Carbon-supported transition metal single-atom catalysts (TM-SACs) demonstrate exceptional promise for the electrochemical oxygen reduction reaction (ORR). Here, we carry out density functional theory (DFT) calculations and reveal a linear correlation between the adsorption free energy of the key intermediate OH (ΔGOH) and the TM-OH bond strength. The TM-OH bond strength is governed by the symmetry-dependent contributions of different d orbitals to the bonding and antibonding interactions at the active site. The local in-plane coordination environment modulates the energy levels of the dxy and \(d_{x^2-y^2}\) orbitals, resulting in the occupancy variation of the out-of-plane d orbitals (dxz, dyz, and \(d_{z^2}\) ). Therefore, we introduce a descriptor ( \(\theta_{\rm{OH}}=\theta_{d_{xz}}+\theta_{d_{yz}}+|1-\theta_{d_{z^2}}|\) , \(\theta_{\rm{d_{xz}}}\) , \(\theta_{\rm{d_{yz}}}\) and \(\theta_{d_{z^2}}\) indicating the occupancy of dxz, dyz, and \(d_{z^2}\) orbitals in the coordinated TM) to predict the catalytic performance of TM-Zx SACs (TM=3d transition metals, Z=N, C, O, x=3, 4, 5) towards ORR. Furthermore, we develop a generalized descriptor φ, which only depends on the geometric and elemental characteristics of the TM, coordinating atoms (Z) and adsorbates. The descriptor can capture both the electronic properties and catalytic activity of TM-Zx-C SACs without the need for additional calculations. Our findings provide an efficient and convenient strategy for optimizing catalytic performance through tailored geometric and electronic configurations.
