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 D nh 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 (perelectron) polarizability for n ! 1 in the direction of the system symmetry axis. The two (degenerate) components of the polarizability on the r h 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 analyzed 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.
K E Y W O R D Scomplete active space self-consistent field, cyclacenes, polarizability, tight-binding, total position spread 1 | I N TR ODU C TI ON First imagined by Edgar Heilbronner in 1954, [1] [n]cyclacenes (cyclic polyacenes) have been a fascinating research topic. A thorough understanding of cyclacenes is important as they could be considered as the shortest zigzag carbon nanotube (CNT) and could be used to model finite-length CNTs in simulations. Furthermore, [n]cyclacene chains have the potential to be used as precursors for the synthesis of zigzag CNTs, allowing for a more controlled way to fabricate this type of carbon nanostructure. [2] Unfortunately, the synthesis of [n]cyclacenes has not yet been realized as it is summarized in a number of reviews. [3][4][5] Besides experimental work on [n]cyclacenes, several computational studies using semi-empirical methods [6][7][8][9][10][11][12][13][14][15][16] and ab initio methods [17][18][19][20][21][22] have been carried out on these systems. The semi-empirical work was focused both on an analysis of the structural properties of the cyclacenes as well as the behavior of electronic properties such as the HOMO-LUMO gap as a function of the system size parameter n. It was found that the gap decreases in an alternating way depending on the parity of n, as more units are added to the system. Depending on the type of semi-empirical Int J Quantum Chem. 2018;118:e25569.