Degao
Zhang
a,
Qian
Lin
a,
Guangjun
Nan
b,
Yi
Zhang
a,
Dawei
Fu
a and
Liyan
Xie
*a
aInstitute for Science and Applications of Molecular Ferroelectrics, Key Laboratory of the Ministry of Education for Advanced Catalysis Materials, Zhejiang Normal University, Jinhua, 321004, P. R. China. E-mail: liyanxie@zjnu.edu.cn
bDepartment of Physics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China
First published on 12th February 2026
Single-atom catalysts (SACs) have shown great promise for electrocatalytic applications such as the oxygen evolution reaction (OER). However, the high surface free energy of the isolated metal sites in SACs results in a generally low metal loading, which limits the density of active sites. Herein, we constructed low- and high-loading SACs on a γ-graphyne (GY) support using a series of transition metals (Fe, Co, Ni, Cu, Rh, Pd, Ag, Ir, and Pt) to study their OER performance. Calculations demonstrate that a high metal loading reduces the OER overpotential of Fe- and Co-GY catalysts, especially for Fe-GY, which shows exceptional activity with an overpotential of only 0.39 V. Notably, the bonding and anti-bonding stabilized energy difference (BASED) analysis indicates that the high loading Fe-GY optimizes the binding strength of *OH and *O intermediates, thereby lowering the overpotential of the rate-determining step (*OH → *O). This change is attributed to the synergy between adjacent Fe atoms, which modifies the charge distribution at the Fe sites, as shown by differential charge and density of states (DOS) analyses. Our findings help pave the way for the rational design of high-loading SACs for electrocatalysis.
Meanwhile, advanced characterization techniques have provided evidence that adjacent sites of SACs exert a mutual influence as the loading density increases. For instance, Li et al. investigated the chemical configuration and local coordination environment of the Fe-SAC material using X-ray absorption spectroscopy (XAS). They observed a shift of the absorption edge toward lower energy with increasing density of Fe sites, revealing a higher electron density at the Fe sites in high-loading Fe-SACs.13 Furthermore, the close proximity of metal centers in high-loading SACs also enables “cooperative catalysis”.14 Thus, given the critical nature of the interactions between adjacent sites in SACs, understanding the fundamental principles is important for the rational design of high-loading SACs.
Complementing the experimental findings, theoretical calculations, such as density functional theory (DFT), were also employed in the study of high-loading SACs to elucidate the interactions between the active sites from an atomic perspective. For example, Jin et al. investigated the interactions between cobalt sites in densely populated Co SACs on N- and O-doped graphene matrix using DFT calculations. Studies have shown that in densely populated Co SACs, the electronic structure of cobalt atoms changes through charge redistribution, leading to a reduced Bader charge and an elevated d-band center, which facilitates the activation of reactants during the trans-stilbene epoxidation.15 Jin and coworkers calculated the magnetic moments of adjacent Fe–N4 sites at varying distances (dsite) in graphene to investigate the influence of iron loading density on the oxygen reduction reaction (ORR) catalytic activity. The calculations show that when dsite values are below 1.6 nm, increased filling of partially occupied d orbitals causes a significant reduction in spin moment, thereby preventing strong adsorption of OH intermediates during the ORR.16 Evidently, theoretical calculations offer unique advantages for understanding the adjacent site interactions in high-loading SACs.
