Microscopic insights into Cu-N-C catalyst stability and leaching mechanisms through orbital interactions

doi:10.21203/rs.3.rs-4871970/v1

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Microscopic insights into Cu-N-C catalyst stability and leaching mechanisms through orbital interactions

https://doi.org/10.21203/rs.3.rs-4871970/v1

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Copper-nitrogen-codoped graphene (Cu-N-C) single-atom catalysts (SACs) feature an intriguing dynamic transformation between copper single atoms and clusters under electrochemical conditions, a behavior absent in the other metal-centered M-N-C SACs. Yet, the underlying cause of this distinctive phenomenon remains poorly understood. Herein, we delve into the modulation of electronic structure in M-N-C SACs by the solvent effects and electrochemical potentials, revealing the leaching mechanisms of copper atoms based on Crystal Field Theory (CFT) and hybrid-solvation constant potential method. We demonstrate that in M-N-C SACs, the orientation of d-orbitals nearest to the Fermi level determines the stability of M-N bonds. The d⁹ electronic configuration of copper imparts the Cu-N bond with the highest sensitivity to external voltage. Meanwhile, it is revealed that proton transfer (PT) on central copper atoms rearranges the energy levels of d-orbitals near the Fermi level, accelerating charge accumulation in the anti-bonding state in Cu-N bonds and ultimately inducing copper atoms leaching. These findings provide microscopic insights into the interaction between electronic orbitals and leaching behaviors in Cu-N-C SACs, advancing the mechanistic understanding of dynamic phenomena in electrochemical systems.

Physical sciences/Chemistry/Catalysis/Electrocatalysis

Physical sciences/Materials science/Theory and computation/Electronic structure

electrocatalysis

dynamic evolution

mechanism

DFT

Electrocatalyst reconstruction, characterized by deviations from the electrocatalyst’s ideal constant state, complicates the identification of true active sites and the establishment of accurate structure-activity relationships^1–4. The advent and maturation of in situ/operando characterization techniques in recent years have catalyzed an increase in studies that demonstrate significant structural and compositional changes in prefabricated electrocatalysts during electrocatalytic reactions^5–8. Despite these advances, a comprehensive understanding of the mechanisms underlying the structural evolution of electrocatalysts remains poorly understood, particularly regarding the density of states, oxidation state, orbital occupancy, etc^9–16. To enhance the practical application of electrocatalysts in electrochemical energy technologies, a deeper insight into the electronic structures of electrocatalysts under electrochemical conditions is essential^17–20.

Single-atom catalysts (SACs), introduced by Zhang et al. in 2011, represent a convergence of the isolated active sites typical of homogeneous catalysts with the structural robustness and ease of separation characteristic of heterogeneous catalysts^21–25. The reduction of metal entities to single atoms typically yields unique electronic structures, featuring discrete and isolated states in contrast to the continuous bands seen in bulk materials. This alteration imparts SACs with a distinctive responsiveness to external stimuli, making them an exemplary platform for investigating dynamic reaction mechanisms^26–28. A typical subclass of SACs, metal-nitrogen-codoped graphene (M-N-C), has emerged as particularly versatile, applicable to a variety of electrochemical reactions^29–32. Among them, Cu-N-C is notable for its intriguing reversible cluster formation under varying reaction conditions, arousing extensive concern.

