A first-principles study of 2D Ni–Fe double metal cyanides for CO electroreduction

Abstract

The development of highly efficient catalysts for CO electrocatalytic reduction (COER), a pivotal process in achieving carbon neutrality, remains a formidable challenge. In this study, first-principles density functional theory (DFT) calculations are employed to investigate the catalytic potential of FeNi(CN)₄, a two-dimensional double metal cyanide (2D DMC) featuring Fe–C≡N–Ni and Fe–N≡C–Ni isostructures. The electronic and magnetic properties of these isostructures were analyzed using the DFT+U approach, with U parameters determined via the linear response method. A comprehensive exploration of the COER mechanism identified a consistent optimal reaction pathway and rate-determining step across different active sites within the isostructures. Notably, the Fe–N≡C–Ni (Fe) site demonstrated superior selectivity, favoring CH₃OH production over CH₄ while effectively suppressing the competing hydrogen evolution reaction (HER). This enhanced selectivity is attributed to site-specific electronic properties that govern intermediate adsorption and reaction energetics. Furthermore, the adsorption energy difference between *CO and *CHO species emerged as a reliable activity descriptor, providing a predictive metric for evaluating COER performance on FeNi(CN)₄ monolayers. By establishing a thermodynamic framework for identifying optimal reaction pathways, this study not only advances the understanding of COER mechanisms but also positions two-dimensional Prussian blue analogues, exemplified by FeNi(CN)₄, as promising platforms for the rational design of highly efficient COER electrocatalysts.

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1. Introduction

The excessive consumption of fossil fuels has resulted in significant carbon dioxide (CO₂) emissions, exacerbating environmental issues such as rising sea levels, extreme weather, and ocean acidification.^1–5 Addressing these issues requires innovative carbon management strategies, among which carbon capture, utilization, and storage (CCUS) has emerged as a promising approach. By capturing CO₂ from industrial emissions and converting it into valuable chemicals and fuels, CCUS not only mitigates carbon emissions but also enhances economic sustainability by transforming waste CO₂ into useful products.^6–10 A key aspect of CCUS involves the electrochemical reduction of carbon monoxide (COER),¹¹ a crucial step in carbon utilization that facilitates the conversion of CO (produced from CO₂ reduction) into energy-rich hydrocarbons and oxygenates, such as methane (CH₄) and methanol (CH₃OH). Despite its importance for the efficient valorization of captured CO₂, COER still faces significant challenges related to catalytic efficiency.^12–15

Among the various electrocatalysts explored for COER, copper-based electrocatalysts have attracted substantial research attention owing to their unique ability to catalyze the conversion of CO into a wide spectrum of hydrocarbons and oxygenated compounds.^13,16–19 The ability of Cu to catalyze the selective reduction of CO into multi-carbon products makes it highly attractive for COER applications.^20,21 However, despite these advantages, Cu-based catalysts suffer from critical limitations, including high overpotentials, low energy efficiency, and poor product selectivity.^22,23 These challenges largely arise from the complex interplay between surface structure, reaction intermediates, and competing pathways, making it difficult to precisely control product distribution. Furthermore, the long-term stability of Cu-based catalysts remains a major concern, as surface restructuring and deactivation frequently occur under electrochemical conditions, leading to performance degradation over time.^24,25

