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Journal articles on the topic 'Or Kekul'e structures)'

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Published: 5 June 2025

Last updated: 1 August 2025

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1

Balaban, Alexandru, and Milan Randić. "Perfect Matchings in Polyhexes, or Recent Graph-theoretical Contributions to Benzenoids." JUCS - Journal of Universal Computer Science 13, no. (11) (2007): 1514–39. https://doi.org/10.3217/jucs-013-11-1514.

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After an introduction on the history of polycyclic aromatic compounds, recent advances in the theory of benzenoids are briefly reviewed. Then using systems with 4, 5, or 6 benzenoid rings for illustration, the partition of the P π-electrons among the rings of the benzenoid is presented, followed by a different way of examining the distribution of these π-electrons which is called the signature of the benzenoid, consisting in six integers from s6 to s1. The P π-electrons are divided between the two sums s6 + s5 + s2 + s1 and s4 + s3 characterizing thereby the closeness of benzenoids to all-reso

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2

Gutman, Ivan. "Kekulé Structures in Fluoranthenes." Zeitschrift für Naturforschung A 65, no. 5 (2010): 473–76. http://dx.doi.org/10.1515/zna-2010-0513.

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Fluoranthenes are polycyclic conjugated molecules consisting of two benzenoid fragments, connected by two carbon-carbon bonds so as to form a five-membered ring. Fluoranthenes possessing Kekul´e structures are classified into three types, depending on the nature of the two carbon-carbon bonds connecting the two benzenoid fragments. Either both these bonds are essentially single (i. e., single in all Kekul´e structures), or both are essentially double (i. e., double in all Kekul´e structures), or one is essentially single and the other is essentially double. All Kekul´ean fluoranthenes have equ

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3

Klein, D. J. "Aromaticity via Kekule structures and conjugated circuits." Journal of Chemical Education 69, no. 9 (1992): 691. http://dx.doi.org/10.1021/ed069p691.

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4

Cyvin, S. J., J. Brunvoll, and B. N. Cyvin. "Distribution of K , the Number of Kekulé Structures in Benzenoid Hydrocarbons Part IV. Benzenoids with 10 and 11 Hexagons." Zeitschrift für Naturforschung A 41, no. 12 (1986): 1429–30. http://dx.doi.org/10.1515/zna-1986-1212.

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An approximate asymptotic formula is derived for the number of normal benzenoids. For this category and h (number of hexagons) = 10 and 11 all numbers of Kekulfe structures were computer and systematized.

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5

Cigher, S., D. Vukičević, and M. V. Diudea. "On Kekulé structures count." Journal of Mathematical Chemistry 45, no. 2 (2008): 279–86. http://dx.doi.org/10.1007/s10910-008-9404-5.

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6

Brendsdal, E., and S. J. Cyvin. "Kekulé structures of footballene." Journal of Molecular Structure: THEOCHEM 188, no. 1-2 (1989): 55–66. http://dx.doi.org/10.1016/0166-1280(89)85025-0.

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7

Křivka, Pavel, and Nenad Trinajstić. "Parity of Kekulé structures revisited." Collection of Czechoslovak Chemical Communications 50, no. 2 (1985): 291–99. http://dx.doi.org/10.1135/cccc19850291.

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8

King, R. Bruce. "Strained Configurations in Three-Dimensional Analogues of Kekulé-Type Structures for Deltahedral Boranes." Collection of Czechoslovak Chemical Communications 67, no. 6 (2002): 751–68. http://dx.doi.org/10.1135/cccc20020751.

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Localized structures analogous to the Kekulé structures for benzenoid hydrocarbons can be constructed for the deltahedral boranes BnHn2-. These localized structures contain exactly three two-center two-electron (2c-2e) B-B bonds and n - 2 three-center two-electron (3c-2e) B-B-B bonds. The number of equivalent such Kekulé-type structures corresponds to the index of the symmetry group of the Kekulé structure, K, in the symmetry group, D, of the deltahedron. Three-dimensional Kekulé-type structures with the following configurations exhibit excessive strain and are therefore unfavorable: (i) struc

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9

Hansen, Pierre, and Maolin Zheng. "The Maximum Number of Kekule Structures of Cata-condensed Polyhexes." Zeitschrift für Naturforschung A 48, no. 10 (1993): 1031–38. http://dx.doi.org/10.1515/zna-1993-1012.

