Cu cluster-anchored bismuthene promoting electrocatalytic reduction of CO₂ into C₂ products: a theoretical study

Abstract

The electrocatalytic CO₂ reduction reaction (eCO₂RR) to value-added multicarbon (C₂) represents a promising carbon-neutral pathway, yet designing efficient catalysts remains challenging. Although Cu-based materials are prominent for C₂, their performance requires further optimization. Here, we employ density functional theory (DFT) to investigate atomically precise Cu_n clusters (n = 1–4) doped on bismuthene (monolayer Bi(001)) as tunable catalysts. Our computations reveal that Cu cluster doped Bi(001) significantly enhances the adsorption capability for key intermediates (COOH* and CO*) and significantly reduces the potential-limiting step (PLS) free energy for CHOCO* formation. However, for Cu₁@Bi(001), the local coordination environment resembles that of pristine Bi(001), leading to a similar reaction mechanism . As the size of Cu clusters increases (Cu₂–Cu₄), the active sites from Bi–Cu shift to Cu–Cu pairs, inducing a mechanistic shift to Cu(111)-like behavior (PLS: CO* → CHO*). Comparative PLS analysis reveals that Cu cluster doped systems outperform pristine Bi(001), and only controlled Cu_n clusters (n = 1–3) can effectively enhance the C₂ selectivity of bismuthene, whereas excessive Cu_n cluster incorporation (n = 4) leads to suboptimal performance. Significantly, through energy and electronic structure analyses, we reveal that the adsorption energy differences of key intermediates, their electron transfer ratios and the “Cu–CHO*” bond strength serve as effective descriptors for PLS free energy, providing an indirect measure of catalytic performance. These findings establish bismuthene as a programmable platform for C₂ synthesis, demonstrating how atomic-scale synergy between Cu clusters and 2D bismuthene substrates can overcome traditional scaling relations in eCO₂RR catalysis.

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1. Introduction

The electrocatalytic CO₂ reduction reaction (eCO₂RR) has emerged as a pivotal strategy for achieving carbon neutrality by converting CO₂ into value-added chemicals.¹ Among various catalysts, bismuth (Bi)-based materials have attracted considerable attention due to their low toxicity, cost-effectiveness, and exceptional selectivity toward formate (HCOOH) production.^2–9 Our prior theoretical studies systematically demonstrated that Bi catalysts with different oxidation states and crystal facets exhibit superior HCOOH selectivity,¹⁰ which aligns with experimental observations of high Faradaic efficiencies (FE > 90%) and current densities (up to −1000 mA cm⁻²).^11–13 Notably, two-dimensional (2D) bismuthene has recently gained prominence owing to its tunable bandgap, high conductivity, and environmental stability,^14–16 enabling breakthroughs in the eCO₂RR. Pioneering studies by Yang et al.¹⁷ and Zhang et al.¹⁸ have established freestanding bismuthene as an outstanding catalyst for HCOOH generation, achieving industrial-grade current densities (>500 mA cm⁻²) with unprecedented long-term stability (>500 h). Additional studies have also highlighted bismuthene's high specific surface area and remarkable electrochemical activity, making it an efficient electrocatalyst for the eCO₂RR.^19–21 Despite these advances, the catalytic potential of bismuthene for producing higher-value C₂ products remains underexplored.

While copper stands as the only known metal capable of catalyzing C–C coupling, existing Cu–bismuthene hybrids still predominantly yield HCOOH rather than C₂ species.^22,23 A notable development came from Song et al., who synthesized a Cu–Bi catalyst that significantly lowers the free energy barrier for CO* formation.²⁴ Furthermore, Rong et al. revealed that, compared to single-atom Cu catalysts, Cu clusters possess higher regional atomic density, enabling stronger binding of multiple CO* species and thereby reducing the energy barrier for C–C coupling, which facilitates the generation of multi-carbon products.²⁵ Therefore, we identify that the key challenge lies in stabilizing the key CO* intermediate—the essential precursor for C₂ formation.²⁶ To address this problem, we propose an “electronic modulation via Cu clusters + 2D bismuthene surface engineering” strategy, wherein atomic-level control of Cu_n cluster size (n = 1–4) on bismuthene enables precise tuning of both CO* stabilization and C–C coupling kinetics.

