class of carbonitride MXenes, has been studied for electrochemical CO₂ reduction to CH₃OH under a solvent effect via the six-electron pathway. Using a first-principles study, Ni@Ti₃CN was found to be stable, with a high negative cohesive energy. According to ab initio molecular dynamics (AIMD), Ni@Ti₃CN was found to be thermally stable at T = 300 K. In addition, the absence of Ni atom aggregation on Ti₃CN is found in the AIMD study. The catalyst exhibited a metallic nature even after decoration with Ni, which is one of the advantages of electrochemical CO₂ reduction, where electrons are readily available for reduction. It was also found that CO₂ reduction is likely to occur at Ni-decorated Ti₃CN, among the other transition metals Fe, Co, Cu, and Ni on the N side of Ti₃CN, as it is exothermic and spontaneous with a negative binding energy. Further, Ni@Ti₃CN resulted in low limiting potential, followed by the lowest overpotential of 0.61 V for the formation of CH₃OH. It also achieved a high faradaic efficiency of ∼99% for the production of CH₃OH. Based on the implementation of the implicit solvation model towards electrochemical CO₂ reduction to CH₃OH, Ni@Ti₃CN exhibits a low overpotential of less than 1 V, and thus we anticipate that it is a promising candidate for electrochemical CO₂ reduction to CH₃OH. Further, these results pave the way for the development of carbonitride-based MXenes as catalysts for electrochemical CO₂ reduction to CH₃OH.

Author contributions

Karthiga Manivannan: methodology, data curation, format analysis, and original draft. Senthilkumar Lakshmipathi: conceptualization, methodology, software, data curation, formal analysis, review, and editing.

Conflicts of interest

The authors declare no conflict of interest.

Data availability

The data supporting this article have been included in the manuscript.

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