Understanding the influence of the electronic structures of central copper atoms on their interactions with electrode potentials and solvent environments is crucial for elucidating the underlying mechanisms and optimizing the design of catalysts. The dynamic behaviors of Cu-N-C SACs have been observed in several electrochemical reactions, including the oxygen reduction reaction (ORR)⁹, nitrate reduction reaction (NO₃RR)¹⁰, and carbon dioxide reduction reaction (CO₂RR)^11–12. These behaviors are characterized by the detectable presence of Cu⁺ and Cu⁰ signals, indicative of copper agglomeration, through operando measurements at working voltage. Especially, this unique behavior is exclusive to M-N-C SACs where M is Cu, whereas SACs with other metals (i.e., Ni, Co, Fe) lack these traits^33–35. Additionally, the emergence of Cu clusters is not restricted to solely Cu-N-C materials. Several Cu-based organic frameworks have shown similar behavior in CO₂RR, where the isolated Cu²⁺ sites ligated to oxygen demonstrate high selectivity for ethanol yield, correlated with Cu clusters³⁶. Similar agglomeration has been observed in studies involving Cu phthalocyanine supported on carbon nanotubes³⁷. With these reports, the electronic characteristics of Cu speciation appear to be closely linked to its geometrical evolution. However, this conjecture remains an open question and the cause behind such special behaviors remains elusive^38–42. Therefore, an in-depth theoretical interpretation that depicts the geometrical and electronic structural dynamics of Cu-N-C SACs in response to reaction voltages, incorporating solvation effects, is highly desired to advance our understanding of their operational mechanisms.

Herein, we aim to elucidate the mechanisms underlying the copper atoms leaching phenomena in Cu-N-C SACs and to ascertain the distinctive properties conferred by the copper central atom in comparison to other metals. Utilizing Crystal Field Theory (CFT), we identify the d_x2−y2 orbital electrons, which predominate in M-N bonding interactions, occupy the Fermi level of Cu-N-C SACs. This distinct occupancy, absent in other M-N-C catalysts, is ensured by the d⁹ electronic configuration of central copper atoms, and engenders a heightened sensitivity of the Cu-N bond strength to external voltage variations. Employing the hybrid-solvation constant potential method, we reveal that the proton transfer (PT) on the copper atoms precipitates a significant perturbation in the energy state near the Fermi level, reordering the energy distribution from discrete to continuous. This transition facilitates an accelerated charge accumulation in the anti-bonding state of the Cu-N bond and leads the Cu-N bonds breaking under working conditions, causing the leaching of the copper atoms. Our work offers a fundamental understanding of the interaction between electronic orbitals and leaching behaviors in Cu-N-C SACs under working conditions.

The d-orbital energy distribution in M-N-C SACs. To understand the structure evolution of Cu-N-C SACs, it is essential to get a deep insight into the electronic states of M-N-C SACs. The M-N-C SACs are inherently composed of two components: the isolated metal center and the N-C substrate, implying that the discrete energy levels of a single metal atom will be altered by the periodic bands of the substrate. Moreover, the metal center with four coordination sites is prevalent in both homogeneous catalysis (e.g., bio-porphyrins) and coordination complexes (such as ML₄ like [Cu(CN)₄]³⁻ and [Ni(CO)₄]). All these inspired us to develop a comprehensive overview of the electronic energy distribution in M-N-C SACs (M = Cu, Ni, Co, Fe), which was achieved through the integration of Crystal Field Theory (CFT) and an analysis of continuous band modification within the periodic N-C substrate²⁶. As illustrated in Fig. 1A, we obtained the evolution diagram of d-orbitals, which is crucial for understanding the behavior of transition metals in SACs—from a state of degenerate energy levels to a continuous energy distribution. Specifically, the orientations of d-orbitals along the x, y axes correspond to their alignment along one M-N bond (SI Appendix, Fig. S1). From the CFT perspective, the interactions between the central metal and its ligands are predominantly electrostatic. In an octahedral configuration, with the metal at the center and six ligands at the vertices, the d_z2 and d_x2−y2 orbitals (e_g orbitals) face the direct path of the approaching ligands and are consequently of higher energy, whereas the d_xy, d_yz, d_xz orbitals (t_2g orbitals), oriented between the ligands’ approach paths, hold lower energy. When the coordination structure transitions to a square planar field, akin to the M-N₄ configuration in M-N-C, a reordering of d-orbital energies occurs. It is found that orbitals with a z component experience a decrease in energy due to reduced electrostatic repulsion from the ligands, thereby becoming stabilized, while the "non-z" orbitals rise in energy, ensuring the overall energy barycenter remains constant.