Through systematic density functional theory (DFT) calculations, we elucidate the critical role of Cu cluster doped Bi(001) in enhancing the eCO₂RR performance. Our findings reveal that (i) Cu cluster doped Bi(001) significantly enhances the adsorption capability for COOH* and CO* intermediates. (ii) The introduction of Cu clusters significantly reduces the PLS free energy for CHO* formation. For the single Cu doped Cu₁@Bi(001), the local coordination environment resembles that of pristine Bi(001), leading to a similar reaction mechanism . In contrast, larger Cu clusters (Cu₂–Cu₄) shift the active sites from Bi–Cu to Cu–Cu pairs, inducing a mechanistic shift to Cu(111)-like behavior (PLS: CO* → CHO*). (iii) Comparative PLS analysis reveals that Cu cluster doped systems outperform pristine Bi(001), and only smaller clusters (n ≤ 3, 0.87–0.89 eV) approach ideal Cu(111) performance. The inferior performance of Cu₄ clusters stems from charge transfer imbalance caused by excessive doping. (iv). Energy and electronic structure analyses reveal that the adsorption energy differences of key intermediates and their electron transfer ratios serve as effective descriptors for PLS free energy, providing an indirect measure of catalytic capability. These findings establish bismuthene as a programmable platform for C₂ synthesis, demonstrating how atomic-scale synergy between Cu clusters and 2D bismuthene substrates can overcome traditional scaling relations in eCO₂RR catalysis.

2. Computational details

2.1 DFT parameters

All DFT calculations were performed using the Vienna Ab initio Simulation Package (VASP 6.4.2)^27,28 with a plane-wave cutoff energy of 450 eV. The Perdew–Burke–Ernzerhof (PBE)²⁹ generalized gradient approximation was employed for exchange–correlation interactions, supplemented by Grimme's DFT-D3 dispersion correction to account for van der Waals forces.³⁰ Initial atomic coordinates for the Bi primitive cell (space group: R3̄m) were obtained from the materials project.³¹ The k-space samplings are set at 9 × 9 × 2 for the primitive cell of Bi and 3 × 3 × 1 for free energy calculations of bismuthene with a (4 × 4 × 1) supercell. Structural relaxations converged when energy changes fell below 10⁻⁶ eV and residual forces dropped below 0.02 eV Å⁻¹ using the conjugate gradient (CG) algorithm.³²

To determine the Gibbs free energy (G) of each species involved in the eCO₂RR, we employed the formula G = E_elec + E_ZPE − TS. Here, E_elec represents the electronic energy obtained from DFT calculations, T is the system temperature, and E_ZPE and S denote the zero-point energy and entropy, respectively. The E_ZPE was calculated using VASPKIT³³ based on the vibration frequency analysis of the optimized ground state structure at 298.15 K and 1.0325 bar. For the S, since DFT calculations assume an ideal gas state, which is not the case for our catalytic system that operates under specific temperature and pressure conditions, we referred to the NIST³⁴ thermodynamics database to obtain the entropy values for small molecules such as H₂(g), CO₂(g) and H₂O(l) at 298.15 K for free energy correction. For adsorbed molecules like COOH*, although adsorption restricts the molecule's motion perpendicular to the surface, leading to a loss of some translational and rotational degrees of freedom, the adsorbed molecule still retains most of its gas-phase entropy. Thus, at a limited temperature, the adsorbed molecule can maintain its thermodynamic activity to a certain extent.³⁵ In our calculations, we fixed the bismuthene slab and only relaxed the adsorbed molecule for frequency analysis to obtain the vibrational frequencies (v_i), which were then post-processed using VASPKIT to derive E_ZPE and TS. The calculated hydrogen electrode (CHE) model was utilized to compute the Gibbs free energy, treating the elementary reaction steps of the eCO₂RR as proton-coupled electron transfer (PCET) processes.³⁶