To overcome these limitations, Prussian blue analogues (PBAs) have emerged as promising candidates for COER, owing to their unique structural characteristics and exceptional catalytic potential. PBAs consist of transition metal centers coordinated with cyano (–N≡C–) ligands, forming porous, periodic networks that offer a large surface area, structural tunability, and cost-effective synthesis.²⁶ Their adjustable metal active sites and uniform catalytic centers make them highly suitable for electrocatalysis, providing enhanced activity and stability.^27–30 Recent advances in materials synthesis, such as the exfoliation of layered structures, have further expanded the catalytic potential of PBAs. Two-dimensional (2D) materials exhibit superior properties compared to their bulk counterparts, including a higher surface-to-volume ratio and an increased density of exposed active sites, both of which enhance catalytic efficiency.³¹ Several studies have already demonstrated the potential of 2D DMCs in catalytic applications. For instance, Ahmad et al. employed 2D layered cobalt tetracyanonickelate ([Co–Ni] PBA) for photocatalytic water splitting to generate hydrogen (H₂),³² while Penche et al. synthesised M′[Ni(CN)₄] (M′ = Ni²⁺, Co²⁺, Fe²⁺, and Mn²⁺) as catalysts for the copolymerization of CO₂ and epoxides.³³ Furthermore, Jinlei Wang et al. developed a highly efficient and stable oxygen evolution reaction (OER) catalyst by utilizing a sulfur-treated two-dimensional CoFe-PBA/CFP material combined with structural optimization and surface chemical modifications.³⁴ These findings highlight the versatility and effectiveness of 2D DMCs in catalysis, demonstrating their capability to facilitate key transformations in sustainable energy applications. Given their structural advantages, 2D DMCs are strong candidates for next-generation COER electrocatalysts. Their porous frameworks facilitate mass transfer, while the well-defined metal centers enable precise control over intermediate formation and reaction pathways. These characteristics not only overcome the limitations of traditional copper-based catalysts but also open new opportunities for optimizing COER efficiency and selectivity. Therefore, exploring 2D DMCs as COER electrocatalysts presents a promising avenue for advancing carbon-neutral energy technologies.

To explore the feasibility of 2D DMCs as COER electrocatalysts, this study focuses on FeNi(CN)₄, an experimentally available 2D DMC featuring Fe–C≡N–Ni and Fe–N≡C–Ni isostructures. The linear response approach was employed to determine the U parameter, and DFT+U calculations were conducted to characterize the magnetic ground states and electronic structures of both isomers. Following electronic structure characterization, CO adsorption and activation at Fe and Ni sites on both isostructures were systematically examined through projected density of states (PDOS), charge density difference, and Bader charge analyses. A comparative thermodynamic analysis was then performed to evaluate potential CO reduction pathways to CH₄ and CH₃OH at the dual metal sites of both structures, considering various reaction mechanisms. The electronic origin of catalytic activity was further analyzed via crystal orbital Hamiltonian population (COHP) analysis. To evaluate selectivity, the influence of the competing hydrogen evolution reaction (HER) was rigorously assessed. Comparisons with previously reported experimental data validated the suitability of FeNi(CN)₄ as a COER electrocatalyst, reinforcing the potential of 2D DMCs in electrocatalytic CO reduction. This work provides critical insights into the electronic and catalytic behavior of 2D DMCs, particularly regarding selectivity, and lays the groundwork for the rational design of next-generation COER electrocatalysts.

2. Computational details

All spin-polarized calculations were performed using Vienna Ab Initio Simulation Package (VASP),³⁵ employing the projector-augmented wave (PAW)^36,37 potential. The exchange–correlation energy was treated using the Perdew–Burke–Ernzerhof (PBE) functional³⁸ within the framework of generalized gradient approximation (GGA).³⁹ To account for dispersion interactions, Grimme's DFT-D3 empirical correction method was applied.⁴⁰ A plane-wave basis set with a kinetic energy cutoff of 500 eV was used. Geometry optimization was considered converged when the total energy change was below 10⁻⁵ eV and the residual atomic forces were less than 0.01 eV Å⁻¹. Hubbard-U corrections (DFT+U) were applied consistently throughout all calculations. The U parameters were determined within VASP using the linear response approach,⁴¹ yielding values of 3 eV for Fe and 4 eV for Ni. A vacuum of 20 Å was introduced along the z-direction to eliminate artificial interactions between periodic images. For structural optimization, a Monkhorst–Pack k-point grid of 3 × 3 × 1 was employed and refined to 6 × 6 × 1 for electronic structure calculations.