Recently, Wu et al. reported γ-graphyne (GY), a novel two-dimensional carbon allotrope.17 Its structure features both hexagonal carbon rings and acetylene bonds, formed by sp- and sp2-hybridized carbon atoms. In addition, He and colleagues calculated the adsorption energies of several transition metal (TM) atoms on graphene (Fig. S1) and GY (Fig. 1a). Their results indicated that TM adsorption is more stable on GY, attributable to the presence of sp-hybridized carbon atoms in its structure.18 Therefore, GY promises to be a suitable support material for synthesizing high-loading SACs. Although previous theoretical studies have established the OER performance of TM-doped GY (TM-GY) systems, research studies on high-loading TM-GY and the interactions between TM sites remain scarce.19,20
Thereby, we systematically calculated and compared the OER activities of both low- and high-loading TM-GY systems (Fig. 1, where TM = Fe, Co, Ni, Cu, Rh, Pd, Ag, Ir, and Pt), aiming to elucidate the influence of metal loading on catalytic performance. Our results demonstrate that, relative to low loading conditions, high loading reduces the overpotential in Fe-, Co-, and Cu-GY catalysts while exerting nearly negligible effects on other TM-GY systems. Stability concerns preclude the inclusion of Pd-GY and Ag-GY systems in the current analysis. Notably, a highly active high-loading Fe-GY catalyst is identified, exhibiting an ultralow overpotential of 0.39 V. Furthermore, mechanistic analysis reveals that synergistic interactions between adjacent Fe atoms in high-loading Fe-GY reshape the local charge distribution. This electronic modulation optimizes both the Fe–O bonding and Fe 3d orbital characteristics, thereby enhancing intermediate binding and boosting OER activity. We believe that these findings provide valuable insights for accelerating the development of highly active, high-loading SACs.
In principle, all 3d, 4d, and 5d TMs can form TM-GY. However, Talib et al. have comprehensively studied the OER activity of low-loading TM-GY, identifying low-loading Fe-, Co-, Ni-, Cu-, Rh-, Pd-, Ag-, Ir-, and Pt-GY exhibiting relatively low overpotentials (0.46 V to 1.20 V).20 Given that high loading has a limited effect on overpotential, only these nine TMs were studied. We first determine the adsorption sites of these TM atoms on GY. For multiple binding sites, including positions above the C6 ring, above the C–C bond, above the C atom, and in the H cavity, literature shows that the metal preferentially adsorbs above the H cavity and binds to six sp-hybridized carbon atoms.19,20 Moreover, a large hexagonal ring formed by six H cavities surrounding a benzene ring replaces the structure shown in Fig. 2a to represent the GY surface. The cavities are labeled H1 to H4 as illustrated in Fig. 2b. We propose that the configuration formed by binding a single TM atom to the H1 cavity of GY corresponds to low-load TM-GY, designated as TM1. Building upon low-load TM-GY, we constructed high-load TM-GY configurations by introducing a second TM atom. This additional atom may adsorb at H2/H3/H4 sites, yielding three distinct configurations: TM1–TM2, TM1–TM3, and TM1–TM4, as shown in Fig. 2c.
Before investigating the catalytic activity of the OER, the stability of TM atoms embedded in GY must be assessed. The low-loading TM-GY has only one configuration (TM1), and its structures are shown in Fig. S2. To determine the most stable configuration of the high-loading TM-GY, we calculated and compared the energies of three possible configurations. As highlighted in red in Table S1, the most stable configurations for high-loading Fe-GY and Pd-GY are TM1–TM3, while for Co-, Ni-, Cu-, Rh-, Ag-, Ir-, and Pt-GY are TM1–TM4. The corresponding optimized structures are illustrated in Fig. S3. Notably, the TM1–TM2 configuration was absent in the studied metals, likely because this structure requires two metal atoms to share two sp-hybridized carbon atoms, destabilizing the system. Fig. 3a and b present the calculated binding energies between TM atoms and the GY surface. For both low-loading and high-loading TM-GY, the TM atom binding energies range from −0.65 to −3.83 eV and −0.57 to −3.92 eV, respectively, indicating strong binding between TM atoms and GY. Fig. 3a and b further quantify the clustering energies of TM atoms on GY, illustrating aggregation propensity, while Fig. S4 presents the adsorption configurations of a TM dimer on GY. Among all TM-GY, TM atoms exhibit negative clustering energies in all cases except low-loading Pd-GY and both low- and high-loading Ag-GY, indicating high dispersion tendencies for the remaining catalysts. In summary, GY serves as an effective carrier for the TM SACs studied here, with the