2.2 Computational models

Bismuthene is inexpensive and non-toxic,⁵ and the Bi(001) facet exhibits high selectivity and Faradaic efficiency in the eCO₂RR,¹⁹ with superior stability compared to other 2D materials like silicene, germanene, and phosphorene.^37,38 To establish a reliable computational model for the electroreduction of CO₂ to C₂ products, we constructed an atomically precise bismuthene structure based on the Bi(001) surface (Fig. S1a and b). The optimized unit cell (space group: R3̄m) exhibits hexagonal symmetry with lattice parameters a = b = 4.56 Å and c = 11.88 Å, which are in excellent agreement with experimental values (a = b = 4.55 Å and c = 11.86 Å).³⁹ For catalytic simulations, a (4 × 4 × 1) supercell containing 32 Bi atoms (lateral dimensions: 18.25 Å × 18.25 Å) was employed. To eliminate spurious periodic interactions, a 15 Å vacuum layer was applied along the c-axis of the bismuthene slab model while maintaining periodicity in the a and b directions. This model, maintaining computational feasibility, provides an ideal platform for subsequent doping studies and reaction mechanism analysis. To precisely modulate the electronic structure of bismuthene for efficient eCO₂RR toward C₂ products, we systematically engineered Cu cluster doped bismuthene configurations with atomic-level precision by incorporating size-controlled Cu clusters (Cu₁–Cu₄) as shown in Fig. S1c. The atomic-scale doping geometries were rigorously optimized through DFT calculations: (i) for Cu₁ doping, a single Cu atom substituting the up-site Bi atom exhibits lower energy and higher stability than the down-site Bi atom (ΔE = −0.001 eV, Fig. S2); (ii) for Cu₂ configurations, the adjacent doping mode exhibits the highest stability with lower energy than isolated doping (ΔE = −0.41 eV, Fig. S3); (iii) for Cu₃ clusters, the up-site-doped triangular configuration demonstrates superior stability with lower energy than down-site-doped configuration (ΔE = −1.64 eV, Fig. S4); (iv) to ensure complete Cu incorporation within the bismuthene, the Cu₄ cluster adopts a planar quadrilateral geometry rather than tetrahedral stacking (ΔE = −1.45 eV, Fig. S5). This controlled doping strategy enables systematic investigation of cluster-size-dependent electronic modulation; meanwhile, all atoms remain in fully relaxed states during the structural optimization process to maintain structural integrity. To assess the stability of the copper cluster-doped materials, we performed ab initio molecular dynamics (AIMD) simulations at 300 K for 10 ps.^40–43 The results confirm that the Cu_n@Bi(001) structures maintain their structural integrity under the simulated electrocatalytic conditions (Fig. S6 and S7).

2.3 Reaction mechanism

The electrocatalytic CO₂ to C₂ pathway necessarily proceeds via C₁ intermediates followed by C–C coupling, as established in seminal studies.⁴⁴ Among the two PCET derived C₁ intermediates (CO* and HCOOH*), only CO* serves as the pivotal precursor for C–C coupling, while HCOOH* predominantly desorbs as a byproduct. Subsequent PCET steps convert CO* → CHO*, enabling the key CHO*–CO* coupling to form CHOCO*—the foundational intermediate for C₂ production. This study systematically investigates six distinct catalytic configurations: pristine Bi(001), Cu₁@Bi(001), Cu₂@Bi(001), Cu₃@Bi(001), Cu₄@Bi(001), and reference Cu(111). The optimized geometries of key intermediates governing the eCO₂RR to C₂ pathway are presented in Fig. S8–S13, providing atomic-level insights into the structure–activity relationships. Building upon this mechanistic framework, we systematically investigate how Cu cluster size doped bismuthene catalysts modulate the C₂ selectivity. Our computational pathway analysis (Fig. 1) systematically addresses three critical aspects: (i) the comparative evaluation of CO* adsorption free energies across distinct catalytic interfaces, (ii) the thermodynamic free energy determination for CHOCO* formation via PLS analysis, and (iii) the size-dependent electronic modulation of Cu clusters in governing interfacial charge transfer during CHOCO* generation.

Fig. 1 Reaction pathways schematic diagram of the eCO₂RR to produce CHOCO* (“*” stands for bismuthene).

