The diverse manifold of electronic states generated by a single carbon defect in a graphene sheet: multireference calculations using a pyrene defect model.

Abstract

Detailed calculations have been performed on the electronic states occurring in a single vacancy defect model based on pyrene from which one of the central carbon atoms has been removed. Complete active space self-consistent field and multireference configuration interaction with singles and doubles calculations have been performed using the 6-31G and 6-31G* basis sets. Two types of defect geometries have been defined: 1) The unrelaxed defect structure based on pyrene and 2) a relaxed structure. In total 12 electronic states have been computed for the unrelaxed structure at C2v symmetry, comprising four singlets, triplets and quintets each. The lowest six states are formed from singlet and triplet states and appear in a rather narrow gap of ∼0.6 eV. The lowest quintet state is found 1.43 eV above the (3) B1 ground state. As predicted from Jahn-Teller distortions, a CC bond is formed between dangling carbon bonds in the (1, 3) B1 states, leading to the formation of a five-membered ring. The (1, 3) A2 states show initial repulsive behavior along the bond formation coordinate until an avoided crossing is reached by which these states are furnished with CC bonding character so that finally also in these cases a CC bond is established. Linear interpolation curves between the initial unrelaxed defect structure and the final optimized structure are used to give an overview of the evolution of electronic states and the occurrence of avoided crossings. Out-of-plane structures are investigated with special emphasis on the carbon atom containing a dangling bond in the relaxed structure. Unpaired electron densities are used to characterize the electronic structure of the different states.