Abstract: MATH/CHEM/COMP 2002, Dubrovnik, June 24-29, 2002



Enumeration of Kekule structures in nanotubes


Istvan Lukovits, Peter Nagy, Jozsef Miklosi,

Franciska H. Karman, and Erika Kalman


Chemical Research Center, H-1525 Budapest, P.O.B. 17, Hungary




Nanotubes (NT) are carbon structures composed of hexagons and, in the case of bent NTs, of pentagons, and heptagons. It is an empirically established fact that the number of Kekulé structures in any benzenoid molecule is a characteristic feature accounting for the stability of the derivative. The aim of these investigations was to determine the number of Kekulé structures, K, and also other indices of aromaticity in various types of NTs. K has been determined for tubulenes1 (i.e. NTs without caps). The aim of this paper was to extend these investigations to include capped NTs (nanocapsules) and also chiral NTs. Therefore zig-zag (polyacenes) and armchair (polyphenantrenes) strips and their cyclic variants have been considered and the “thickness” of these strips was gradually extended. Preliminary results indicate that there is no difference between strips and their cyclic analogues, but there is a profound difference in the aromaticity of cyclic polyacenes and polyphenantrene strips. The aromaticity of chiral strips may be in between these limits. The presence of caps stabilises the polyacene strips, but (most probably) does not affect aromaticity of polyphenantrene strips. The present approach will allow us to investigate modified NTs as well.


1H. Sachs, P. Hansen, M. Zheng, Commun. Math. Chem. 33 (1996) 169.