3. Results and discussion

3.1 Predicting surface properties of Cu cluster doped bismuthene

The activity, selectivity, and stability of electrocatalytic reactions are fundamentally governed by electrochemical interfacial kinetics.^45,46 In particular, the eCO₂RR involves catalytic transformations where both electrons and protons accumulate at the material interface.⁴⁷ To predict the influence of Cu cluster doping on the eCO₂RR performance of bismuthene materials, we first investigated the effects of Cu incorporation on the interfacial electronic structure. Charge density analysis (Fig. 2a–f) reveals that Cu cluster doped Bi(001) alters surface electronic distribution compared to pristine Bi(001) and Cu(111) surfaces. Quantitatively, the Cu₁ to Cu₄ clusters gain 0.08, 0.17, 0.04, and 0.14 electrons respectively, demonstrating pronounced charge redistribution between the Cu clusters and Bi atoms. Interestingly, the enhanced charge density around Cu sites may provide additional electrons for adsorption and stronger orbital interactions between Cu and small molecules.

Fig. 2 Electronic structure analysis of Cu cluster doped Bi(001) surfaces. (a–f) Charge density plots for (a) pristine Bi(001), (b) Cu₁@Bi(001), (c) Cu₂@Bi(001), (d) Cu₃@Bi(001), (e) Cu₄@Bi(001), and (f) Cu(111) surfaces. (g) The total density of states (TDOS) and the positions of the d-band center (ε_d) were calculated for the corresponding surfaces.

In addition, the total density of states (TDOS) of the Cu cluster-doped Bi(001) system was analyzed (Fig. 2g). Quantitative analysis shows that the d-band center (ε_d) of Cu(111) is located at −2.24 eV. In comparison, the ε_d values for Cu₁@Bi(001), Cu₂@Bi(001), Cu₃@Bi(001), and Cu₄@Bi(001) are −1.91 eV, −1.86 eV, −1.92 eV, and −2.18 eV, respectively. This systematic upward shift toward the Fermi level, relative to the Cu(111) surface, confirms that the Cu cluster-doped bismuthene can enhance the adsorption capacity for small molecules, even surpassing that of pure Cu.

3.2 Cu clusters lower COOH*/CO* adsorption free energy

Although the calculated surface electron density distribution and d-band center positions provide preliminary evidence for enhanced catalytic performance upon Cu cluster doping, deeper mechanistic understanding requires analysis of key intermediate adsorption energetics. We systematically evaluated the adsorption free energies of key intermediates (G^COOH*_ads and G^CO*_ads) on six catalytic surfaces: Bi(001), Cu₁@Bi(001), Cu₂@Bi(001), Cu₃@Bi(001), Cu₄@Bi(001), and Cu(111) (Fig. 3a). The G^COOH*_ads values were determined to be −0.73, −1.19, −1.52, −1.27, −1.05, and −1.64 eV, respectively, demonstrating that Cu-doped surfaces significantly enhanced the stabilization of COOH* compared to pristine Bi(001). More strikingly, the G^CO*_ads values (−0.08, −0.71, −1.15, −0.77, −0.91, and −1.20 eV) reveal that pristine Bi(001) exhibits weak CO* adsorption, explaining its poor C–C coupling activity. In contrast, Cu cluster doped Bi(001) shows substantially increased CO* adsorption strength, facilitating CO* stabilization on Cu sites for subsequent C–C coupling. This substantial variation in adsorption strength would consequently modulate the reaction free energy barriers, as schematically illustrated in Fig. 3b. The enhanced molecular adsorption capacity following Cu cluster doping correlates well with our earlier findings of d-band center upshifts toward the Fermi level, collectively explaining the observed adsorption enhancement.