The Gibbs free energy change (ΔG) for each elementary step of the COER process was evaluated using the computational hydrogen electrode (CHE) model proposed by Nørskov et al.⁴² According to this model, the free energy change for each step is calculated as:

where ΔE, ΔE_ZPE, and ΔS represent the DFT calculated reaction energy, zero-point vibrational energy, and entropy change associated with each elementary step, respectively. T is the temperature, set at 298.15 K, while C_P represents the heat capacity at constant pressure. The term eU accounts for the applied potential, and ΔG_pH represents the free energy correction due to pH variations, which is calculated as:where k_B is the Boltzmann constant. Assuming a constant pH throughout each elementary step, ΔG_pH was set to zero. The correction for zero-point energy (ΔE_ZPE) and the entropy term (−TΔS) were determined based on the vibrational frequencies of the adsorbed intermediates. These frequency calculations were performed with adsorbate relaxation while keeping the FeNi(CN)₄ monolayer and metal atoms fixed.

To compare the catalytic activity along different COER pathways, the potential-determining step (PDS) was identified as the elementary step with the largest thermodynamic barrier. The limiting potential (U_L), representing the minimum negative potential required to drive the reaction exothermically, was calculated using the following equation:

where ΔG_max is the highest Gibbs free energy change along the optimal reaction pathway at zero potential and e is the elementary charge. A less negative U_L value indicates higher catalytic activity.

3. Results and discussion

3.1. Structure and electronic properties

Upon exfoliation from its hydrated structure, the FeNi(CN)₄ nanosheet adopts a planar configuration characterized by a cyanide-bridged molecular square. The optimized structure of FeNi(CN)₄ is illustrated in Fig. 1a, where the Fe and Ni atoms are coordinated to cyanide ligands in two distinct configurations, forming the Fe–C≡N–Ni and Fe–N≡C–Ni isostructures. The optimized lattice parameters are a = b = 10.13 Å, with bond lengths of d_Fe–C = 1.92 Å, d_N–C = 1.17 Å, d_N–Ni = 1.98 Å, d_Fe–N = 2.06 Å, and d_C–Ni = 1.83 Å. The magnetic and electronic properties of the isostructures were further explored using DFT+U calculations, with U values derived from the linear response method, yielding U_eff (Fe) = 3 eV and U_eff (Ni) = 4 eV, as detailed in Fig. S1 (ESI†). The magnetic ground state was determined by comparing the total energies of a ferromagnetic (FM) configuration and five representative antiferromagnetic (AFM) configurations. These magnetic structures are illustrated in Fig. S2 and S3 (ESI†), with the corresponding total energies summarized in Tables S1 and S2 (ESI†). The results indicate that the AFM configuration is more stable than the FM one for both Fe–C≡N–Ni and Fe–N≡C–Ni isostructures, confirming an antiferromagnetic ground state. The electron localization function (ELF), shown in Fig. 1b, confirms the presence of strong interatomic bonding, indicating robust structural stability. The band structures and DOSs presented in Fig. 1c reveal band gaps of 0.95 eV for Fe–C≡N–Ni and 2.62 eV for Fe–N≡C–Ni, revealing the semiconducting behavior of both isostructures.

Fig. 1 (a) Top and side views of the optimized structures of FeNi(CN)₄, where blue and red spheres represent the C and N atoms, while the yellow and green spheres represent Fe and Ni metal atoms, respectively. These metal atoms are bonded to –C≡N– in two distinct configurations: Fe–N≡C–Ni and Fe–C≡N–Ni, resulting in two isostructures. (b) Sliced electron localization function (ELF) map of FeNi(CN)₄ isostructures. (c) Band structures and density of states (DOSs) of FeNi(CN)₄ isostructures, with the left panel corresponding to the Fe–N≡C–Ni isostructure and the right panel representing the Fe–C≡N–Ni isostructure.

3.2. Adsorption of CO on FeNi(CN)₄

CO adsorption and activation are critical steps in COER, as they often dictate the subsequent catalytic reduction pathway. Variations in adsorption configurations can lead to distinct reaction mechanisms. At the Fe site of the Fe–C≡N–Ni isostructure, three possible CO adsorption configurations were examined: C-end, O-end, and side-on (CO-side). However, the side-on configuration spontaneously transformed into the O-end mode during structural optimization, indicating its instability. As a result, only the C-end and O-end configurations are depicted in Fig. 2a. Among them, the C-end mode exhibited a stronger interaction with the Fe site, characterized by a shorter Fe–C bond distance of 2.03 Å and a favorable adsorption energy of −2.15 eV. In contrast, the O-end mode showed weaker binding, with a longer Fe–C bond distance of 2.70 Å and a less favorable adsorption energy of −1.57 eV. These results suggest that the C-end configuration offers the most stable and chemically interactive adsorption mode, and was selected as the initial state for subsequent COER pathway investigation. Similar trends were observed at other active sites within both isostructures, as summarized in Fig. S4–S7 (ESI†).