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Abstract Let H denote a simply-connected cata-condensed polyhex. It is shown that if H has three hexagons in a row it does not have a maximum number of Kekulé structures. Otherwise, its number of Kekulé structures is equal to its number of sets of disjoint hexagons (including the empty set). These results lead to an efficient algorithm to determine simply-connected cata-condensed polyhexes with a maximum number of Kekulé structures. A table of such values of H with up to 100 hexagons is provided.

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10

Vukicevic, Damir, Jelena Djurdjevic, and Ivan Gutman. "On the number of Kekulé structures of fluoranthene congeners." Journal of the Serbian Chemical Society 75, no. 8 (2010): 1093–98. http://dx.doi.org/10.2298/jsc091207077v.

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The Kekul? structure count K of fluoranthene congeners is studied. It is shown that for such polycyclic conjugated ?-electron systems, either K = 0 or K ? 3. Moreover, for every t ? 3, there are infinitely many fluoranthene congeners having exactly t Kekul? structures. Three classes of Kekul?an fluoranthenes are distinguished: (i) ?0 - fluoranthene congeners in which neither the male nor the female benzenoid fragment has Kekul? structures, (ii) ?m - fluoranthene congeners in which the male benzenoid fragment has Kekul? structures, but the female does not, and (iii) ?fm - fluoranthene congeners

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11

Hashimoto, Shingo, and Kazukuni Tahara. "Theoretical Study on the Structures, Electronic Properties, and Aromaticity of Thiophene Analogues of Anti-Kekulene." Chemistry 4, no. 4 (2022): 1546–60. http://dx.doi.org/10.3390/chemistry4040102.

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We predict the geometries, electronic properties, and aromaticity of thiophene analogues of anti-kekulene with six to nine thiophene rings 1–4, together with those of cyclobutadithiophenes (CDTs) and anti-kekulene as reference compounds, using density functional theory calculations. Investigation of the simplest reference compounds, CDTs, reveals that the local aromaticity of their thiophene rings is influenced by their fused position (b- or c-bond) to the four-membered ring (4MR). A thiophene ring fused at the b-position (b-TR) retains its aromatic character to some extent, whereas the aromat

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12

Li, Jiayue. "Overview of benzene and exploration of benzene structure." Theoretical and Natural Science 21, no. 1 (2023): 245–52. http://dx.doi.org/10.54254/2753-8818/21/20230889.

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Benzene is a hydrocarbon the simplest aromatics. But the search for benzenes structure has been tortuous. This article mainly introduces the basic properties of benzene. From the physical properties of benzene to the chemical properties of benzene to the uses of benzene. In this work, we also summarize the process of scientists exploration of benzene structure and introduce the background of benzene. Of all the structures of benzene, the Kekule structure is the most recognized structure. We have proved the correctness of the Kekule structure by the product of the ozonation decomposition reacti

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13

Nguyen, Ngoc Hieu, and Van Hung Le. "Geometrical Structure of Carbon Nanotubes with Alternation Pattern." Advanced Materials Research 811 (September 2013): 157–62. http://dx.doi.org/10.4028/www.scientific.net/amr.811.157.

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In this paper we consider the geometrical structure of carbon nanotubes with artificially inplanebond alternation. The quinoid and the Kekule structures of carbon nanotubes with two differentbond lengths are fully described for various symmetries, including chiral and achiral carbon nanotubes.Consideration of the geometrical structure or the atomic structure is the first step for studies of carbonnanotubes with dimerization structures.

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14

Vukičević, Damir, and Milan Randić. "On Kekulé structures of buckminsterfullerene." Chemical Physics Letters 401, no. 4-6 (2005): 446–50. http://dx.doi.org/10.1016/j.cplett.2004.11.098.

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15

Miličević, Ante, Sonja Nikolić, and N. Trinajstić. "Coding and Ordering Kekulé Structures†." Journal of Chemical Information and Computer Sciences 44, no. 2 (2004): 415–21. http://dx.doi.org/10.1021/ci0304270.

