Tantalum based single, double, and triple atom catalysts supported on g-C₂N monolayer for effective nitrogen reduction reaction: a comparative DFT investigation

Abstract

Design of efficient and low cost electrocatalysts for the reduction of N₂ molecule to NH₃ in a green manner remains a great challenge in the 21st century. Herein, we have used density functional theory based first principle simulations to systematically investigate the nitrogen reduction reaction (NRR) ability of single, double, and triple Ta-atom catalysts anchored to C₂N monolayer. Our results demonstrate that the single and triple Ta-atom catalysts anchored to C₂N monolayer act as superior catalysts for the NRR via alternating and distal pathways as compared to the Ru(0001) stepped surface. In particular, the triple Ta-atom catalyst anchored to C₂N shows enhanced NRR performance with a limiting potential of −0.72 V which is comparable to the experimentally reported Ru based single atom catalyst. Further, all the three catalysts were found to be highly selective for NRR with an enhanced ability to suppress the competitive hydrogen evolution reaction. Electronic structure analysis revealed that the enhanced ability of Ta₃@C₂N catalyst to effectively capture and reduce N₂ molecule could be attributed to the built up of localized d states near the fermi level, thereby aiding in strong electron transfer into the antibonding orbitals of N₂. Thus, our findings propose a highly active catalyst for the NRR with an emphasis on the importance of triple atom-based catalysts for electrocatalytic applications.

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1. Introduction

Conversion of atmospheric nitrogen (N₂), one of the most abundant and chemically inert molecules in nature, into ammonia (NH₃) at a large scale is of paramount importance for producing fertilizers to speed up agricultural growth for sustenance of life on earth.^1–3 Further, a high gravimetric hydrogen density coupled with ease of liquification makes ammonia a safe carbon free energy storage intermediate with no emission of harmful greenhouse gases like carbon dioxide into the atmosphere.^4,5 At present the industrial conversion of N₂ to NH₃ follows the conventional Haber–Bosch process which is highly energy-intensive and results in release of significant amount of harmful greenhouse gases into the atmosphere.^6–8 To achieve more sustainable and environmentally friendly way of ammonia production on an industrial scale, design of efficient electrocatalysts is the core component to make the nitrogen reduction reaction (NRR) kinetically and thermodynamically feasible.

Over the years, transition metal-based systems at different length scales have been at the facade of research for electrocatalyst design for efficient reduction of N₂. For example, two-dimensional transition metal dichalcogenides,⁹ nitrides and carbides,¹⁰ and boron nanosheets^11–13 have demonstrated improved electrocatalytic activity for activation and reduction of N₂ molecule to NH₃. In addition, size selected monometallic and bimetallic transition metal clusters^14,15 supported on variable supports have been thoroughly explored as catalysts for NRR. The catalytic performance of nanomaterials for NRR has been shown to be highly dependent on factors such as size, shape, crystal phase and degree of amorphization.¹⁶ Although a wide variety of nanomaterials have been explored and developed for the electrocatalytic NRR, the efficiency of NRR is still not comparable for the industrial synthesis of NH₃.

Recently size reduction of matter to a few atoms has been foreseen to be a valuable strategy to boost the catalytic ability of materials.^17–21 Particularly single atom catalysts consisting of single metal atoms dispersed on variable supports has proven to be effective for catalysing diverse reactions. The drastic improvement in the catalytic ability of SACs has been ascribed to factors such as maximum atom utilization, unique quantum size effects and unsaturated catalytic sites.^22–24 Due to these reasons increasing number of studies have been carried out to understand the NRR ability of transition metal-based SACs dispersed on different types of supporting materials. For example, Liu et al.²⁵ using extensive density functional theory-based simulations on 20 different transition metal SACs dispersed on three different nitrogen-doped carbon substrates proposed a two-step strategy for improving the NRR activity. By further tuning the adsorption strength of the key intermediates as a function of the coordination environment of the already predicted promising SACs, the authors concluded that Ru@g-C₃N₄ and Rh@g-C₃N₄ act as best NRR catalysts. Sun and co-workers²⁶ revealed that the coordination environment around the single molybdenum catalyst plays an important role in the NRR by tuning the d-band center around the Fermi level. Further, many theoretical works^27–43 have been carried out to understand the underlying intrinsic factors controlling the activity of a wide variety of SACs anchored to different supports, leading to successful descriptors for designing promising SAC candidates for efficient NRR.