Fig. 3 Mechanistic studies of intermediate adsorption and electronic structure modulation. (a) Calculated adsorption free energies for key reaction intermediates G^COOH*_ads and G^CO*_ads on six catalytic surfaces: pristine Bi(001), Cu_n cluster doped Bi(001) (n = 1–4), and Cu(111). (b) Schematic diagram of catalytic performance. Atomic-scale electronic structure characterization through electron localization function (ELF), charge density difference and Bader charge analyses for (c) Bi(001), (d) Cu₁@Bi(001), (e) Cu₂@Bi(001), (f) Cu₃@Bi(001), (g) Cu₄@Bi(001), and (h) Cu(111) surfaces. Yellow and cyan isosurfaces in charge density plots (isosurface level = 0.002 e Å⁻³) represent electron accumulation and depletion, respectively.

Furthermore, electron localization function (ELF) and charge density difference analyses provide atomic-scale insights: (i) the highly delocalized electrons between CO and Bi(001) (Fig. 3c) result in minimal charge transfer (0.05e), consistent with weak adsorption; (ii) Cu doping induces pronounced electron localization at Cu–CO interfaces (Fig. 3d–g), as evidenced by Bader charge analysis revealing progressive electron transfer of 0.17, 0.32, 0.36, and 0.49 e for Cu₁ to Cu₄ configurations, respectively, representing a 3.4–9.8 fold enhancement in charge donation capacity relative to the pristine Bi(001) surface; (iii) comparative ELF analysis reveals excessive electron delocalization on the Cu(111) surface (Fig. 3h), whereas the Cu cluster doped Bi(001) system achieves optimal electronic modulation through synergistic Cu–Bi interactions. Specifically, the Bi atoms serve as an electron donor that dynamically regulates the electronic states of Cu clusters, while the Cu sites provide localized adsorption centers with tailored d-band characteristics. This bifunctional cooperation creates an ideal electronic environment that simultaneously stabilizes CO intermediates and lowers the kinetic barrier for C–C coupling.

3.3 Calculation of the potential-limiting steps of the eCO₂RR to CHOCO*

The thermodynamic feasibility of the eCO₂RR to C₂ products is predominantly governed by the reaction steps following the formation of the key CO* intermediate, particularly the transformations of CO* → CHO* or the coupling between CO* and CHO* species. To precisely identify the PLS, we systematically calculated the free energy barriers for the complete eCO₂RR to C₂ pathway. As revealed in Fig. 4, the PLS for pristine Bi(001) corresponds to the conversion with a substantial free energy of 1.24 eV (Fig. 4a). Upon single Cu atom doped Bi(001) (Cu₁@Bi(001)), the PLS remains unchanged , while the free energy of the PLS is significantly reduced to 0.87 eV (Fig. 4b). Remarkably, further increasing the Cu cluster size (Cu₂–Cu₄ systems) not only shifts the PLS to the CO* → CHO* step but also lowers the free energy of the PLS to 0.89 eV, 0.87 eV, and 1.05 eV, respectively (Fig. 4c–e). This trend demonstrates that (i) Cu cluster doped Bi(001) consistently lowers the PLS free energy for CHOCO* generation during the eCO₂RR, improving reaction thermodynamics – a phenomenon directly linked to d-band center upshifting near the Fermi level that enhances catalytic performance. (ii) For the single Cu doped Cu₁@Bi(001), the local coordination environment resembles that of pristine Bi(001), leading to a similar reaction mechanism. In contrast, larger Cu clusters (Cu₂–Cu₄) shift the active sites from Bi–Cu to Cu–Cu pairs, inducing a mechanistic shift to Cu(111) (Fig. 4f). (iii) Comparative PLS analysis reveals that Cu cluster doped systems outperform pristine Bi(001); only smaller clusters (n ≤ 3, 0.87–0.89 eV) approach ideal Cu(111) (0.86 eV) performance. The inferior performance of Cu₄ clusters stems from charge transfer imbalance caused by excessive doping. Furthermore, we evaluated the competing hydrogen evolution reaction (HER) (Fig. S14 and S15). The HER barrier on pristine Bi(001) is 1.25 eV, comparable to its eCO₂RR PLS (1.24 eV). In contrast, the HER barriers on Cu_n@Bi(001) (n = 1–4) and Cu(111) are significantly higher—2.25 eV, 2.28 eV, 1.58 eV, 2.06 eV, and 2.40 eV, respectively—greatly exceeding their eCO₂RR PLS (1.05 eV). This demonstrates that copper cluster doping simultaneously enhances the eCO₂RR and suppresses the HER. These computational insights validate our “electronic modulation via Cu clusters + 2D bismuthene surface engineering” strategy for overcoming the inherent electronic limitations of bismuthene catalysts.