Based on the above analysis, we deduced the d-orbital energy level diagram for the central metal atom within the M-N-C framework. This approach moves beyond traditional models that treat ligands as merely point charges. Instead, it acknowledges the complexity of the bonding between nitrogen atoms and the central metal, offering a more detailed representation of the interactions that shape the electronic structure of these catalysts. The differential charge density of Cu-N-C (Fig. 1B) is calculated to illustrate the nuances of M-N interactions. This visualization highlights not only the charge interactions within the x-y plane, which align with the electrostatic interactions described by CFT, but also emphasizes the crucial role of interactions involving z-oriented electrons between adjacent atoms. Considering the structural configuration of the N-C substrate, which typically forms a six-membered ring, the valence electrons of N atoms tend to form a sp² hybridization within the x-y plane while a p_z orbital along the z-axis. Figure 1C illustrates the permissible electron interactions between Cu and N atoms according to the symmetry matching principle. The σ bond formed by the d_x2−y2 of Cu and the sp² orbitals of N atoms tends to modify the energy level of copper d-orbitals into a configuration reminiscent of ML₄ complexes. Additionally, two π bonds formed by d_xz-p_z and d_z2-p_z increase the energy levels of orbitals with a z component. Due to the structural symmetry in M-N-C, the d_yz orbitals behave similarly to the d_xz orbitals, and the "non-z" orbitals are lowered in energy. Finally, considering the effect of energy level broadening caused by lattice periodicity, a comprehensive picture of the d-orbital energy distribution is achieved (Fig. 1A). Note that different central metals possess distinct d-orbital electronic configurations, especially those near the Fermi level which significantly influence the catalytic activity and stability of M-N-C SACs under electrochemical reaction conditions.

To further enhance our understanding of electronic properties in these systems, we analyzed the projected density of states (PDOS) for various metal atoms in M-N-C SACs (M = Cu, Ni, Co, Fe) with consideration of the spin effect (Fig. 1D, SI Appendix, Fig. S2). Due to structural symmetry, the energy distributions of d_yz and d_xz orbitals overlap. The observed trend in PDOS variation across different metal atoms aligns with the preceding analysis of energy distribution. Specifically, in Cu-N-C catalysts, we find that the d_x2−y2 orbitals, predominantly involved in M-N bonding interactions, are occupied at the Fermi level due to copper’s unique d⁹ electronic configuration. In contrast, in other M-N-C catalysts, the Fermi level is primarily occupied by d_xz or d_z2 electrons, which play a less significant role in stabilizing the M-N bonds. Consequently, the Cu-N bond strength is more susceptible to external voltage changes under electrochemical reduction conditions compared to other catalysts. Further exploration the Cu-N orbital interactions through projected crystal orbital Hamilton population (pCOHP) analysis, as depicted in Fig. 1E and SI Appendix, Fig. S3, shows a dominant presence of electrons in an anti-bonding state near the Fermi level, which is inherently unfavorable for M-N bond formation in M-N-C systems. Therefore, it is foreseeable that the level up of Femi level induced by the external voltage is detrimental to the stability of the system. So far, the d-orbital energy distribution of pristine M-N-C SACs are thoroughly clarified from the view of the orbital interactions between atoms.