Beyond SACs, double and triple atom catalysts comprising two and three metal atoms anchored to suitable supports have emerged as potential catalysts.⁴⁴ In the case of NRR, some of the recent theoretical studies^45–49 concluded that mono and hetero-atomic double atom catalysts (DACs) act as better catalysts with enhanced activity and selectivity as compared to their corresponding SACs. Similarly, triple atom catalysts (TACs)^50,51 of different metal atoms have also been investigated in some of the very recent research works for NRR. In one such interesting study,⁵² Fe₃ and Fe₄ catalysts supported on nitrogen-doped graphene demonstrated better catalytic activity with low limiting potential for nitrogen reduction compared to single and double Fe atom catalysts. Similarly, spin-polarized density functional theory calculations by Li et al.⁵³ on Mo_x (x = 1–4) supported on graphdiyne (GDY) revealed that Mo₃ acts as a superior catalyst for NRR. In contrast to the above studies, single and double atom catalysts of Cu were found to be proficient for catalysing NRR by Ma and co-workers⁵⁴ during the computational evaluation of transition metal™ single, double and triple atom catalysts (TM = Mn, Fe, Co, Ni) supported on graphdiyne monolayers. The above studies inspire us to perform a comparative investigation on single, double, and triple atom catalysts for NRR. Thus, in this work, we have carried out spin-polarized density functional theory calculations to understand NRR activity of tantalum based single, double, and triple atom catalysts. Further, the justification for choosing tantalum in the current study lies in the fact that experimental studies have shown that small-sized gas-phase tantalum clusters strongly bind and activate nitrogen molecule. For example, Fryzuk and coworkers,⁵⁵ recognized based on spectroscopic and quantum chemical analysis the ability of di-nuclear Ta complexes to bind N₂ molecule in side-on and end-on geometries. Geng et al.⁵⁶ using Fourier transform ion cyclotron resonance mass spectroscopy identified a planar four-membered Ta₂N₂⁺ structure to be the key intermediate for mediating N₂ to NH₃ conversion similar to a Haber–Bosch-like process. Geng et al.⁵⁷ further revealed that N=N undergoes complete cleavage in a thermal reaction with Ta₂N⁺ through a degenerate ligand exchange mechanism under standard conditions. More recently Ma and co-workers⁵⁸ photoelectron spectroscopy results corroborated by quantum chemical calculations by Ma and co-workers showed that N₂ is strongly activated by Ta₃N₃H and Ta₃N₂ cluster anions with the hydrogen atom playing a crucial role in the reactivity.

To evaluate the NRR activity of Ta-based single, double, and triple atom catalysts, we employed the g-C2N monolayer as the substrate. Apart from exhibiting a very high thermal and kinetic stability,⁵⁹ g-C2N possesses uniformly distributed nanopores with pyrazinic sp² nitrogen atoms. Further, the benzene rings in the g-C₂N monolayer are connected by nitrogen atoms generating a partial negative charge on the nitrogen atoms,⁶⁰ thereby providing suitable sites for adsorption, and enhancing the propensity of stabilizing single, double, and triple atom catalysts.

