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The nonplanar character of graphene with a single carbon vacancy defect (SV) is investigated utilizing a pyrene-SV model system by way of complete active space self-consistent field theory (CASSCF) and multi-reference configuration interaction singles and doubles (MRCISD) calculations. Planar structures were optimized with both methods showing the 3B1 state as the ground state with three energetically close states within an energy range of 1 eV. These planar structures constitute saddle-points. However, upon following the out-of-plane imaginary frequency yields more stable (by 0.22 to 0.53 eV), but non-planar structures of CS symmetry. Of these, the 1A’ structure is the lowest in energy and is strongly deformed into an L-shape. Following a further out-of-plane imaginary frequency in the non-planar structures leads to the most stable, but most deformed singlet structure of C1 symmetry. In this structure a bond is formed between the carbon atom with the dangling bond and a carbon of the cyclopentadienyl ring. This bond stabilizes the structure by more than 3 eV compared to the planar 3B1 structure. Higher excited states were calculated at MR-CISD level showing a grouping of four states low in energy and higher states starting around 3 eV. 

The biradicaloid character of different types of polycyclic aromatic hydrocarbons (PAHs) based on small band gaps is an important descriptor to assess their opto-electronic properties.