Fig. 2 (a) CO adsorption on Fe–C≡N–Ni (Fe): optimized structures of C-end and O-end adsorption configurations. (b) Charge density difference of Fe–N≡C–Ni (Fe) with adsorbed CO. (c) Projected density of states (PDOS) for *CO adsorption on FeNi(CN)₄, showing Fe-3d, Ni-3d, and CO-2p interactions.

Fig. S8 (ESI†) presents the calculated adsorption energies (E_ads) of CO molecules on four active sites: Fe–N≡C–Ni (Fe), Fe–N≡C–Ni (Ni), Fe–C≡N–Ni (Fe), and Fe–C≡N–Ni (Ni), with E_ads values of −1.68, −1.67, −2.15, and −2.17 eV, respectively. These results indicate strong CO binding across all configurations. Correspondingly, the C–O bond length elongates from 1.13 Å in the gas phase to 1.14–1.15 Å upon adsorption, reflecting its activation. The charge density difference plots shown in Fig. 2b (other configurations in Fig. S9, ESI†) further elucidate the nature of CO adsorption. More interfacial charge accumulation is observed at the Fe–N=C–Ni (Fe) (0.05 e⁻) and Fe–C≡N–Ni (Ni) (0.09 e⁻) sites. In contrast, less charge redistribution occurs at the Fe–N=C–Ni (Ni) (0.03 e⁻) and Fe–C≡N–Ni (Fe) (0.02 e⁻) sites.

To further elucidate the adsorption behavior of CO molecules, the projected density of states (PDOS) was calculated for the most stable CO adsorption configurations at each active site, as shown in Fig. 2c. The results reveal that clear orbital hybridization emerges between the p-orbitals of adsorbed CO molecules and the d-orbitals of the metal atoms, indicating significant electronic interactions. Significant orbital overlap near the Fermi level suggests enhanced electron transfer between the adsorbate and the catalyst surface, thereby facilitating activation and promoting the progression of COER.

3.3. Reaction mechanism and thermodynamics of COER on FeNi(CN)₄ isostructures

Based on the C-end adsorption configuration of CO molecules, several potential reaction pathways were considered for subsequent investigation, as illustrated in Fig. 3a. Hydrogenation of the adsorbed CO molecule can occur at either the carbon or oxygen atoms, yielding *CHO and *COH intermediates, respectively. The *CHO pathway can proceed through successive steps to generate *CH₂O and *OCH₃, ultimately resulting in the formation of methanol (CH₃OH). In contrast, the *COH pathway can follow a hydrogenation–dehydration route to yield *C, which is further hydrogenated to *CH, *CH₂, *CH₃, and finally methane (CH₄). Alternatively, both *CHO and *COH intermediates may undergo further hydrogenation through *CHOH and *CH₂OH, eventually producing *CH₃OH.

Fig. 3 (a) Proposed reaction pathways for COER. (b) The free energy diagrams of the optimal reaction pathways of COER by FeNi(CN)₄.

To unravel the detailed reaction mechanism of FeNi(CN)₄-catalyzed COER, all reaction intermediates shown in Fig. 3a were fully optimized, and the corresponding Gibbs free energy changes (ΔG) for each elementary step were calculated. The resulting free energy diagrams, shown in Fig. 3b, reveal notable differences in reaction energetics between the two isostructures, Fe–N≡C–Ni and Fe–C≡N–Ni, highlighting the influence of active site identity and structural configuration on catalytic behavior.