exception of these three material types. Consequently, these exceptional cases will be excluded from subsequent catalytic investigations. Furthermore, the climb image driven elastic band (Cl-NEB) method was employed to examine the possibility of Fe atom migration among the most stable adsorption sites in the Fe-GY catalyst. Two migration pathways were considered: diffusion between adjacent H cavities, and diffusion from an H cavity to a C6 cavity. As shown in Fig. S10, both the low- and high-loading Fe-GY exhibit high energy barriers for these processes, with values of 1.80 eV, 3.42 eV, 1.59 eV, and 1.60 eV, respectively. Since Fe atoms adsorbed in the C6 cavity are unstable in the high-loading case, the corresponding migration pathway was excluded from consideration. Therefore, the aggregation of adsorbed Fe atoms can be reliably ruled out.27
![]() | ||
| Fig. 3 Binding and clustering energies of TM atoms in (a) low-loading TM-GY and (b) high-loading TM-GY. | ||
Subsequently, we performed a comprehensive investigation and comparison of the OER catalytic activity of TM-GY. The OER proceeds via four fundamental steps, as detailed in Fig. 4. Therefore, we calculated the free energy barrier for each step of every catalyst under acidic conditions (pH = 0) and determined the overpotential of all active sites using eqn (S6) in the SI, as shown in Fig. S5. In the figure, the low-loading TM-GY has only one metal site, whereas the high-loading TM-GY has two possible sites, which are labeled with numbers to indicate their identities. In addition, to more intuitively reflect the differences in catalyst activity between low and high loads, we presented the obtained overpotential data in a bar chart and highlighted the overpotential differences between the two load conditions, as shown in Fig. 5. For Fe and Co, the overpotential of TM-GY under high loading decreased by 0.64 and 0.13, respectively, relative to the low loading condition, indicating that increasing the loading can significantly enhance their OER catalytic activity. However, for Ni, Cu, Rh, Ir, and Pt, the overpotential difference in TM-GY between high and low loading is very small, ranging from −0.09 V to +0.01 V, indicating that increasing the loading has almost no effect on the catalytic activity of these TM-GY. Due to the instability of low-loading Pd-GY, the Pd-GY system is excluded from the current analysis. Notably, The high-loading Fe-GY catalyst exhibits significantly higher activity than other studied catalysts, with an overpotential of 0.39 V—superior to the commonly used IrO2 (0.56 V).28
![]() | ||
| Fig. 4 Schematic illustration of the OER mechanism on the TM-GY material, where * denotes the TM site. | ||
![]() | ||
| Fig. 5 OER overpotential differences between low- and high-loading TM-GY. The numerals 1, 3 and 4 denote the TM site labeling. | ||
To reveal the origin of the high catalytic activity of high-loading Fe-GY, the Gibbs free energy barriers of both low- and high-loading Fe-GY were first analyzed. As shown in Fig. 6a, at U = 0 V and pH = 0, both low- and high-loading Fe-GY exhibit the same trend: all reaction steps are energetically uphill. However, compared to the low-loading Fe-GY, the high-loading Fe-GY exhibits a more uniform intermediate free energy distribution. This significantly reduces the energy barrier of the rate-determining step (RDS) for the *OH → *O conversion from 2.25 eV to 1.63 eV (site 1)/1.62 eV (site 3), with the corresponding overpotential decreasing from 1.02 V to 0.40 V/0.39 V. Furthermore, the free energy diagrams of sites 1 and 3 nearly overlap, indicating that the two sites are equivalent. This equivalence arises because the chemical environments of the two metal sites in the TM1–TM3 configuration are identical, as demonstrated in Fig. 2c. Therefore, only site 3 with lower overpotential was considered in subsequent studies.
Changes in the OER activity of a catalyst often result from alterations in the binding strength between oxygen-containing intermediates and the catalyst. Fig. 6b displays the adsorption energies of oxygen-containing intermediates on low- and high-loading Fe-GY. As the Fe loading increases, the adsorption energies of *O and *OOH become more negative, while that of *OH becomes less negative. Consequently, the adsorption of O and OOH on the catalyst strengthens, whereas the adsorption of OH weakens. Relative to low-loading Fe-GY, the high-loading Fe-GY demonstrates optimized adsorption behavior that equalizes intermediate free energies, thereby substantially reducing overpotential, consistent with our previous analysis. Focusing on the RDS for the high-loading Fe-GY, the overpotential reduction stems from enhanced O adsorption and weakened OH adsorption.