2. Computational details

In this work, plane-wave density functional theory as implemented in Vienna ab initio simulation package (VASP)^61–63 was used to perform spin-polarized first-principles calculations with the electron–ion interaction being described by the projector augmented wave (PAW) method.⁶⁴ The exchange-correlation energy is treated by the Perdew–Burke–Ernzerhof (PBE) functional⁶⁵ and Grimme's semiempirical DFT-D3 scheme⁶⁶ of dispersion correction was employed to account for the weak van der Waals (vdW) interaction. A kinetic energy cut off 500 eV was used for the plane-wave basis. 10⁻⁷ eV was set as the convergence criteria for the energy and structure optimizations were performed until the Hellmann–Feynman force on each atom was less than 10⁻³ eV Å⁻¹. A 2 × 2 C₂N monolayer supercell with a vacuum space of 15 Å along the z-direction was applied to avoid the interaction between two periodic units. Further, a Monkhorst–Pack mesh⁶⁷ of 3 × 3 × 1 for structural optimization and 6 × 6 × 1 for the calculation of electronic properties was used.

The binding energy per atom (E_b) for the Ta based catalysts⁴⁵ on the C₂N monolayer and the N₂ adsorption energy on the Ta_n@C₂N catalysts were obtained using the given below equations

E_ads = E_N2 + E_Tan@C2N − E_Tan@C2N–N2

where E_C2N and E_Tan@C2N are the total energies of the C₂N monolayer without and with the added Ta_n species, respectively. E_Tan is the total energy of the isolated Ta-monomer, dimer, and trimer species whereas E_N2is the energy of the isolated N₂ molecule and E_Tan@C2N–N2 is the energy of the N₂ adsorbed on Ta_n@C₂N catalysts.

The reaction free energy (ΔG) for each elementary step was calculated based on the computational hydrogen electrode (CHE) model proposed by Nørskov and co-workers^68–70 by the following equation

ΔG = ΔE + ΔE_ZPE − TΔS + ΔG_U + ΔG_pH

In this equation, ΔE is the reaction energy obtained from DFT calculations. ΔE_ZPE and TΔS are the contributions of the zero-point energy and entropy to ΔG, respectively, which were obtained from the vibrational frequency calculations using VASPKIT code.⁷¹T is the temperature and taken as 298.15 K, and ΔS is the entropy change. The zero-point and entropic corrections to the free energy of the gas phase and the adsorbed species along the most favourable reaction pathways are presented in Table S1.† ΔG_U = neU is the free energy contributed by electrode potential; e and U are the number of electrons transferred and the electrode potential applied, respectively. ΔG_pH = k_BT × ln10 × pH is the free energy correction due pH which is assumed to be zero in this study. The value of limiting potential (U_L) is determined from the potential-determining step (PDS) involving the most positive free energy change (ΔG_max) as

3. Results and discussion

We begin with a discussion on the structure, stability, and electronic properties of Ta_n (n = 1–3) species adsorbed on the C₂N monolayer. To obtain the most stable structure of Ta_n@C₂N systems, several possible adsorption patterns of Ta_n on C₂N were considered. Fig. 1(a) represents the lowest energy structures of Ta_n@C₂N catalysts with relevant geometrical parameters. The binding energy per atom of the Ta-monomer, dimer, and trimer species with C₂N monolayer are also given in Fig. 1(a). As can be seen from the figure, the single Ta atom prefers to remain in the C₂N plane with two Ta–N bonds and a significantly large binding energy of 8.50 eV. For the Ta₂@C₂N, one of the Ta resides inside the C₂N plane and the second Ta atom is pushed slightly above the C₂N plane while as for Ta₃@C₂N all the three Ta atoms reside above the C₂N monolayer plane. The calculated binding energy per atom for the Ta₂@C₂N and Ta₃@C₂N were found to be 10.06 and 9.87 eV, respectively. Interestingly, the calculated binding energy for the Ta monomer, dimer and trimer is higher than the reported cohesive energy per atom of 8.10 eV for bulk Ta. We also evaluated the thermal stabilities of Ta_n@C₂N systems by carrying out ab initio molecular dynamics (AIMD) simulations at 900 K (see Fig. 1(b)) for a time of 10 picoseconds with the help of NVT ensemble and Nose–Hoover thermostat as implemented in the CP2K package.⁷² AIMD simulations reveal that all the atoms in the studied catalysts vibrate about their equilibrium positions with no significant structural deformation. To further understand the stability of Ta-based catalysts, we carried out climbing image nudged elastic band (CI-NEB) calculations⁷³ to evaluate the barrier for diffusion of tantalum atom from the nanopores of g-C2N to the hexagonal rings. The results (Fig. S1†) reveal that not only is the diffusion highly endergonic with an energy requirement of 6.12 eV but also entails a very large diffusion barrier of 6.57 eV. The significantly large binding energies compared to bulk Ta metal and negligible structural deformation around 900 K indicate the enhanced thermal stability of Ta_n@C₂N catalysts.

