3 years ago

A theoretical study on cyclacenes: Analytical tight-binding approach

A theoretical study on cyclacenes: Analytical tight-binding approach
Thierry Leininger, Noelia Faginas-Lago, Gian Luigi Bendazzoli, Stefano Battaglia, Hai-Anh Le, Stefano Evangelisti
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∞ in the direction of the system symmetry axis. The two (degenerate) components of the polarizability on the σh symmetry plane, conversely, remain finite for n∞. 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∞. 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. Cyclacenes have been challenging chemists for many years, but despite all efforts they have not been synthesized yet. Nonetheless, their properties are fascinating and, thus, often investigated from a theoretical perspective. In this work, two properties of such systems, namely the total position spread and the polarizability, have been obtained analytically within the tight-binding approximation and studied as a function of the system size.

Publisher URL: http://onlinelibrary.wiley.com/resolve/doi

DOI: 10.1002/qua.25569

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