Fig. 4 Reaction free energy profiles for the electrochemical CO₂ reduction to CHOCO* on Cu clusters doped Bi(001) surfaces (Cu_n@Bi(001), n = 1–4). (a) Pristine Bi(001), (b) Cu₁@Bi(001), (c) Cu₂@Bi(001), (d) Cu₃@Bi(001), (e) Cu₄@Bi(001), and (f) Cu(111) as references. For n ≥ 2 systems (c–e), two distinct catalytic configurations are presented: green curves represent the reaction pathway where CHO* and CO* intermediates are adsorbed at Bi and Cu sites, respectively, while blue curves correspond to co-adsorption at dual Cu sites. Notably, the Cu–Cu coupling pathway consistently exhibits lower potential-limiting step (PLS) energy barriers compared to the Bi–Cu scenario. All optimized adsorption configurations are provided in the SI (Fig. S8–S13).

3.4 Electronic structure analysis of CO* to CHO*

Comparative analysis of the PLS for CHO* generation via the HCOOH* and CO* pathways reveals a general preference for the CO* intermediate on Cu cluster-doped Bi(001) (Fig. S16). In addition, by systematic computation of the complete free energy landscape for eCO₂RR to C₂ products, we identify a distinct shift in the PLS from to CO* → CHO* upon Cu_n doped Bi(001) (n = 2–4). This transition is mechanistically elucidated by examining the correlation between intermediate adsorption energetics and PLS barriers. Fig. 5a reveals an inverse relationship between the adsorption free energy difference (ΔG_ads = G^CHO*_ads − G^CO*_ads) and PLS free energy, where Cu₂@Bi(001) (0.19 eV) and Cu₃@Bi(001) (0.20 eV) systems exhibit near-ideal differentials comparable to that of Cu(111) (0.21 eV), while Cu₄@Bi(001)'s minimal ΔG_ads difference (approaching 1.07 eV) corresponds to the elevated PLS (1.05 eV). These results indicate that the differential adsorption energy of key intermediates related to the PLS can serve as an effective descriptor for catalytic activity of the eCO₂RR to C₂. Charge density difference and Bader charge analyses (Fig. S17) demonstrate enhanced electron transfer to CHO* on Cu cluster doped surfaces (0.28–0.38e) vs. pristine Bi(001) (0.27e), and the charge transfer disparity (ΔQ = |Q_CHO* − Q_CO*|, Table S1) shows remarkable correlation with PLS barriers when normalized (Fig. 5b). Notably, Cu₄@Bi(001) exhibits a pronounced charge imbalance of 20% (0.16|e|), which correlates with its maximal PLS. In contrast, Cu₂@Bi(001) (10%, 0.06|e|) and Cu₃@Bi(001) (10%, 0.07|e|) demonstrate significantly reduced charge redistribution, approaching the near-neutral characteristics of the Cu(111) reference (2%, 0.01|e|), thus establishing interfacial charge transfer efficiency as a key descriptor. Crystal orbital Hamiltonian population (COHP) analysis of CHO* further uncovers the fundamental bond-strength–activity relationship: the ICOHP energies of the Cu–C bond follow Cu(111) (−2.10 eV, 1.93 Å) > Cu₃@Bi(001) (−1.81 eV, 1.94 Å) > Cu₂@Bi(001) (−1.48 eV, 2.07 Å) > Cu₄@Bi(001) (−1.26 eV, 2.07 Å); therefore, integrated COHP confirms stronger covalent character in systems exhibiting lower PLS barriers (Fig. 5c and S18). Generally, these multiscale electronic structure analyses collectively demonstrate that optimal C–C coupling requires (i) balanced intermediate adsorption strengths, (ii) regulated interfacial charge transfer, and (iii) strengthened metal–adsorbate covalent interactions. These insights provide clear design principles for future catalysts. The key strategies include tuning the size of doped metal clusters (e.g., Cu clusters with n ≤ 3) to optimize the electronic structure and leveraging 2D substrates like bismuthene as electron donors to modulate the interaction between the dopant and key intermediates. Furthermore, machine learning can be integrated in the future to screen a wider range of metal-2D substrate combinations.