Pristine M-N-C SACs’ behaviors under external potential. The above findings prompted us to investigate the impact of external potential on the pristine M-N-C structure. Employing the hybrid-solvation constant potential method, we obtained the variations in bond length and integrated projected crystal orbital Hamilton population (IpCOHP) in response to potential changes (Fig. 1F). As the system undergoes a shift towards a more negative potential, the electron numbers in system increase. The relationship between the potential and number of added electrons (Δq) is illustrated in SI Appendix, Fig. S4. Notably, all M-N bond lengths and strengths in pristine M-N-C SACs exhibit negligible alterations even when the potential drop reaches 1V, indicating the inherent stability of pristine M-N-C SACs under typical electrochemical reaction conditions. SI Appendix, Fig. S5 illustrates how the PDOS of d electrons in the central metal varies across different M-N-C SACs under different working potentials. We found that although the Fermi level rises as the potential shifts towards more negative values, the resultant increase in the number of electrons occupying the anti-bonding states is not sufficient to deform the structure of catalysts due to existing energy gaps in the electronic states adjacent to the Fermi level. This finding inconsistent with experimental observations where the Cu-N-C SACs are detected to undergo dramatic structure evolution highlights the importance of considering proton effect on the behavior and stability of these catalyst systems^9–12.

Cu-N-C SACs’ behaviors with proton transport. Here, we highlighted that the proton transport (PT) processes have non-negligible effects on the structural transformation of the Cu-N-C SACs. Previous investigations suggested that proton adsorption on nitrogen sites (denoted as H-N) serves as the primary impetus for the leaching of copper single atoms during CO₂RR, as observed through AIMD simulations¹⁴. However, this study had overlooked the vital role of the interaction between copper and proton. To elucidate the impact of proton adsorption on copper atom of Cu-N-C, we obtained the optimized structures of Cu-N-C, proton-adsorbed Cu-N-C (H-Cu-N-C), and models of N-site hydrogenation at a neutral charge state (Fig. 2A, SI Appendix, Fig. S6). The progressive elongation of the longest Cu-N bond length with increasing H-N sites, as illustrated in Fig. 1b. In the Cu-N-C model, the occurrence of H-N sites leads to minor change to Cu-N bonds (1.92 Å, 2.02 Å, 2.14 Å, 2.14 Å and 2.14 Å for IS, 1H, 2H, 3H and 4H, respectively), and the central Cu atom almost keep its position in the substrate plane. In comparison, in the H-Cu-N-C model, due to the initial proton on Cu, the copper atom tends to shift from the nitrogen-carbon (N-C) plane as the H-N sites occur, altering the stability of system significantly. With increasing number of proton adsorption on the N atoms, the Cu atom protrudes more significantly above the N-C plane, and the Cu-N bonds are elongated and ultimately broken (2.01 Å, 2.83 Å, 3.21 Å, 3.53 Å and 3.10 Å for IS, 1H, 2H, 3H and 4H, respectively). This bond-breaking phenomenon is not observed in the Cu-N-C model, where proton is not adsorbed on Cu and the proton adsorption on N atoms only induces minimal bond length alterations of N-C bonds. We then compared the proton adsorption energy on N sites in Cu-N-C and H-Cu-N-C models (Fig. 2B) and found that the N-H bond formation energies are lower within the H-Cu-N-C configurations throughout the process, indicating a more feasible occurrence of N-H bonds in H-Cu-N-C systems. These findings highlight the critical role of protonation in the destabilization and subsequent leaching of the central Cu atom.

An unresolved question is whether the initial proton adsorption predominantly occurs on the Cu atom. To addressing this issue, we obtained the proton adsorption free energies under different external voltages, with water as the proton source. Three adsorption scenarios were examined: a single proton adsorption on N or Cu, and two protons co-adsorption on N and Cu. As depicted in Figs. 2C and 2D, proton adsorption on Cu is energetically most favorable at the applied potential in the range of 0.0 ~ 1.0 V (vs RHE), indicating that H-Cu bond formation likely precedes. As the electrochemical potential shifts negatively (< -1.0 V_RHE), co-adsorption becomes prevalent, suggesting that the proton adsorption on the Cu-N-C surface initiates with the central Cu atom, subsequently involving N sites. This pattern of adsorption underscores a sequential process of proton transfer (PT): as the potential becomes more negative and proton adsorption events increase, Cu-N bonds start to break, leading to the aggregation of Cu atoms into clusters. This sequential initiation and progression of PT processes elucidate the dynamics of structural changes in Cu-N-C catalysts.

