All the calculations were performed by means of the density functional theory (DFT) using double numerical plus polarization functions (DNP) basis sets and the DFT semi-core pseudopotentials (DSPP) were exploited for relativistic effects which replaces core electrons by a single effective potential 24, implemented in the DMol3 package 25. The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional 26 and a 4.6 Å global orbital cutoff was used in fine quality. To consider the van der Waals forces, Grimme scheme is used in all calculations. A k-point mesh of at least (8×8×1) points was used to sample the Brillouin zone of the smallest supercells by Monkhorst–Pack 27 scheme was used for the calculation of energy and other properties. To model extended graphene sheet, a supercell of graphene with 72 carbon atoms corresponding to 6×6 unit cells was considered and periodic boundary conditions were applied. The supercells of graphene were set to 14.80×14.80×20 Å3. A vacuum width of 20 Å was considered to avoid interaction between graphene sheets in adjacent boxes. To evaluate the interaction of ozone molecule with pure and doped graphene sheets, the adsorption energy and binding energy was calculated by
Ead = Etot – Es – Eo (1)
Eb= Etot – Es-v – Em (2)
where, Etot and Es are the total energy of adsorbed ozone molecule on the pure or doped graphene sheets and the total energy of the pure or doped graphene sheets, respectively. Eo denotes the energy of ozone molecule. Es-v and Em are the total energy of the graphene sheet with single vacancy and transition metal atom, respectively.
Several effort have been made to use quantum reactivity descriptors 28 containing energy gap (Eg). The energy gap has the following available equation:
Eg = ELUMO – EHOMO (3)
where EL and EH are the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) energies.