To further reveal the origin of the high activity, we introduce the bonding and anti-bonding orbitals stable electron intensity difference (BASED) theory, applying it to analyze bonding/anti-bonding states and elucidate O/OH–TM bonding interactions.29 Qiao et al. developed the BASED theory by integrating D-band center, Crystal Orbital Hamilton Population (COHP), and Molecular Orbital (MO) theory to establish a generalized descriptor for quantifying adsorption intensity, expressed as
| ICOHPbond (eV) | ε bond (eV) | ICOHPanti (eV) | ε anti (eV) | BASED (eV2) | |
|---|---|---|---|---|---|
| (Fe1-1)Fe–O | −2.56 | −3.60 | 0.58 | −1.23 | 8.52 |
| (Fe1–Fe3-3)Fe–O | −2.79 | −3.49 | 0.85 | −0.81 | 9.03 |
| (Fe1-1)Fe–OH | −2.70 | −6.06 | 0.90 | −3.21 | 13.49 |
| (Fe1–Fe3-3)Fe–OH | −2.60 | −4.96 | 0.98 | −1.64 | 11.28 |
This variation stems from significant modulation of the Fe 3d projected density of states (PDOS) under high-loading condition. Fig. 8(a and b) show the Fe 3d PDOS of low- and high-loading Fe-GY, and respectively contain the O 2p PDOS of O free radical (Fig. 8a) and OH free radical (Fig. 8b). The contribution of O 2s is negligible. Furthermore, corroborated by spin-polarized COHP analysis in Fig. S6, we deduce: In the spin-up PDOS, the Fe 3d state exhibits continuous distributions at both low- and high-loading Fe-GY, with the d-band center upshifting from −4.97 eV at low loading to −4.41 eV at high loading. Consequently, the bonding and anti-bonding orbitals formed by Fe sites and O/OH free radical at high loading also shift to higher energies, as displayed in Fig. 7(a and b). However, the spin-down PDOS for Fe 3d orbitals is discontinuous, with the region near the Fermi-level playing a key role in bonding. The spin-down Fe 3d PDOS of low-loading Fe-GY has two distinct peaks at the Fermi-level that strongly couple with nearby O/OH states to form bonding orbitals at lower energies (anti-bonding orbital is disregarded). In the high-loading Fe-GY, the energy levels of these two peaks decrease to around −1.8 eV. Therefore, the Fe–O/OH coupling weakens, and the formed bonding orbitals upshift, as shown in Fig. 7(a and b). Conclusively, modifications in the spin-polarized Fe 3d PDOS of high-loading Fe-GY drive an upshift in both εbond and εanti.
Fundamentally, both the altered electron transfer at Fe–O and modified Fe 3d PDOS in high-loading Fe-GY originate from synergistic interactions between adjacent metal centers. The charge density difference and Bader charge between Fe atoms and the GY were calculated for low- and high-loading Fe-GY to investigate charge transfer and redistribution, as shown in Fig. 8(c and d). Fig. S7(c and d) displays the optimized structures of Fe-GY. Compared to the low-loading, the number of electrons transferred from Fe atoms to GY in the high-loading Fe-GY remained largely unchanged (0.76 e → 0.75 e). However, distortion occurred in the charge accumulation and depletion regions around Fe sites, signifying synergistic interactions between adjacent Fe atoms in the high-loading Fe-GY. This interatomic interaction ultimately reshaped the local charge distribution around Fe centers. This directly or indirectly affects charge transfer during subsequent adsorption of oxygen-containing intermediates. Moreover, charge distribution is intrinsically linked to the density of states (DOS), which characterizes electronic state distribution. Consequently, alteration in charge distribution ultimately modify the Fe 3d PDOS. In addition, Fig. S8 presents the DOS of the six carbon atoms within the H1 hole in pure GY, the DOS of the six carbon atoms within the H3 hole in the Fe1 structure, and the 3d PDOS of the Fe atom (corresponding carbon atomic positions are illustrated in Fig. S7). A noticeable change is observed in the DOS of the Fe1–H3 compared to that of GY-H1. This indicates that the synergistic interaction between adjacent metal centers alters the bonding between the H3 hole and the iron atoms, ultimately leading to changes in the electronic properties of Fe1–Fe3.
| This journal is © the Owner Societies 2026 |