2.8 DFT Calculations
The present first principle DFT calculations are performed with the projector augmented wave (PAW) method37,38 in Vienna ab initio simulation package (VASP). The exchange-functional is treated using the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE)37 functional. The cut-off energy of the plane-wave basis is set at 450 eV for optimize calculations of atoms and cell optimization. The vacuum spacing in a direction perpendicular to the plane of the catalyst is at least 12 Å. The Brillouin zone integration is performed using 4×4×1 Monkhorst-Pack k-point sampling for a primitive cell39. The self-consistent calculations apply a convergence energy threshold of 10-5 eV. The equilibrium lattice constants are optimized with maximum stress on each atom within 0.03 eV/Å. The Hubbard U (DFT+U) corrections for 3d transition metal by setting according to the literature40. The binding energy is calculated using the following Eq (4):
Eads=Etotal-(Em+E1) (4)
where the Etotal is the energy of structure with adsorbed structure, Em is the energy of N-doped carbon structure, E1 is the energy of the single atom or clusters.
The free energy was calculated using the following Eq (5):
G=E+ZPE-TS (5)
where G, E, ZPE and TS are the free energy, total energy from DFT calculations, zero point energy and entropic contributions (T was set to be 298K), respectively.