Fig. 1 (a) Top and side view of Ta_n@C₂N catalysts with relevant geometrical parameters. The numbers in black at the bottom are the calculated binding energy per atom in eV of the Ta_n (n = 1–3) species with C₂N monolayer. (b) Variation of energy with respect to the AIMD simulation time in picoseconds for Ta_n@C₂N catalysts.

Since activation and adsorption of N₂ is the first step towards N₂ reduction process, we next looked at the N₂ capturing ability of these catalysts by calculating the N₂ adsorption energies in different possible adsorption modes. As can be seen from Fig. 2, nitrogen was adsorbed through side-on and end-on modes with two Ta–N and one Ta–N bonds, respectively. Table 1 highlights the computed nitrogen adsorption energies and N–N bond lengths of nitrogen molecule adsorbed on the single, double, and triple Ta atom catalysts. Our results indicate that the end-on mode of binding of N₂ is preferred over the side-on mode in the Ta monomer whereas side-on mode is preferred over end-on mode for the Ta dimer and trimer catalysts. Further, there is a significant increase in the adsorption energy of N₂ molecule in the side-on mode as we go from Ta₁ to Ta₃. A slight difference in N₂ adsorption energy is noted in end-one mode of N₂ adsorption. The calculated N₂ adsorption energies for side-on and end-on modes were found to be 0.78, 1.88 and 3.37 eV, and 1.46, 1.35 and 1.43 eV, respectively for the single, double, and triple atom catalysts. Bader charge analysis (Table 1) demonstrates that the charge transfer to adsorbed N₂ from the catalysts is larger in the side-on (0.47 to 1.65 e) mode than in the end-on (0.26 to 0.40 e) mode. The stronger binding and enhanced charge transfer with respect to the side-on N₂ adsorption mode is also reflected by the more significant charge redistribution in charge density plots (Fig. 2) and increase in the population of p-states of N₂ near the Fermi level (Fig. S3†). The electron transfer results in the occupation of the antibonding orbitals of the N₂ molecule and subsequent N–N bond elongation. It can therefore be observed from Table 1 that the increase in N–N bond length up on adsorption follows the order Ta₃@C₂N > Ta₂@C₂N > Ta₁@C₂N in the side-on mode, whereas the end-on mode of N₂ adsorption reveals almost similar N–N bond length.

Fig. 2 Top and side view of side-on and end-on N₂ adsorption configurations on (a) Ta₁@C₂N (b) Ta₂@C₂N and (c) Ta₃@C₂N catalysts with relevant geometrical parameters. Charge density difference plots of side-on and end-in N₂ adsorption configurations on (e) Ta₁@C₂N (f) Ta₂@C₂N and (g) Ta₃@C₂N catalysts. The isosurface level is set to 0.004 e Å⁻³. Pink indicates the electron density accumulation area, and light green indicates the electron density depletion area.

