Conjugated circuits currents in hexabenzocoronene and its derivatives formed by joining proximal carbons

The conjugated circuits model is applied to heterocycles containing divalent sulfur. A novel parametrization is introduced for 4n + 2 and 4n conjugated circuits containing a single sulfur atom. The relative aromatic stabilities of a number of heterocyclic systems containing divalent sulfur are studied. Comparison is made whenever possible with earlier reported resonance energies of these compounds, obtained by using Huckel MO and SCF π-MO models, and appropriate reference structures. Special attention is given to positional isomers. An explanation of the differences amongst such isomers is given.

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Conjugated Circuits

Introduction to the Theory of Benzenoid Hydrocarbons ◽

10.1007/978-3-642-87143-6_6 ◽

1989 ◽

pp. 79-91

Author(s):

Ivan Gutman ◽

Sven Josef Cyvin

Keyword(s):

Conjugated Circuits

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Combinatorics of Edge Symmetry: Chiral and Achiral Edge Colorings of Icosahedral Giant Fullerenes: C80, C180, and C240

Symmetry ◽

10.3390/sym12081308 ◽

2020 ◽

Vol 12 (8) ◽

pp. 1308

Author(s):

Krishnan Balasubramanian

Keyword(s):

Equivalence Classes ◽

Group Symmetry ◽

Irreducible Representations ◽

Inversion Method ◽

High Symmetry ◽

Edge Colorings ◽

Edge Group ◽

Resonance Energies ◽

Conjugated Circuits ◽

Cycle Indices

We develop the combinatorics of edge symmetry and edge colorings under the action of the edge group for icosahedral giant fullerenes from C80 to C240. We use computational symmetry techniques that employ Sheehan’s modification of Pόlya’s theorem and the Möbius inversion method together with generalized character cycle indices. These techniques are applied to generate edge group symmetry comprised of induced edge permutations and thus colorings of giant fullerenes under the edge symmetry action for all irreducible representations. We primarily consider high-symmetry icosahedral fullerenes such as C80 with a chamfered dodecahedron structure, icosahedral C180, and C240 with a chamfered truncated icosahedron geometry. These symmetry-based combinatorial techniques enumerate both achiral and chiral edge colorings of such giant fullerenes with or without constraints. Our computed results show that there are several equivalence classes of edge colorings for giant fullerenes, most of which are chiral. The techniques can be applied to superaromaticity, sextet polynomials, the rapid computation of conjugated circuits and resonance energies, chirality measures, etc., through the enumeration of equivalence classes of edge colorings.

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