  Graphene clusters consisting of 24 to 150 carbon atoms and hydrogen
termination at the zigzag boundary edges have been studied, as well as clusters
disordered by vacancy(s). Density Function Theory and Gaussian03 software were
used to calculate graphene relative stability, desorption energy, band gap,
density of states, surface shape, dipole momentum and electrical polarization
of all clusters by applying the hybrid exchange-correlation functional
Beke-Lee-Yang-Parr. Furthermore, infrared frequencies were calculated for two
of them. Different basis sets, 6-31g**, 6-31g* and 6-31g, depending on the
sizes of clusters are considered to compromise the effect of this selection on
the calculated results. We found that relative stability and the gap decreases
according to the size increase of the graphene cluster. Mulliken charge
variation increase with the size. For about 500 carbon atoms, a zero HOMO-LUMO
gap amount is predicted. Vacancy generally reduces the stability and having
vacancy affects the stability differently according to the location of
vacancies. Surface geometry of each cluster depends on the number of vacancies
and their locations. The energy gap changes as with the location of vacancies
in each cluster. The dipole momentum is dependent on the location of vacancies
with respect to one another. The carbon-carbon length changes according to each
covalence band distance from the boundary and vacancies. Two basis sets, 6-31g*
and 6-31g**, predict equal amount for energy, gap and surface structure, but
charge distribution results are completely different.
