Fig. 5: Theoretical investigations.

a Electron density differences top views and Bader charge diagram for Co–N4–C, Co–P1N3–C, Co–P2N2–C, Co–P3N1–C. Blue and yellow represents for electron depletion and accumulation, respectively. b HER free energy profile for the water dissociation process. c H adsorption energy calculations at the P or N site in Co–PxN4-x–C (x = 0, 1, 2, 3). d The diagram of △GH* over corresponding catalysts. e The plots of the △GH*, △GOH* and △Gw as function of different Co–PxN4-x–C (x = 0, 1, 2, 3) models. f Snapshots of the atomic structure of the Co–PxN4-x–C catalysts during the MD simulations at varied temperature. g Co–N and Co–P bond length statistics in the Co–PxN4-x–C catalysts during MD simulations.