Fig. 5 Mechanistic analysis of the CO* → CHO* transformation. (a) Correlation between the adsorption free energies of CO* and CHO* intermediates (G^CO*_ads and G^CHO*_ads) and the potential-limiting step (PLS) energy barrier for CO* → CHO* conversion. (b) Relationship between the charge transfer efficiency and the corresponding PLS barrier. (c) Calculated Cu–C bond strengths (ICOHP values) and bond lengths for CHO* adsorption configurations across different catalytic surfaces. All energy values are referenced to the Fermi level.

4. Conclusions

Through systematic DFT calculations, we have investigated the complete eCO₂RR to C₂ pathway on Cu cluster doped bismuthene systems (Bi(001), Cu₁@Bi(001), Cu₂@Bi(001), Cu₃@Bi(001), Cu₄@Bi(001), and Cu(111)). The results demonstrate that Cu cluster doped Bi(001) significantly enhances the adsorption capability for COOH* and CO*. More importantly, we found that Cu clusters significantly reduce the PLS free energy for CHOCO* formation, improving the thermodynamic efficiency of the CO₂RR. For Cu₁@Bi(001), the local coordination environment resembles that of pristine Bi(001), leading to a similar reaction mechanism , and the PLS free energy is substantially lowered from 1.24 eV (Bi(001)) to 0.87 eV. However, as the Cu cluster size increases (Cu₂–Cu₄), the PLS shifts to CO* → CHO*, and the active sites for C–C coupling transition from Bi–Cu to Cu–Cu pairs, exhibiting a reaction mechanism analogous to that of Cu(111), with free energies of 0.89 eV (Cu₂), 0.87 eV (Cu₃), and 1.05 eV (Cu₄) vs. 0.86 eV for Cu(111). Generally, comparative PLS analysis reveals that Cu cluster doped bismuthene outperforms pristine Bi(001), only smaller clusters (n ≤ 3) approach ideal Cu(111), and the inferior performance of Cu₄ clusters stems from charge transfer imbalance caused by excessive doping. Subsequently, building upon these findings, we systematically investigated the relationship between intermediate adsorption energetics and the PLS free energy. Significantly, we identified three key descriptors for PLS energy: (i) the adsorption energy difference between critical intermediates, (ii) the electron transfer ratio, and (iii) the “Cu–CHO*” bond strength. These parameters establish quantitative structure–activity relationships that serve as predictive metrics for evaluating catalytic performance. These theoretical results indicate that bismuthene materials can serve as an effective substrate for C₂ synthesis and prove that the synergistic effect of “electronic modulation via Cu clusters + 2D bismuthene surface engineering” can overcome the thermodynamic barriers in the eCO₂RR process.

Author contributions

M. Z. is responsible for the data organization and writing of the original manuscript. H. L. is responsible for formal analysis and review. J. Y. and H. Z. are responsible for the software. R. C. and L. L. are responsible for supervision and final approval. All authors have given approval to the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Data availability

All data needed to evaluate the conclusions are present in the article and/or the supplementary information (SI). Supplementary information: optimized atomic configurations of bismuthene, Cu clusters (Cu₁–Cu₄), and Cu_n@Bi(001) (n = 1–4), along with AIMD simulations of these systems. Key intermediates along the CO₂RR pathway toward CHOCO* formation, and calculated Gibbs free energy diagrams for the HER. Charge density difference and Bader charge analysis for CHO*, as well as the correlation derived from COHP analysis of the Cu–C bond in the CHO* intermediate, are provided. See DOI: https://doi.org/10.1039/d5ta07179h.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (21978294 and 22076149), the Innovative Team Program of Natural Science Foundation of Hubei Province (2023AFA027), the Natural Science Foundation of Hubei Province (no. 2024AFB240), and the start-up funding from Wuhan Textile University (no. 20220321).

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Footnote

† Equal contribution.

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