A theoretical study on cyclacenes: Analytical tight-binding approach

We present a theoretical study of cyclacene molecules performed at tight-binding level. The orbital energies and eigenvectors have been analytically computed, and exact expressions for the axial component of the total position spread and polarizability tensors have been obtained. In absence of dimerization, the system has a Dnh symmetry, where n is the number of hexagonal units. The energy bands present no gap at the Fermi level, and to this fact it corresponds a diverging (per- electron) polarizability for n ! 1 in the direction of the system symmetry axis. The two (degener- ate) components of the polarizability on the rh symmetry plane, conversely, remain finite for n ! 1. The total position spread tensor presents a qualitatively different behavior, since all the three components of the position spread per electron remain finite for n ! 1. The results are ana- lyzed and discussed for both axial and planar components separately as these are affected differently with respect to the increasing system size. Both dipole polarizability and total position spread have been computed using an ab initio approach for the smallest systems, to compare the analytical tight-binding expressions with a higher-level theory.