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16

R.B.M. "Kekulé Structures in Benzenoid Hydrocarbons." Journal of Molecular Structure 197 (June 1989): 373–74. http://dx.doi.org/10.1016/0022-2860(89)85179-8.

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17

Trinajstić, Nenad, and Damir Vukičević. "Mathematical studies of Kekulé structures." Structural Chemistry 18, no. 6 (2007): 807–12. http://dx.doi.org/10.1007/s11224-007-9241-3.

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18

Hall, George G. "Aromaticity measured by Kekulé structures." International Journal of Quantum Chemistry 39, no. 4 (1991): 605–13. http://dx.doi.org/10.1002/qua.560390407.

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19

Cyvin, S. J. "Enumeration of kekulé structures: Chevrons." Journal of Molecular Structure: THEOCHEM 133 (November 1985): 211–19. http://dx.doi.org/10.1016/0166-1280(85)85018-1.

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20

Cyvin, S. J., B. N. Cyvin, and I. Gutman. "Number of Kekule Structures of Systems with Repeated Units." Zeitschrift für Naturforschung A 42, no. 2 (1987): 181–86. http://dx.doi.org/10.1515/zna-1987-0211.

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21

Deogun, Jitender S., Xiaofeng Guo, Wandi Wei, and Fuji Zhang. "Catacondensed hexagonal systems with smaller numbers of Kekule structures." Journal of Molecular Structure: THEOCHEM 639, no. 1-3 (2003): 101–8. http://dx.doi.org/10.1016/s0166-1280(03)00602-x.

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22

Hu, Xiaoguang, Lei Zhao, Hanjiao Chen, et al. "Air stable high-spin blatter diradicals: non-Kekulé versus Kekulé structures." Journal of Materials Chemistry C 7, no. 22 (2019): 6559–63. http://dx.doi.org/10.1039/c8tc05150j.

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23

Gutman, Ivan, Damir Vukičević, Ante Graovac, and Milan Randić. "Algebraic Kekulé Structures of Benzenoid Hydrocarbons†." Journal of Chemical Information and Computer Sciences 44, no. 2 (2004): 296–99. http://dx.doi.org/10.1021/ci030417z.

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24

Graovc, A., D. Babić, and M. Strunje. "Enumeration of kekulé structures in polymers." Chemical Physics Letters 123, no. 5 (1986): 433–36. http://dx.doi.org/10.1016/0009-2614(86)80037-9.

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25

Cyvin, S. J., and I. Gutman. "Kekulé structures and their symmetry properties." Computers & Mathematics with Applications 12, no. 3-4 (1986): 859–76. http://dx.doi.org/10.1016/0898-1221(86)90430-x.

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26

Bogaerts, Mathieu, Giuseppe Mazzuoccolo, and Gloria Rinaldi. "Invariant Kekulé structures in fullerene graphs." Electronic Notes in Discrete Mathematics 40 (May 2013): 323–27. http://dx.doi.org/10.1016/j.endm.2013.05.057.

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27

Cyvin, S. J., and B. N. Cyvin. "Enumeration of kekulé structures: Prolate pentagons." Journal of Molecular Structure: THEOCHEM 152, no. 3-4 (1987): 347–50. http://dx.doi.org/10.1016/0166-1280(87)80075-1.

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28

Rong-Si, Chen, and S. J. Cyvin. "Enumeration of kekulé structures: perforated rectangles." Journal of Molecular Structure: THEOCHEM 200 (October 1989): 251–60. http://dx.doi.org/10.1016/0166-1280(89)85058-4.

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29

Shimizu, Akihiro. "m-Quinodimethane-Based Fused-Ring Diradicals with Singlet and Triplet Ground States." Chemistry 7, no. 2 (2025): 40. https://doi.org/10.3390/chemistry7020040.

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Diradicals have attracted the attention of chemists due to their unique electronic structures and properties originating from unpaired electrons. One of the fundamental motifs of diradicals is quinodimethane; p- and o-quinodimethanes are singlet Kekulé hydrocarbons, while m-quinodimethane is a triplet non-Kekulé hydrocarbon. Most of the hydrocarbon diradicals studied to date have been limited to p- and o-quinodimethane-based non-fused-ring and fused-ring open-shell singlet diradicals and m-quinodimethane-based non-fused-ring triplet diradicals. In this account, studies on m-quinodimethane-base

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30

Sakurai, Katsunori, and Kichisuke Nishimoto. "Intrinsic energy of partial structure." Collection of Czechoslovak Chemical Communications 53, no. 10 (1988): 2339–52. http://dx.doi.org/10.1135/cccc19882339.

