  The electronic states occurring in a double vacancy defect for graphene
nanoribbons have been calculated in detail based on a pyrene model. Extended ab
initio calculations using the MR configuration interaction (MRCI) method have
been performed to describe in a balanced way the manifold of electronic states
derived from the dangling bonds created by initial removal of two neighboring
carbon atoms from the graphene network. In total, this study took into account
the characterization of 16 electronic states (eight singlets and eight
triplets) considering unrelaxed and relaxed defect structures. The ground state
was found to be of 1Ag character with around 50% closed shell character. The
geometry optimization process leads to the formation of two five-membered rings
in a pentagon octagon pentagon structure. The closed shell character increases
thereby to ~70%, the analysis of unpaired density shows only small
contributions confirming the chemical stability of that entity. For the
unrelaxed structure the first five excited states (3B3g, 3B2u, 3B1u, 3Au and
1Au) are separated from the ground state by less than 2.5 eV. For comparison,
unrestricted density functional theory (DFT) calculations using several types
of functionals have been performed within different symmetry subspaces defined
by the open shell orbitals. Comparison with the MRCI results gave good
agreement in terms of finding the 1Ag state as ground state and in assigning
the lowest excited states. Linear interpolation curves between the unrelaxed
and relaxed defect structures also showed good agreement between the two
classes of methods opening up the possibilities of using extended nanoflakes
for multistate investigations at DFT level.
