Fig. 5: Experimental verification of ARSC.

a The relationships between ∆G(*OH) vs. ϕ_xx on 760 X-Y sites for 4 coordination structures. Insets: local zoom-in of the ∆G(*OH)-ϕ_xx lines. b Volcano relationship between U_L(ORR) vs. ARSC, defined as (1 + kα) × ϕ_xy on X-Y sites. X is Ru, Os, Fe, and Co; Y is Co, Ni, Rh, Pd, Ir, and Pt. c AC-HAADF-STEM images of Co-Co-NC and the intensity distributions corresponding to areas A1 and A2. Insets: DFT model of Co-Co-Qv3. d The normalized XANES spectra at Co K-edge. e The k³-weighted FT-EXAFS spectra at Co K-edge. f ORR polarization curves recorded at a scan rate of 5 mV s⁻¹ at 1600 rpm in 0.1 M KOH at 25 °C for Co-Co/Ir-NC and commercial Pt/C (with iR compensation, compensating resistance: 4.8 ± 0.1 Ω, 4.7 ± 0.1 Ω, 6.2 ± 0.3 Ω, respectively, catalyst loading: 0.25 mg cm⁻²). g OER polarization curves recorded at a scan rate of 5 mV s⁻¹ in 1.0 M KOH at 25 °C for Co-Co/Ir-NC and commercial IrO₂ (with iR compensation, compensating resistance: 5.1 ± 0.2 Ω, 4.7 ± 0.1 Ω, 4.5 ± 0.1 Ω, respectively, catalyst loading: 0.125 mg cm⁻²). h The experimental ORR activity as a volcano-like function of ARSC. The experimental activity is investigated by E_1/2, which are taken from 28 published papers (Supplementary Table 15) and this work (Co-Co/Ir-NC), including a total of 17 different dual-atom sites. The error bar represents the differences in E_1/2 between multiple works with the same dual-atom site. i ORR polarization curves of a Co-Co-NC before and after 10,000 potential cycles (with iR compensation, compensating resistance: 4.8 ± 0.1 Ω, catalyst loading: 0.25 mg cm⁻²). j OER polarization curves of Co-Co-NC before and after 200-h-long working at 10 mA cm⁻² (with iR compensation, compensating resistance: 5.1 ± 0.2 Ω, catalyst loading: 0.125 mg cm⁻²).