  The electronic properties of graphene nano-flakes (GNFs) with different edge
passivation is investigated by using density functional theory. Passivation
with F and H atoms are considered: C$_{N_c}$ X$_{N_x}$ (X=F or H). We studied
GNFs with $10<N_c<56$ and limit ourselves to the lowest energy configurations.
We found that: i) the energy difference $\Delta$ between the highest occupied
molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO)
decreases with $N_c$, ii) topological defects (pentagon and heptagon) break the
symmetry of the GNFs and enhance the electric polarization, iii) the mutual
interaction of bilayer GNFs can be understood by dipole-dipole interaction
which were found sensitive to the relative orientation of the GNFs, iv) the
permanent dipoles depend on the edge terminated atom, while the energy gap is
independent of it, and v) the presence of heptagon and pentagon defects in the
GNFs results in the largest difference between the energy of the spin-up and
spin-down electrons which is larger for the H-passivated GNFs as compared to
F-passivated GNFs. Our study shows clearly the effect of geometry, size,
termination and bilayer on the electronic properties of small GNFs.This study
reveals important features of graphene nano-flakes which can be detected using
Raman spectroscopy.