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A modified model Hamiltonian has been proposed for the analysis of a given partial structure in the molecule. With this Hamiltonian, some interesting mirror image relationships have been derived. The calculated results for the intrinsic energies of hexagons (Benzene Character) in hydrocarbons showed that the stability of hexagon is well correlated with the number of Kekule structures.

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31

Cyvin, S. J., B. N. Cyvin, and I. Gutman. "Number of Kekulé Structures of Five-Tier Strips." Zeitschrift für Naturforschung A 40, no. 12 (1985): 1253–61. http://dx.doi.org/10.1515/zna-1985-1211.

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Benzenoid systems called regular t-tier strips are examined. 27 classes of benzenoids belonging to the regular 5-tier strips can be distinguished. Combinatorial formulas are developed for the number of Kekulé structures of all these classes.

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32

El-Basil, Sherif. "Kekul� structures as graph generators." Journal of Mathematical Chemistry 14, no. 1 (1993): 305–18. http://dx.doi.org/10.1007/bf01164473.

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33

Rogers, Kevin M., and Patrick W. Fowler. "ChemInform Abstract: Leapfrog Fullerenes, Hueckel Bond Order and Kekule Structures." ChemInform 32, no. 16 (2001): no. http://dx.doi.org/10.1002/chin.200116026.

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34

Ferro-Costas, David, and Ricardo A. Mosquera. "Revisiting Lewis dot structure weightings: a pair density perspective." Physical Chemistry Chemical Physics 17, no. 11 (2015): 7424–34. http://dx.doi.org/10.1039/c4cp05548a.

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35

Eom, Daejin, and Ja-Yong Koo. "Direct measurement of strain-driven Kekulé distortion in graphene and its electronic properties." Nanoscale 12, no. 38 (2020): 19604–8. http://dx.doi.org/10.1039/d0nr03565c.

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36

Prabhu, S., M. Arulperumjothi, Muhammad Usman Ghani, Muhammad Imran, S. Salu, and Bibin K. Jose. "Computational Analysis of Some More Rectangular Tessellations of Kekulenes and Their Molecular Characterizations." Molecules 28, no. 18 (2023): 6625. http://dx.doi.org/10.3390/molecules28186625.

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Cycloarene molecules are benzene-ring-based polycyclic aromatic hydrocarbons that have been fused in a circular manner and are surrounded by carbon–hydrogen bonds that point inward. Due to their magnetic, geometric, and electronic characteristics and superaromaticity, these polycyclic aromatics have received attention in a number of studies. The kekulene molecule is a cyclically organized benzene ring in the shape of a doughnut and is the very first example of such a conjugated macrocyclic compound. Due to its structural characteristics and molecular characterizations, it serves as a great mod

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37

Lin, Xuhui, Zhenhua Chen та Wei Wu. "The driving force for Π-bond localization and bond alternation in trisannelated benzenes". Physical Chemistry Chemical Physics 19, № 4 (2017): 3019–27. http://dx.doi.org/10.1039/c6cp06915k.

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38

Lukovits, István, Ante Graovac, Erika Kálmán, et al. "Nanotubes: Number of Kekulé Structures and Aromaticity." Journal of Chemical Information and Computer Sciences 43, no. 2 (2003): 609–14. http://dx.doi.org/10.1021/ci020059k.

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39

Morikawa, Tetsuo. "Enumeration of Kekulé structures in polyradical polyhexes." Computers & Chemistry 20, no. 2 (1996): 159–65. http://dx.doi.org/10.1016/0097-8485(95)00070-4.

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40

Lin, Yixun, and Fuji Zhang. "Recognizing Kekulé structures in polycyclic aromatic hydrocarbons." Journal of Molecular Structure: THEOCHEM 342 (October 1995): 197–200. http://dx.doi.org/10.1016/0166-1280(95)90119-1.