Proton transport effect on the d-orbital energy distribution in M-N-C SACs. The above findings suggested the non-negligible effects of proton transport on the inherent stability of Cu-N-C SACs under working conditions. Please note that only Cu-N-C systems in M-N-C SACs are claimed to exhibit aggregation behavior while SACs incorporating other metals are kept in their original configurations. In this regard, we extended our models into the H-M-N-C SACs and further explored the underlying electronic states modification brought by the proton adsorption. Take the H-Cu-N-C systems as an example, the proton approaches the Cu-N-C surfaces from z direction (Fig. 3A), inducing the redistribution of charge density of the system. The charge density difference before and after the proton adsorption revealed the transfers of electrons from the copper to the proton and z axis to x-y plane (Figs. 3B and 3C). With the consideration of the orientation of d-orbitals, the PDOS further obtained to clarify the underlying modulation mechanisms by PT process. We found a collectively significant feature where the d_z2 orbitals exhibit a noticeable split in energy levels due to the interaction with H along the z direction (SI Appendix, Fig. S7 and S8). Notably, a portion of the d_z2 electron states rise above the Fermi level, resulting in a redistribution of electrons. This redistribution leads to a significant alteration of the electron distribution around the Fermi level, affecting the charge accumulation behavior of system under operational conditions critically. Especially, in H-Cu-N-C system, the energy level reordering leads to an additional occupancy of the d_x2−y2 orbitals by electrons from the d_z2 orbital, causing the Fermi level to traverse the continuous energy spectrum (Fig. 3D) which is not available in the pristine Cu-N-C SACs. Further pCOHP analysis indicates that the Cu-N bonds strength in H-Cu-N-C is determined by the d_x2−y2-p antibonding state (Fig. 3E), consistent with the situation in Cu-N-C, and it is the 4s,p orbitals of the copper metal that stabilize the Cu-H bond, as the states below the Fermi level are all bonding states when considering the 4s,p interaction with the adsorbed proton. Taking account of the interaction of all related atomic orbitals, we present a detailed energy level evolution diagram illustrating the effects of proton adsorption in Fig. 3F. The most notable change observed in H-Cu-N-C system is the transition of energy levels around the Fermi level from discrete to continuous, impacting the overall system behavior.

Electronic states of H-M-N-C SACs with external potential: copper atom leaching mechanisms of Cu-N-C SACs. Next, we aim to clarify the connection between potential-dependent structural dynamics and the orbital characteristics in H-M-N-C systems, further elucidating mechanisms of copper atoms leaching. Figure 4A illustrates the bond lengths and IpCOHP values of M-N bonds in H-M-N-C systems under various potentials, along with the correspondence between potential and electrons (SI Appendix, Fig. S9). It is observed that Cu-N bonds exhibit distinct response behaviors compared to other central metals as the potential becomes more negative. The central copper atom tends to move away from the plane of the C-N substrate, leading to the elongation of Cu-N bonds (SI Appendix, Fig. S10). The bond strength of Cu-N significantly decreases, as the quantitative indicator IpCOHP value of the Cu-N bond turns positive with the potential becoming more negative. Meanwhile, it is noted that other M-N bonds are less affected by the influence of external potential variation, further explaining the unique dynamic behavior of the central copper atom. To further analyze the relationship between M-N bond strength and the electron occupation number in the d_x2−y2 orbitals, the variations of the number of electrons (N_e) of Bader charge in the central metal M of M-N-C and H-M-N-C under different potentials are obtained in Fig. 4B and 4C. And the PDOS of central metals under different potentials are presented in SI Appendix, Fig. S8. It is found that different metals exhibit diverse responses, and the charge distribution before and after proton adsorption shows significant differences as well. In pristine M-N-C structures, which had been confirmed as relatively stable under working conditions, the Co and Fe metal centers exhibit stronger electron aggregation behavior than Ni and Cu. The d_x2−y2 orbital electrons, crucial for M-N bond stability, are far from the Fermi level, leading to the relatively stable behavior of Fe/Co-N-C as well as Ni-N-C. The number of electrons accumulated at the Cu atom is small and not sufficient to cause atom leaching behavior. However, PT process greatly alters the electron behaviors in H-M-N-C systems and enhances the charge accumulation in the central Cu atom in H-Cu-N-C. As shown in Fig. 4C, the N_e of the Cu atom significantly increases compared to the situation in Cu-N-C. The underlying mechanisms can be attributed to the reordering of energy levels induced by proton adsorption, which alters the energy states around the Fermi level from discrete to continuous, accelerating the response of charge numbers to external potential.

