Fig. 8: DFT calculated profiles of free energy.

Top- and side- view of atomic structure models for (a, c) Co3N; (b, d) PW-Co3N; e The free-energy diagram of HER at the equilibrium potential for Co3N and PW-Co3N, H* denotes that intermediate adsorbed hydrogen; f The d band of density of states (DOS) of Co3N and PW-Co3N; g Water adsorption energy on Co3N and PW-Co3N; Top-(h) and side-(i) view of charge density difference analysis for PW-Co3N with the cyan region representing charge depletion and the yellow region representing charge accumulation. The isosurface value is 0.012 eÅ−3; j The free-energy profiles of HzOR on the Co3N and PW-Co3N surfaces. The inset in (j) are the most stable configurations of the each adsorbed intermediate on the Co site.