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41

Hall, George G. "Enumeration of Kekulé structures by matrix methods." Chemical Physics Letters 145, no. 2 (1988): 168–72. http://dx.doi.org/10.1016/0009-2614(88)80172-6.

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42

Kiang, Yuan-Sun. "Determinant of adjacency matrix and kekulé structures." International Journal of Quantum Chemistry 18, S14 (2009): 541–47. http://dx.doi.org/10.1002/qua.560180855.

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43

Gutman, I., Y. N. Yeh, S. L. Lee, H. Hosoya, and S. J. Cyvin. "Calculating the Determinant of the Adjacency Matrix and Counting Kekulé Structures in Circulenes." Zeitschrift für Naturforschung A 49, no. 11 (1994): 1053–58. http://dx.doi.org/10.1515/zna-1994-1110.

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44

Greeni, A. Berin, and V. Vinitha Navis. "Acyclic Coloring of Certain Graphs." Journal of Advanced Computational Intelligence and Intelligent Informatics 27, no. 1 (2023): 101–4. http://dx.doi.org/10.20965/jaciii.2023.p0101.

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A graph G with acyclic coloring has no two adjacent vertices with the same color and no bichromatic cycle. Also, the coloring results in a forest when any two-color classes are combined. The concept of acyclic coloring plays a pivotal role in the computation of Hessians, Kekule structures classification, coding theory, and statistical mechanics. In this paper, the acyclic chromatic number of generalized fan graph, generalized Möbius ladder graph and flower snark graph have been determined.

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45

Miller, Ian J. "Semiclassical Quantum Mechanics, Bond Delocalization and the Mills - Nixon Effect." Australian Journal of Chemistry 50, no. 8 (1997): 795. http://dx.doi.org/10.1071/c96161.

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Conjugated π electrons in a ring system are described in terms of a transverse wave propagated along the carbon skeleton. Kekule benzene is forbidden because the π electron quantal wave self-interferes. The characteristics of an aromatic system are expressed in terms of the weighted combination of Kekule structures, and resonance energy occurs through combining canonical structures with conservation of momentum. The resonance energy of benzene is calculated as 1·045 times the energy difference between two carbon-carbon single bonds and one double bond, or 162 kJ/mol on one bond energy scheme.

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46

Witek, Henryk A., and Johanna Langner. "Clar Covers of Overlapping Benzenoids: Case of Two Identically-Oriented Parallelograms." Symmetry 12, no. 10 (2020): 1599. http://dx.doi.org/10.3390/sym12101599.

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We present a complete set of closed-form formulas for the ZZ polynomials of five classes of composite Kekuléan benzenoids that can be obtained by overlapping two parallelograms: generalized ribbons Rb, parallelograms M, vertically overlapping parallelograms MvM, horizontally overlapping parallelograms MhM, and intersecting parallelograms MxM. All formulas have the form of multiple sums over binomial coefficients. Three of the formulas are given with a proof based on the interface theory of benzenoids, while the remaining two formulas are presented as conjectures verified via extensive numerica

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47

Rogers, Kevin M., and Patrick W. Fowler. "Leapfrog fullerenes, Hückel bond order and Kekulé structures." Journal of the Chemical Society, Perkin Transactions 2, no. 1 (2001): 18–22. http://dx.doi.org/10.1039/b007520p.

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48

Wang, Wen-Huan, An Chang, and Dong-Qiang Lu. "Unicyclic Graphs Possessing Kekulé Structures with Minimal Energy." Journal of Mathematical Chemistry 42, no. 3 (2006): 311–20. http://dx.doi.org/10.1007/s10910-006-9096-7.

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49

Hosoya, Haruo, and Ivan Gutman. "Kekulé structures of hexagonal chains—some unusual connections." Journal of Mathematical Chemistry 44, no. 2 (2007): 559–68. http://dx.doi.org/10.1007/s10910-007-9329-4.

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50

Bodroža, O., I. Gutman, S. J. Cyvin, and R. Tošić. "Number of Kekulé structures of hexagon-shaped benzenoids." Journal of Mathematical Chemistry 2, no. 3 (1988): 287–98. http://dx.doi.org/10.1007/bf01167208.

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