High-Level Multireference Investigations on the Electronic States in Single-Vacancy (SV) Graphene Defects Using a Pyrene-SV Model

The nonplanar character of graphene with a single carbon vacancy (SV) defect is investigated utilizing a pyrene-SV model system by way of complete-active-space self-consistent field theory (CASSCF) and multireference configuration interaction singles and doubles (MR-CISD) calculations. Planar structures were optimized with both methods, showing the 3B1 state to be the ground state with three energetically close states within an energy range of 1 eV. These planar structures constitute saddle points. However, following the out-of-plane imaginary frequency yields more stable (by 0.22 to 0.53 eV) but nonplanar structures of C s 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 nonplanar structures leads to the most stable but most deformed singlet structure of C 1 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 the MR-CISD level, showing a grouping of four states low in energy and higher states starting around 3 eV.