The above inference can be further supported by the difference in the N_e on Co and Fe atoms between the M-N-C and H-M-N-C systems. The N_e value for Fe and Co decreases in the H-M-N-C compared to that in M-N-C, and it is found that the electron energy level near the Fermi level in these metal-related systems changes from continuous to discrete, which is opposite to what occurs in the Cu-related system and consistent with the proposed inference. Meanwhile, in the H-Ni-N-C system, although the Fermi level traverses the continuous energy level comprised of the d_x2−y2 and d_z2, the variation in N_e on the Ni atom is negligible, which appears to contradict our conclusions regarding the connection between N_e and the energy level state around the Fermi level. Further calculations of the N_e on the adsorbed proton and the electron state of H-Ni-N-C provide satisfactory explanations (SI Appendix, Figs. S11-S13). The calculations demonstrate that the increase in N_e caused by the negative potential accumulates in the adsorbed proton rather than the commonly assumed metal centers. The internal mechanism behind this behavior lies in the continuous electron state of the adsorbed proton near the Fermi level, which acts as a competitor and gains the upper hand against electron aggregation in the Ni atom. This effect is minor in the H-Cu-N-C systems, as the energy level of the adsorbed proton near the Fermi level is discrete. Overall, our calculations indicate that the proton-induced energy level reordering leads to the unique response behavior of central Cu atom under working conditions, endowing the Cu-N-C SACs with distinctive properties. Figure 4D shows the PDOS variation of the d_x2−y2 orbital as the potential becomes negative. It is found that N_e occupying the d_x2−y2 greatly increases under electrochemical conditions, enhancing the anti-bonding effect between the Cu-N bond and leading the Cu atom to move away from the C-N surface. Combined with the N-H effect, a comprehensive picture of the copper atom leaching behavior in Cu-N-C SACs under working conditions is completed (Fig. 4E). It is concluded that PT process on the central copper atom facilitates subsequent electron transportation (ET), a phenomenon unique to copper due to its d⁹ electron configuration. The facilitated ET process enhances the anti-bonding states between the Cu-N bond, leading to the elongation and instability of the Cu-N bond and the tendency of the copper atom to move away from the C-N surface. Subsequent PT processes on N sites as the potential becomes more negative further weaken the Cu-N bond strength and eventually break the Cu-N bond, facilitating the leaching behavior of Cu atoms.

Based on the above analysis, the Cu d⁹ electron configuration and the reaction conditions (electrochemical potential, water solvent effect) are the internal and external factors, respectively, that drive the unique dynamic evolution of the Cu-N-C SACs. Given these findings, it is plausible that similar dynamic structural evolution phenomena might also occur in other Cu-based catalytic systems^36–37. The internal microscopic mechanisms elucidated for the Cu-N-C SACs herein provide a valuable framework for understanding these phenomena. Of course, note that not all Cu-based catalytic systems exhibit this behavior, underscoring the significant role of the Cu coordination environment. On the other hand, when silver (Ag) atoms from the same main group replace copper in the Cu-N-C configuration, it is found that the d_x2−y2 orbital electrons of Ag-N-C demonstrate a diminished sensitivity to external stimuli under reaction conditions due to the weak interaction between Ag and proton, in comparison to their copper counterparts. It would further explain that there is no dynamic structure evolution in Ag-N-C SACs as observed in the experiment⁴³. This fact manifests that the realization of energy rearrangement induced by orbital interactions near the Fermi level is the key to dynamic evolution in M-N-C SACs. In a word, at the electronic level, we elucidate the leaching mechanisms of copper atoms in Cu-N-C SACs and emphasize the need for orbital interactions. Moreover, the exact mechanism of Cu leaching and agglomeration was elucidated. As shown in the section “Reoxidation process of copper cluster to atomic dispersion state” in SI Appendix, we revealed that the hydroxyl groups attached to the Cu cluster facilitate the reoxidation process of Cu cluster to atomic dispersion under positive potentials.

