On the metal-insulator transition in dimerized linear Hueckel chains

The metal-insulator transition is investigated in the case of linear chains described by a one-electron Hueckel Hamiltonian. In these systems, the transition is a consequence of a dimerization of the chain bond length, that induces a similar dimerization of the hopping integral. Three indicators of the chain character are considered: the Highest Occupied Molecular Orbital (HOMO) - Lowest Unoccupied Molecular Orbital (LUMO) gap, the Polarizability and the Localization Tensor. In the case of even open chains, the behavior of the large chains depends in a crucial way on the alternating structure of the hopping integrals. If the ending atoms of the chain are weakly bonded to their neighbors, the energy spectrum of the Hamiltonian shows the presence of two quasi-degenerated eigenvalues, and all the indicators would predict a (spurious) metallic behavior. It is shown that, if the corresponding eigenvectors are removed from the Hamiltonian, the ordinary insulating behavior of alternating chains is recovered.