Three methanol-producing pathways with low limiting potential were identified:

*CO → *CHO → *CHOH → *CH₂OH → *CH₃OH (1)

*CO → *CHO → *CH₂O → *CH₂OH → *CH₃OH (2)

*CO → *CHO → *CH₂O → *OCH₃ → *CH₃OH (3)

Additionally, two methane-producing pathways were identified:

*CO → *CHO → *CHOH → *CH₂OH → *CH₂ → *CH₃ → CH₄ (4)

*CO → *CHO → *CH₂O → *CH₂OH → *CH₂ → *CH₃ → CH₄ (5)

For the Fe–N≡C–Ni structure, methanol-producing pathways were more favorable than methane routes, with pathway (3) being thermodynamically preferred as its final three steps proceed exothermically (Fig. S10 and S11, ESI†). In all cases, the initial *CO → *CHO hydrogenation emerged as the potential-determining step (PDS). At the Fe–N≡C–Ni (Fe) site, this step exhibited the lowest ΔG_max of 0.45 eV, yielding a limiting potential U_L of −0.45 V. In contrast, a U_L value of −0.89 V was determined for the Fe–N≡C–Ni (Ni) site.

In the Fe–C≡N–Ni structure, a similar trend was observed, where methanol-producing pathways were consistently more favorable than those leading to methane formation (Fig. S12 and S13, ESI†). Among the evaluated routes, pathway (2) was identified as the most favorable for the Fe–C≡N–Ni structure, exhibiting an optimal ΔG_max of 0.48 eV and a corresponding U_L of −0.48 V at the Ni site. This performance closely matches that of the Fe–N≡C–Ni (Fe) site (ΔG_max = 0.45 eV, U_L = −0.45 V). These two active sites therefore represent the most kinetically and thermodynamically accessible configurations for selective CH₃OH production.

As summarized in Table 1, both kinetic and thermodynamic analyses indicate a clear preference for methanol production over methane, especially at the two optimal active sites. Although CH₄ pathways are thermodynamically accessible, they require substantially higher overpotentials and are thus less favorable under standard conditions.

Table 1 Comparison of theoretically predicted COER activity and selectivity across previously reported catalysts

System	Product	U L (V)	Ref.
Nb2P	CH4	−0.51	43
3Mn-C2N	CH4	−0.44	44
Cu2B2	CH4	−0.59	45
Cu(100)	CH4	−0.73	46
Fe–N≡C–Ni (Fe)	CH4	−1.03	Present work
Fe–N≡C–Ni (Ni)	CH4	−1.00	Present work
Fe–C≡N–Ni (Fe)	CH4	−0.81	Present work
Fe–C≡N–Ni (Ni)	CH4	−1.78	Present work
HS B-CoPc	CH3OH	−0.43	47
Cu(110)	CH3OH	−0.72	48
Ni55NP	CH3OH	−0.56	49
Fe–N≡C–Ni (Fe)	CH3OH	−0.45	Present work
Fe–N≡C–Ni (Ni)	CH3OH	−0.89	Present work
Fe–C≡N–Ni (Fe)	CH3OH	−0.81	Present work
Fe–C≡N–Ni (Ni)	CH3OH	−0.48	Present work

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Finally, benchmarking against literature-reported COER catalysts (Table 1) reveals that the U_L values for CH₃OH generation over Fe–N≡C–Ni (Fe) and Fe–C≡N–Ni (Ni) (−0.45 V and −0.48 V, respectively) are comparable to or better than those of state-of-the-art systems (−0.43 to −0.72 V) from theoretical aspects, further affirming the high catalytic potential of these configurations for efficient and selective CO-to-CH₃OH conversion.

3.4. Suppression of the hydrogen evolution reaction (HER)

Hydrogen evolution reaction (HER) is a well-known competing process during CO electroreduction (COER), often affecting product selectivity. According to the Brønsted–Evans–Polanyi (BEP) relationship, reactions with lower ΔG are kinetically favored. Therefore, evaluating the thermodynamics of the HER is essential for understanding the selectivity of FeNi(CN)₄ catalysts toward COER.

