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Kekulé Counts, Clar Numbers, and ZZ Polynomials for All Isomers of (5,6)-Fullerenes C₅₂–C₇₀

by Henryk A. Witek and Rafał Podeszwa

Molecules 2024, 29(17), 4013; https://doi.org/10.3390/molecules29174013 - 24 Aug 2024

Viewed by 1673

We report an extensive tabulation of several important topological invariants for all the isomers of carbon

(5, 6)

-fullerenes

C_{n}

with n = 52–70. The topological invariants (including Kekulé count, Clar count, and Clar number) are computed and reported [...] Read more.

We report an extensive tabulation of several important topological invariants for all the isomers of carbon

(5, 6)

-fullerenes

C_{n}

with n = 52–70. The topological invariants (including Kekulé count, Clar count, and Clar number) are computed and reported in the form of the corresponding Zhang–Zhang (ZZ) polynomials. The ZZ polynomials appear to be distinct for each isomer cage, providing a unique label that allows for differentiation between various isomers. Several chemical applications of the computed invariants are reported. The results suggest rather weak correlation between the Kekulé count, Clar count, Clar number invariants, and isomer stability, calling into doubt the predictive power of these topological invariants in discriminating the most stable isomer of a given fullerene. The only exception is the Clar count/Kekulé count ratio, which seems to be the most important diagnostic discovered from our analysis. Stronger correlations are detected between Pauling bond orders computed from Kekulé structures (or Clar covers) and the corresponding equilibrium bond lengths determined from the optimized DFTB geometries of all 30,579 isomers of C₂₀–C₇₀. Full article

(This article belongs to the Special Issue Multiconfigurational and DFT Methods Applied to Chemical Systems—2nd Edition)

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47 pages, 6519 KiB

Open AccessArticle

ZZ Polynomials for Isomers of (5,6)-Fullerenes C_n with n = 20–50

by Henryk A. Witek and Jin-Su Kang

Symmetry 2020, 12(9), 1483; https://doi.org/10.3390/sym12091483 - 9 Sep 2020

Cited by 13 | Viewed by 2963

Abstract

A compilation of ZZ polynomials (aka Zhang–Zhang polynomials or Clar covering polynomials) for all isomers of small (5,6)-fullerenes C

_{n}

with n = 20–50 is presented. The ZZ polynomials concisely summarize the most important topological invariants of the fullerene isomers: the number of [...] Read more.

A compilation of ZZ polynomials (aka Zhang–Zhang polynomials or Clar covering polynomials) for all isomers of small (5,6)-fullerenes C

_{n}

with n = 20–50 is presented. The ZZ polynomials concisely summarize the most important topological invariants of the fullerene isomers: the number of Kekulé structures K, the Clar number

C l

, the first Herndon number

h_{1}

, the total number of Clar covers C, and the number of Clar structures. The presented results should be useful as benchmark data for designing algorithms and computer programs aiming at topological analysis of fullerenes and at generation of resonance structures for valence-bond quantum-chemical calculations. Full article

(This article belongs to the Section Chemistry: Symmetry/Asymmetry)

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