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Open AccessArticle
Kekulé Counts, Clar Numbers, and ZZ Polynomials for All Isomers of (5,6)-fullerenes C52–C70
by
Henryk A. Witek
Henryk A. Witek 1,*
and
Rafał Podeszwa
Rafał Podeszwa 2,*
1
Department of Applied Chemistry and Institute of Molecular Science, National Yang Ming Chiao Tung University, Hsinchu 300093, Taiwan
2
Institute of Chemistry, University of Silesia in Katowice, Szkolna 9, 40-006 Katowice, Poland
*
Authors to whom correspondence should be addressed.
Molecules 2024, 29(17), 4013; https://doi.org/10.3390/molecules29174013 (registering DOI)
Submission received: 18 July 2024
/
Revised: 13 August 2024
/
Accepted: 19 August 2024
/
Published: 24 August 2024
Abstract
We report an extensive tabulation of several important topological invariants for all the isomers of carbon -fullerenes with . 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 C–C.
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MDPI and ACS Style
Witek, H.A.; Podeszwa, R.
Kekulé Counts, Clar Numbers, and ZZ Polynomials for All Isomers of (5,6)-fullerenes C52–C70. Molecules 2024, 29, 4013.
https://doi.org/10.3390/molecules29174013
AMA Style
Witek HA, Podeszwa R.
Kekulé Counts, Clar Numbers, and ZZ Polynomials for All Isomers of (5,6)-fullerenes C52–C70. Molecules. 2024; 29(17):4013.
https://doi.org/10.3390/molecules29174013
Chicago/Turabian Style
Witek, Henryk A., and Rafał Podeszwa.
2024. "Kekulé Counts, Clar Numbers, and ZZ Polynomials for All Isomers of (5,6)-fullerenes C52–C70" Molecules 29, no. 17: 4013.
https://doi.org/10.3390/molecules29174013
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