As shown in Fig. 4a, the HER free energy diagrams indicate that Fe–N≡C–Ni (Fe, Ni) and Fe–C≡N–Ni (Fe) exhibit larger absolute ΔG values for the HER, suggesting weaker HER activity. To further illustrate COER selectivity, the free energy of the COER potential-determining step (*CO → *CHO) is plotted against the HER free energy in Fig. 4b. Points located below the diagonal line represent systems favoring COER, while those above the line indicate HER dominance. Only Fe–N≡C–Ni (Fe) falls well below the diagonal line, confirming its strong preference for COER and effective suppression of the HER. These results highlight the favorable selectivity of FeNi(CN)₄ catalysts at the Fe–N≡C–Ni (Fe) site for methanol production over hydrogen evolution.

Fig. 4 (a) Free energy diagram of the HER and (b) reaction free energy of the PDS (*CO → *CHO) of COER against that of the HER for FeNi(CN)₄. The region below the parity line indicates COER selectivity, while the region above indicates HER selectivity.

3.5. Origin of COER activity

The catalytic performance of a COER catalyst is closely related to the adsorption energy of key reaction intermediates. To investigate the origin of FeNi(CN)₄ monolayer activity, we analyzed the interaction between the catalyst and *CO species, as the *CO → *CHO step was previously identified as the potential-determining step (PDS) for these systems.

The crystal orbital Hamilton population (COHP) analysis was performed to evaluate the bonding characteristics between *CO and the catalyst. As shown in Fig. 5a, the bonding states of *CO lie below the Fermi level, while antibonding states reside above it. If antibonding states are partially filled below the Fermi level, the *CO adsorption weakens. To quantify the interaction strength, we integrated the –COHP up to the Fermi level to obtain the *ICOHP values (Fig. 5b), where more negative values indicate stronger *CO binding. Among all systems, Fe–C≡N–Ni (Ni) exhibits the most negative *ICOHP, implying the strongest *CO adsorption. However, despite this strong interaction, its catalytic activity is lower than that of Fe–N≡C–Ni (Fe). This discrepancy suggests that the balance between *CO and *CHO adsorption plays a critical role in governing COER activity. Therefore, we calculated the energy difference between CO and CHO (corresponding to the rate-determining step) and observed a clear linear correlation with the limiting potential (Fig. 5c), demonstrating that this thermodynamic parameter serves as an effective descriptor for catalytic performance. This suggests that the energy difference between CO and CHO adsorption is a more reliable indicator of catalytic performance than the absolute binding strength of either intermediate.

Fig. 5 (a) Crystal orbital Hamilton population (COHP) bonding analysis of *CO adsorbed on FeNi(CN)₄, (b) calculated –ICOHP versus ΔE*CO for *CO adsorbed on FeNi(CN)₄ and (c) the computed COER limiting potential as a function of the difference between the adsorption energies of *CHO and *CO species.

4. Conclusions

In conclusion, we have systematically investigated the activity and selectivity of electrocatalytic COER on FeNi(CN)₄ monolayers using DFT calculations. The exposed Fe and Ni sites serve as active centers via a donation/back-donation mechanism, effectively trapping and activating CO molecules through a favorable C-end adsorption configuration. Free energy analyses revealed the optimal reaction pathways across different configurations, with *CO → *CHO consistently identified as the potential-determining step. Among all systems, Fe–N≡C–Ni (Fe) exhibited the highest catalytic performance for CH₃OH production, featuring the lowest limiting potential (–0.45 V) and effective suppression of the HER. Furthermore, the difference in adsorption strengths between *CO and *CHO intermediates was found to correlate linearly with the limiting potential, offering a reliable descriptor for COER activity. These insights not only deepen our understanding of COER mechanisms on FeNi(CN)₄ monolayers but also highlight the importance of site-dependent optimization. Future work may focus on engineering the coordination environment and electronic structure around such active sites to further enhance the activity, selectivity, and stability of COER catalysts.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

All data supporting the findings of this study are available within the article and its ESI.† Additional computational details or raw data files are available from the corresponding authors upon reasonable request.

Acknowledgements

This work was financially supported by the Hunan Provincial Natural Science Foundation of China (2021JJ30686 and 2023JJ40621).

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Footnote

† Electronic supplementary information (ESI) available: The computational details and results, including Hubbard's U parameters, considered magnetic configurations, adsorption geometries, charge density difference analyses, and free energy profiles, are provided. See DOI: https://doi.org/10.1039/d5nj01664a

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