In summary, our investigation thoroughly examines the dynamic behavior of Cu-N-C SACs under operational conditions from a microscopic perspective based on Crystal Field Theory (CFT) and hybrid-solvation constant potential method. The findings underscore the crucial role of the Cu d⁹ electronic configuration in facilitating the structural evolution of Cu-N-C, which account for the difference between other metals M-N-C. The unique Cu d⁹ electronic configuration results in the d_x2−y2 orbitals occupying the Fermi level of Cu-N-C system, which is instrumental in determining the bonding behavior of the Cu-N bond. Under the working condition, the PT process at the central Cu atom modifies the electron states near the Fermi level from discrete to continuous. This energy state alternations facilitate ET to accumulate in the anti-bonding state of the Cu-N bond, elongating and weakening the Cu-N bond. As the potential shifts to negative values, subsequent PT on N sites further increased the anti-bonding state charge occupancy and weaken the Cu-N bond strength, eventually leading to the Cu-N bonds dissociate and leaching of copper atoms. This study offers a comprehensive microscopic examination of the dynamic evolution of Cu-N-C SACs, establishing a foundation for an in-depth understanding of the Cu SACs reconstruction in electrochemical reactions.

Density Functional Theory (DFT) calculations, incorporating spin polarization, were conducted using the Vienna Ab initio Simulation Package (VASP)^44–45. Core-valence interactions were addressed via the Projector-Augmented Wave (PAW) method⁴⁶, while exchange-correlation effects were evaluated using the Perdew-Burke-Ernzerhof (PBE) functional under the Generalized Gradient Approximation (GGA)⁴⁷, augmented by the DFT-D3 method to account for van der Waals interactions⁴⁸. Single-atom catalysts (SACs) based on M-N-C configurations were modeled using a graphene supercell framework with lattice parameters set to 9.93 Å and 8.35 Å, respectively. To eliminate interactions among periodic slabs, a 20 Å vacuum layer was introduced in all slab models. Structural optimizations and electronic property analyses utilized γ-centered k-meshes of 3 × 3 × 1 and 7 × 7 × 1, respectively, with an energy cutoff set at 520 eV. Convergence criteria were established at 0.01 eV/Å for maximal forces and 10^− 6 eV for electronic steps. Incorporation of the hybrid-solvation constant potential method, as implemented by VASPsol^49–50, included an explicit water bilayer to facilitate accurate modeling of long-range electrostatic and hydrogen-bond interactions between reactants and solvent molecules. This approach was complemented by the Poisson-Boltzmann implicit solvation model, setting the Debye length to 3.0 Å to simulate charge compensation and fixing the relative permittivity at 78.4 to accurately represent the aqueous electrolyte environment. The cavity formation energy was disregarded by setting the TAU parameter to 0. The electrode potential referenced to the standard hydrogen electrode (SHE) is formulated as

$$\:U\left(\:\text{V}/\text{S}\text{H}\text{E}\right)\:=\:{W}_{\text{f}}/e\:-\:4.6\:\text{V}\:$$

