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 B 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 symmetry. Of these, the A' 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 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 B 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.