Table 1 Nitrogen binding energy (E_ads) in eV, N–N (R_N–N) bond length and Bader charges (Q_b) on the N₂ molecule adsorbed on Ta_n@C₂N based catalysts

System	Binding mode	E ads (eV)	R N–N (Å)	Q b (e)
Ta@C2N	Side-on	0.78	1.19	−0.47
	End-on	1.46	1.15	−0.39
Ta2@C2N	Side-on	1.88	1.26	−1.02
	End-on	1.35	1.13	−0.26
Ta3@C2N	Side-on	3.37	1.42	−1.65
	End-on	1.43	1.15	−0.40

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To further understand N₂ binding energy trends, we performed detailed electronic structure analysis using projected density of state (PDOS) calculations. As can be seen from Fig. 3 that the PDOS of Ta₁@C₂N has an appreciable contribution of Ta d-states near the Fermi level in the spin-up channel. Moreover, the contribution of Ta d-states increases linearly from Ta₁@C₂N to Ta₃@C₂N (Fig. 3, cyan box). This increase in the electronic population of Ta d-states near the Fermi level facilitates the charge transfer and enables effective N₂ adsorption. Indeed, a linear relationship (Fig. S3 and Table S1†) between the total integrated PDOS of Ta d-states near the Fermi level (in the range of −2.0 – 0.0 eV) versus the binding energies of N₂ rationalizes the increase in corresponding N₂ binding energies for side-on mode. To further quantify the N₂ binding energy results, we plotted the IPDOS of N₂ p-states near Fermi level (−2.0–0.0 eV) against N₂ binding energy. Interestingly, a linear relationship between the N₂ p-states IPDOS and binding energy was identified (Fig. S3†), suggesting that the binding energy of N₂ in the side-on mode results due to strong hybridization between N₂ p- and Ta d-states. In the end-on mode, N₂ binds with catalysts through a single nitrogen atom, therefore, the overlap of N₂ p-states with metal d-states is expected to be lower than the side-on mode. The visual inspection of PDOS (Fig. 4) clearly confirms that the extent of hybridization of N₂ (p) with Ta (d) states near Fermi level follow the order Ta₁@C₂N > Ta₃@C₂N > Ta₂@C₂N, explaining the N₂ binding energy trends qualitatively. Additionally, as the side-on and end-on modes of adsorption of N₂ molecules involves different nature of N₂ binding, the relationship between N₂ binding energies and N₂ p-states IPDOS is found to be mode dependent (Fig. S3c†).

Fig. 3 Spin-polarized orbital projected DOS (oPDOS) of (a) Ta₁@C₂N (b) Ta₂@C₂N and (c) Ta₃@C₂N catalysts. Colour codes for PDOS: grey – total, red – carbon (p), blue – nitrogen (p), and green – Ta (d). Fermi level is set has been zero. The PDOS is truncated within −12 to 8 eV for the sake of clarity.

Fig. 4 Spin-polarized oPDOS for the N₂ adsorbed configurations on Ta_n@C₂N in the side-on (a) Ta₁@C₂N (c) Ta₂@C₂N (e) Ta₃@C₂N and end-on (b) Ta₁@C₂N (d) Ta₂@C₂N (f) Ta₃@C₂N, mode. The population of Ta (d) states near Fermi level is highlighted with cyan boxes. Colour codes for PDOS: grey – total, red – carbon (p), blue – nitrogen (p), and green – Ta (d). Fermi level is set has been zero. The PDOS is truncated within −12 to 8 eV for the sake of clarity.

We next explored the transformation of N₂ to two NH₃ molecules via the three already well-known mechanisms for NRR. According to earlier studies, the alternating and distal mechanisms are associated with end-on mode of adsorption whereas the enzymatic mechanism is associated with side-on mode of adsorption. In the distal mechanism, the proton–electron pairs initially attack the nitrogen atom not attached to the catalyst surface resulting in the formation of the first NH₃ molecule and then the formation of the second NH₃ molecule by attacking the left-over N-atom. In contrast, the alternating and enzymatic mechanisms involve the alternate attack of the proton–electron pairs on the two N atoms leading to the consecutive formation of two NH₃ molecules. It is important to mention here that although N₂ adsorbs strongly in the end-on mode in single atom tantalum catalyst and side-on mode on the double and triple atom tantalum catalysts, the side-on mode in single tantalum catalyst and the end-on modes in the double and triple tantalum catalysts are also considerably thermodynamically favorable. Thus, in an ensemble picture the side-on mode for single atom and end-on mode of N₂ adsorption for double and triple atom catalysts will also be populated, thereby, making it imperative to evaluate all the three known pathways i.e., alternating, distal, and enzymatic for NRR on these catalysts. Before, we investigate the detailed NRR mechanism on the Ta_n@C₂N catalysts, earlier studies have exclusively pointed that due to the inert nature of the N≡N triple bond, the first proton–electron pair transfer step requires a large input of energy and is quite often the PDS. Therefore, we calculated the ΔG values for the step on all the three catalysts for both side-on and end-on N₂ modes and are presented in Table 2.

