Systematic Construction and Calculation of Electronic Properties of Fullerene Series Related by Rotational Symmetry: From Fullerenes to Bicapped Nanotubes

Abstract

The results herein demonstrate that the methods of circumscribing and the facile calculation of Hückel molecular orbital (HMO) eigenvalues by mirror-plane fragmentation have a broad application in the construction of carbon cluster series and the systematic study of trends in their electronic properties. In comparing open-ended nanotubes and their isomeric elongated fullerenes (bicapped nanotubes), we show that the former are more aromatic but the latter are more conjugated and that progressive elongation increases aromaticity and conjugation in both. Recursion equations that will allow one to obtain the eigenvalues to all 5-endcapped nanotubes are given.

Combinatorics of Supergiant Fullerenes: Enumeration of Polysubstituted Isomers, Chirality, Nuclear Magnetic Resonance, Electron Spin Resonance Patterns, and Vibrational Modes from C70to C150000

“…Pioneered by the Nobel-winning discovery of Buckminsterfullerene, C 60, several studies have focused on the formation and synthesis, − chirality, ,− spherical aromaticity, ,− electronic and spectroscopic properties of both large fullerenes and their derivatives, − orbitals, aromaticity, and related properties of larger fullerenes, nanomaterials, and related benzenoids, − culminating into a recent combinatorial design of molecular seeds for chirality-controlled synthesis of nanotubes . Owing to the aesthetic beauty of the spherical dome and icosahedral symmetry of many of the fullerene molecular structures, several studies have been carried out on symmetry, combinatorics, chirality, enumeration of conjugated circuits and ring currents, aromaticity, spherical aromaticity, and superaromaticity, and polysubstituted isomers along with graph and group theoretical studies of fullerenes over the years. − <...…”

“…Combinatorial enumerations are especially useful in planning and execution of a controlled synthesis of derivatives of fullerenes and nanomaterials for which the number of isomers tends to explode combinatorially. Combinatorial tools have also provided Clar’s sextets and related measures for the rapid computations and enumerations of conjugated circuits, which have in turn resulted in efficient computation of resonance energies, conjugated circuits, and electronic and magnetic properties of fullerenes and related benzenoids thus providing new insight into aromaticity and superaromaticity. − …”