Recently, TM and P co-doped carbon SACs have caught extensive attentions due to the similar properties with N and exhibit the resembled configurations with TM-N4-C systems, as displayed in Figure , the single TM atom embeds graphene sheet with the tetra-coordinates P (TMP4). Via DFT calculations, for the final optimized structures (the corresponding stable configurations are illustrated in Figure ), the details of binding energies (Eb), and TM-P bond lengths are listed in Table , the negative values of Eb certify the stability of TMP4. Meanwhile, the bader charge analysis was conducted to evaluate the strong interactions between P4-C and TM atoms (Table ). And the transferred charges from TM atoms to P4-C induce to the TM atom charged positively, hence, the site of charged TM will be regarded as the adsorption and catalytic centers during the ORR/OER process. Figure depicts the DOS of P4-C and TiP4, more electronic states will be introduced to the gap near the Fermi level by the d orbitals of TM atoms when they embed to P4-C, which promotes the increased electric conductivity and may devoted to strengthening the ORR/OER electrocatalytic performance. For the ORR/OER process, the adsorption free energies of OH* (∆𝐸 𝑂𝐻 * ), O* (∆𝐸 𝑂 * ) and OOH* (∆𝐸 𝑂𝑂𝐻 * ) on catalyst surface determine the free energy of each reaction step. As a matter of common knowledge, the ideal catalyst will provide a 1.23V reaction free energy for every step of ORR/OER with no overpotential, thus, for designing the novel catalysts, the suitable adsorption free energies of intermediates should be guaranteed to maintain the low reaction overpotential. In this work, the adsorption free energies for OH*, O* and OOH* on TMP4 are compared and listed in Figure , which clearly demonstrates that the ∆𝐸 𝑎𝑑𝑠 of species containing oxygen are determined by the optimized TMP4 structures. Moreover, it can be confirmed that the TMP4 catalysts prefer to capturing hydroxide group with the relatively lower ∆𝐸 𝑂𝐻 * ranging from -2.15 to 1.5 eV. For all intermediates adsorption on TMP4, the changes of free energy are similar with the increased TM atomic numbers (3d, 4d and 5d elements). The strongest chemical bond formed between OH and HfP4 and TaP4.