where the − 4.6 V is the absolute electrode potential of the SHE benchmarked in VASPsol and the $\:{W}_{\text{f}}$ is the work function of system⁵¹. The values of $\:U\left(\:\text{V}/\text{S}\text{H}\text{E}\right)$ were further regulated to the reversible hydrogen electrode (RHE) scale by a potential shift of 0.059 × pH, here the pH refers to 7 in aqueous solutions during the calculation process. The total energy of the charged slab $\:E\left(\text{U}\right)$ at the corresponding potential U was calculated as

$$\:E\left(U\right)={E}_{\text{D}\text{F}\text{T}\:}+\:{\int\:}_{0}^{q}⟨\overline{{V}_{\text{t}\text{o}\text{t}}}⟩\text{d}q+q{W}_{\text{f}}$$

including energy corrections for it is necessary to add or remove electrons and the associated background charge on the electronic energy derived from self-consistent calculations. $\:{E}_{\text{D}\text{F}\text{T}\:}$denotes the DFT energy determined by VASPsol and $\:⟨\overline{{V}_{\text{t}\text{o}\text{t}}}⟩$ represents the average electrostatic potential of the entire cell space. The $\:E\left(\text{U}\right)$ and the electrode potential follow the quadratic function as

$$\:E\left(U\right)=\:-\frac{1}{2}C{\left(U-{U}_{\text{P}\text{Z}\text{C}}\right)}^{2}+{E}_{\text{P}\text{Z}\text{C}}$$

where $\:C$, $\:{U}_{\text{P}\text{Z}\text{C}}$ and $\:{E}_{\text{P}\text{Z}\text{C}}$ are the values of system’s capacitance, the values of potential of zero charge (PZC), and the energy of the system at the PZC, respectively. The fitted data of systems involved are available in SI Appendix, Fig. S14-S16 and Tables S1-S9. The free energy of each species, $\:G\left(U\right)$, was determined by further considering the zero-potential energy ($\:ZPE$) and entropy ($\:-TS$) contributions, which are derived from vibrational frequency analysis. The potential-dependent reaction free energy ($\:{E}_{free}$) of proton adsorption, $\:{\text{H}}^{+}+\:{e}^{-}+\:*\:\to\:\:\text{*}\text{H}\:$, was calculated as follows⁵²:

$$\:{E}_{free}=G\left({\text{*}\text{H}}_{{q}_{2}}\right)-G\left({*}_{{q}_{1}}\right)-\frac{G\left({\text{H}}_{2}\right)}{2}+\left|e\right|U-({q}_{2}-{q}_{1}){W}_{f}$$

where $\:{q}_{1}$ and $\:{q}_{2}$ are the net charges on the catalyst before and after proton adsorption, which are determined by the constraint as

$$\:{W}_{f}\left({\text{*}\text{H}}_{{q}_{2}}\right)=\:{W}_{f}\left({*}_{{q}_{1}}\right)={W}_{f}$$

and $\:G\left({\text{*}\text{H}}_{{q}_{2}}\right)$ and $\:G\left({*}_{{q}_{1}}\right)$ are the free energies of system before and after proton adsorption under applied potential U. To elucidate the intricacies of local orbital interactions, a projected crystal orbital Hamilton population (pCOHP) analysis was conducted utilizing the LOBSTER software suite^53–54. Further, the strength and contributions of individual orbitals to the chemical bonding were quantitatively assessed through integrated pCOHP (IpCOHP) evaluations. The computational output from VASP was refined using the VASPKIT tool⁵⁵.

Author Contributions:

Z. C. and Y. C. conceived and designed the project; X. Z performed the DFT calculations; H. W., Y. F., Z. C., H. L., and Y. C. discussed the density functional theory results. X. Z., Y. C., Y. F., H. L., and Z. C. wrote and revised the manuscript. All authors commented on the final manuscript.

Competing Interest Statement:

The authors declare no competing interests.

Classification

Physical Science - Chemistry.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (12164009) and the Sichuan Science and Technology program (2022ZYD0024).

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Microscopic insights into Cu-N-C catalyst stability and leaching mechanisms through orbital interactions

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