Table 2 Potential determining step (PDS) and limiting potential (U_L) for NRR along the studied reaction pathways on Ta_n@C₂N based catalysts

Catalyst	Pathway	ΔG*NNH	PDS	U L (V)
Ta1@C2N	Alternating	0.79	*N–N + H^+ + e^− → *N–NH	−0.79
	Distal	0.79	*N–NH2 + H^+ + e^− → *N + NH3	−1.39
	Enzymatic	0.21	*NH–*NH2 + H^+ + e^− → *NH2–*NH2	−0.97
Ta2@C2N	Alternating	0.94	*N–N + H^+ + e^− → *N–NH	−0.94
	Distal	0.94	*N–NH + H^+ + e^− → *N–NH2	−1.15
	Enzymatic	−0.51	*NH2–*NH2 + H^+ + e^− → *NH2–NH3	−1.04
Ta3@C2N	Alternating	0.09	*NH–NH2 + H^+ + e^− → *NH2–NH2	−1.11
	Distal	0.09	*NH + H^+ + e^− → *NH2	−0.72
	Enzymatic	−0.42	*NH2–*NH2 + H^+ + e^− → *NH2 + NH3	−2.48

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Intriguingly, the end-on mode of Ta-monomer along the alternating and dimer catalysts along the alternating and distal pathways require large energy for the first step of hydrogenation. In sharp contrast, for the Ta-trimer catalyst, a small amount of energy is required for the first step of hydrogenation along alternating/distal pathways, indicating the potential of these catalysts for high NRR activity. The most favourable reaction pathway for NRR on the Ta_n@C₂N catalysts is presented in Fig. 5 and detailed reaction pathways with the images of various intermediates and corresponding limiting potential are given in ESI.†Table 2 depicts the potential-determining step with the limiting potential along the studied alternate, distal and enzymatic pathways on Ta-based single, double, and triple atom catalysts. From Fig. 5 and Table 2, one can see that the limiting potential value for the most favourable pathway for formation of two NH₃ molecules on Ta₂@C₂N is −0.94 V. Contrastingly, the limiting potential values for the most favourable pathways on Ta₁@C₂N and Ta₃@C₂N are −0.79 and −0.72 V respectively. To simulate the solvent effect on the most favourable reaction pathways, we used VASPsol code⁷⁴ with an implicit solvent model. The reaction free energy profiles for the most favourable reactions pathways after including the solvent corrections are presented in Fig. S7.† As can be seen from the figure, the inclusion of the solvent effect leads to an appreciable change in the relative stability of different intermediates along the NRR pathways for the Ta-single and double atom catalysts, whereas the NRR pathway for the triple atom catalyst reveals no significant change as compared to gas phase calculations. We note an increase in the limiting potential from −0.94 to −1.56 V for the Ta-double atom catalyst. However, importantly the single and triple atom catalysts reveal slightly lower limiting potentials of −0.76 and −0.70 V respectively as compared to the gas phase results. It is important to mention here that for the completion of the catalytic cycle, the second NH₃ must undergo desorption from the single, double, and triple atom catalysts. The calculations reveal that this step requires 0.82, 1.20 and 1.42 eV of energy for single, double, and triple Ta-atom catalysts, which is comparable or lower than the recently reported results.^46,75,76 Also, it is reported this obstacle can be overcome either by the energy released by the subsequent hydrogenation steps⁷⁵ of NH₃ formation or protonation of NH₃ to NH₄⁺ under acidic conditions.^27,77 Finally, for comparison, the calculated limiting potential values for the Ta-monomer and trimer catalysts are in close proximity with already experimentally reported Ru SAC catalyst^78,79 supported on nitrogen-doped carbon (U_L = −0.73/−0.77 V) and much lower that of R(0001) stepped surface⁸⁰ (U_L = −0.98 V), which has the best NRR performance among bulk metal catalysts.

