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.