On the theoretical analysis of the lowest many-electron states for cyclic zigzag graphene nano-ribbons

We have calculated the optical and magnetic properties of the four lowest many-body states for cyclic zigzag graphene nano-ribbons (GNRs). The results have been obtained within the semi-empirical restricted frozen Hartree?Fock approximation. Firstly, we obtained one-determinant numerical and analytical coincident results. We detected the existence of two degenerate open-shell molecular orbitals (MOs) o, o?. Due to this degeneracy, some of the mentioned results do depend on any (arbitrary) orthogonal transformation between these two MOs. We have improved these preliminary results by using linear combinations of two determinants, which are eigenfunctions of the operators, which commute with t…