Fig. 5 Most favourable reaction pathway for NRR on (a) Ta₁@C₂N (b) Ta₂@C₂N and (c) Ta₃@C₂N catalysts with corresponding limiting potentials. The sub-figures represent the optimized geometries of the different reaction intermediates involved in the reaction pathways.

Further, hydrogen evolution reaction (HER) is the main competing reaction for NRR as the proton-electron pair required for N₂ reduction can easily cover the catalyst surface, thereby reducing the selectivity for NRR. As per the CHE model, the free energy change for N₂ and H adsorption respectively for NRR and HER provides a useful estimate of the reaction selectivity. Therefore, the adsorption free energies of *N₂ and *H are calculated and plotted in Fig. 6. As can be seen from the figure, all the three Ta-catalysts preferentially adsorb N₂ compared to H, indicating a higher selectivity for NRR than HER. Thus, from the above results, we conclude that the Ta-timer catalyst supported on a C₂N monolayer acts as better catalysts for NRR than Ta-monomer and dimer catalysts.

Fig. 6 Calculated adsorption free energies of N₂ molecule and H atom on the Ta_n@C₂N catalysts. The free energy change for N₂ adsorption has been calculated using end-on mode for Ta₁@C₂N and side-on mode for Ta₂@C₂N and Ta₃@C₂N catalysts.

4. Conclusions

In summary, density functional theory calculations were carried on single, double, and triple Ta-atom catalysts anchored on the C₂N monolayer for electrochemical reduction of nitrogen. Importantly, Ta₃@C₂N catalyst with appropriate electronic structure was found to be the most promising candidate for NRR with high thermal stability, strong N₂ adsorption ability, a low limiting potential and good NRR selectivity. We expect the current work could lead to further investigations to stimulate the design of triple atom catalysts of varying metal atoms for efficient NRR and other electrocatalytic applications.

Author contributions

A. R., I. A., and A. M. performed the theoretical calculations. M. A. D. and S. K. conceptualized the study and carried out the advising. M. D. performed and conceptualized the electronic structure analysis. All authors contributed to the preparation of the manuscript.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

M. A. D. acknowledges the Start-up Research Grant (SRG/2020/000654) of SERB, India and M. D. acknowledges the Core Research Grant (CRG/2020/005626) of SERB, India for financial support toward the completion of this work. We acknowledge National Supercomputing Mission (NSM) for providing computing resources of ‘PARAM Brahma’ at IISER Pune, which is implemented by C-DAC and supported by the Ministry of Electronics and Information Technology (MeitY) and Department of Science and Technology (DST), Government of India.

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Footnote

† Electronic supplementary information (ESI) available: Zero-point and entropic corrections to the free energy of the gas phase and the adsorbed species along the most favourable reaction pathways, diffusion energy barrier plot of Ta atom from the cavity of g-C₂N to the hexagonal ring, IPDOS of Ta d-states and N₂ p-states near the Fermi level, detailed free energy diagrams for the NRR pathways on the studied catalysts, solvation effect corrected most favourable free energy pathways, activation barriers for side-on to end-on transition for N₂ adsorption on Ta₂ and Ta₃ catalysts, and coordinates of various adsorbed species along the most favourable pathways of NRR on Ta_n@C₂N catalysts. See DOI: 10.1039/d1cy01292d

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