A combination of Clar number and Kekulé count as an indicator of relative stability of fullerene isomers of C60

Zhang, Heping; Ye, Dong; Liu, Yunrui

doi:10.1007/s10910-010-9706-2

Cited by 18 publications

(16 citation statements)

References 34 publications

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“…However, out of the 18 fullerenes with Clar number 8, C 60 has the largest Kekulé count. 208 Fowler showed that leapfrog transforms of fullerenes not only are closed shell, but also have the maximum proportion of benzenoid hexagons. 209 …”

Section: Topological Properties Of Fullerenesmentioning

confidence: 99%

The topology of fullerenes

Schwerdtfeger

Wirz

Avery

2014

WIREs Comput Mol Sci

183

168

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Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96–145. doi: 10.1002/wcms.1207Conflict of interest: The authors have declared no conflicts of interest for this article.For further resources related to this article, please visit the WIREs website.

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Section: Topological Properties Of Fullerenesmentioning

confidence: 99%

The topology of fullerenes

Schwerdtfeger

Wirz

Avery

2014

WIREs Comput Mol Sci

183

168

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“…So, the maximality of Kekulé counts of fullerene isomers may not correspond to the highest stability. Zhang et al [72] turned to investigating a significant role of the Clar numbers of fullerenes in their stabilities. Zhang and Ye [73] obtained the sharp upper bound for the Clar number of fullerenes as follows.…”

Section: Stability Indicatorsmentioning

confidence: 99%

Advances of Clar's Aromatic Sextet Theory and Randic´'s Conjugated Circuit Model

Zhang¹

2011

TOOCJ

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Clar's aromatic sextet theory provides a good means to describe the aromaticity of benzenoid hydrocarbons, which was mainly based on experimental observations. Clar defined sextet pattern and Clar number of benzenoid hydrocarbons, and he observed that for isomeric benzenoid hydrocarbons, when Clar number increases the absorption bands shift to shorter wavelength, and the stability of these isomers also increases. Motivated by Clar's aromatic sextet theory, three types of polynomials (sextet polynomial, Clar polynomial, and Clar covering polynomial) were defined, and Randic´'s conjugated circuit model was also established. In this survey we attempt to review some advances on Clar's aromatic sextet theory and Randic´'s conjugated circuit model in the past two decades. New applications of these polynomials to fullerenes, and calculation methods of linear independent and minimal conjugated circuit polynomials of benzenoid hydrocarbons are also presented.

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“…Only relatively recently was it understood that the correct perspective comes not only from looking at the number of Kekulé structures, but also at their Clar numbers, i.e., the maximal number of aromatic Clar sextets [56] that can be accommodated by the fullerene graph. Zhang and collaborators demonstrated [57] that the icosahedral C 60 indeed has the highest Kekulé count among the isomers of C 60 with the largest Clar number, Cl = 8. There exists 18 of such isomers and the second highest Kekulé count among them is 11,259, about 10% lower than for the I h isomer.…”

Section: Introductionmentioning

confidence: 99%

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

Witek

Kang

2020

Symmetry

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A compilation of ZZ polynomials (aka Zhang–Zhang polynomials or Clar covering polynomials) for all isomers of small (5,6)-fullerenes Cn 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 Cl, the first Herndon number h1, 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.

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A combination of Clar number and Kekulé count as an indicator of relative stability of fullerene isomers of C60

Cited by 18 publications

References 34 publications

The topology of fullerenes

The topology of fullerenes

Advances of Clar's Aromatic Sextet Theory and Randic´'s Conjugated Circuit Model

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

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