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Journal articles on the topic 'Kekulé structures'

Author: Grafiati

Published: 2 June 2025

Last updated: 19 July 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

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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15

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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16

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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17

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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18

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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19

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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20

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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21

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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22

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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23

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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24

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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25

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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26

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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27

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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28

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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29

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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30

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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31

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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32

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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33

Tošić, R., and S. J. Cyvin. "Enumeration of Kekulé structures in benzenoid hydrocarbons: “flounders”." Journal of Mathematical Chemistry 3, no. 4 (1989): 393–401. http://dx.doi.org/10.1007/bf01169020.

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34

Dias, Jerry Ray. "Kekulé structures and algebraic or corrected structure count." Journal of Molecular Structure: THEOCHEM 206, no. 1-2 (1990): 1–10. http://dx.doi.org/10.1016/0166-1280(90)85001-4.

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35

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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36

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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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

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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39

Witek, Henryk A., and Rafał Podeszwa. "Kekulé Counts, Clar Numbers, and ZZ Polynomials for All Isomers of (5,6)-Fullerenes C52–C70." Molecules 29, no. 17 (2024): 4013. http://dx.doi.org/10.3390/molecules29174013.

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We report an extensive tabulation of several important topological invariants for all the isomers of carbon (5,6)-fullerenes Cn 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,

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40

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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41

Ghorbani, Modjtaba, and Ehtram Naserpour. "Study of Some Nanostructures by Using Their Kekulé Structures." Journal of Computational and Theoretical Nanoscience 10, no. 9 (2013): 2260–63. http://dx.doi.org/10.1166/jctn.2013.3195.

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42

Klavžar, Sandi, Aleksander Vesel, Petra Žigert, and Ivan Gutman. "Binary coding of Kekulé structures of catacondensed benzenoid hydrocarbons." Computers & Chemistry 25, no. 6 (2001): 569–75. http://dx.doi.org/10.1016/s0097-8485(01)00068-7.

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43

Gutman, Ivan, and Sven J. Cyvin. "A new method for the enumeration of kekulé structures." Chemical Physics Letters 136, no. 2 (1987): 137–40. http://dx.doi.org/10.1016/0009-2614(87)80431-1.

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44

Gutman, I., and S. J. Cyvin. "Number of Kekulé structures in antikekulene and its homologs." Journal of Molecular Structure: THEOCHEM 288, no. 1-2 (1993): 85–91. http://dx.doi.org/10.1016/0166-1280(93)90097-u.

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45

Sheng, Rong-qin. "Identification of the Kekulé, structures of a hexagonal system." Chemical Physics Letters 142, no. 3-4 (1987): 196–99. http://dx.doi.org/10.1016/0009-2614(87)80921-1.

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46

Gutman, Ivan, and Sven J. Cyvin. "The number of Kekulé, structures in long benzenoid chains." Chemical Physics Letters 147, no. 1 (1988): 121–25. http://dx.doi.org/10.1016/0009-2614(88)80235-5.

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47

Cyvin, S. J. "The number of Kekulé structures for primitive coronoids (cycloarenes)." Chemical Physics Letters 147, no. 4 (1988): 384–88. http://dx.doi.org/10.1016/0009-2614(88)80253-7.

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48

Zeng, Chenjie, Yuxiang Chen, Chong Liu, Katsuyuki Nobusada, Nathaniel L. Rosi, and Rongchao Jin. "Gold tetrahedra coil up: Kekulé-like and double helical superstructures." Science Advances 1, no. 9 (2015): e1500425. http://dx.doi.org/10.1126/sciadv.1500425.

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Magic-sized clusters, as the intermediate state between molecules and nanoparticles, exhibit critical transitions of structures and material properties. We report two unique structures of gold clusters solved by x-ray crystallography, including Au40and Au52protected by thiolates. The Au40and Au52clusters exhibit a high level of complexity, with the gold atoms in the cluster first segregated into four-atom tetrahedral units—which then coil up into a Kekulé-like ring in the Au40cluster and a DNA-like double helix in Au52. The solved structures imply a new “supermolecule” origin for revealing the

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49

Qian, Jianguo, and Fuji Zhang. "On the number of Kekulé structures in capped zigzag nanotubes." Journal of Mathematical Chemistry 38, no. 2 (2005): 233–46. http://dx.doi.org/10.1007/s10910-005-5410-z.

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50

Zhang, Lianzhu, Shouliu Wei, and Fuliang Lu. "The number of Kekulé structures of polyominos on the torus." Journal of Mathematical Chemistry 51, no. 1 (2012): 354–68. http://dx.doi.org/10.1007/s10910-012-0087-6.

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