Are thermodynamic and kinetic stabilities correlated? A topological index of reactivity toward electrophiles used as a criterion of aromaticity of polycyclic benzenoid hydrocarbons

Journal of Chemical Information and Modeling

Volumn 49, Issue 2, 2009, Pages 369-376

  Ciesielski, Arkadiusz ^a,b   Krygowski, Tadeusz M ^b   Cyrański, Michał K ^b   Dobrowolski, Michał A ^b   Balaban, Alexandra T ^c  

^a INSTITUTE OF BIOCHEMISTRY AND BIOPHYSICS   (Poland)

^b UNIVERSITY OF WARSAW   (Poland)

^c TEXAS A AND M UNIVERSITY AT GALVESTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AROMATIZATION; HYDROCARBONS; MAGNETIC SUSCEPTIBILITY; MOLECULES; TOPOLOGY;

AROMATICITY INDICES; BENZENOID HYDROCARBONS; ELECTROPHILIC SUBSTITUTIONS; KINETIC STABILITY; LOCALIZATION ENERGY; NUMERICAL CHARACTERISTICS; RESONANCE ENERGIES; TOPOLOGICAL INDEX;

POLYCYCLIC AROMATIC HYDROCARBONS;

BENZENE; POLYCYCLIC HYDROCARBON;

ARTICLE; CHEMISTRY; KINETICS; THERMODYNAMICS;

BENZENE; KINETICS; POLYCYCLIC COMPOUNDS; THERMODYNAMICS;

EID: 65249134407     PISSN: 15499596     EISSN: 1549960X     Source Type: Journal    
DOI: 10.1021/ci800400b     Document Type: Article

References (103)

1. McWeeny, R. Couhon's Valence; Oxford University Press: Oxford, U.K., 1979; Preface.
2. Concluding remarks by the following: Bergmann E. D. In Aromaticity, Pseudoaromaticity, Antiaromaticity, Proceedings of an International Symposium held in Jerusalem 1970; Bergmann, E. D., Pullman, B., Eds.; Israel Academy of Science and Humanities: Jerusalem, 1971.
3. For other, wider use of the term, see: (a) Minkin, V. I.; Glukhovtsev, M. N.; Simkin, B. Ya. Aromaticity and Antiaromaticity; Wiley: New York, 1994.
4. (b) Special issue devoted to aromaticity. Chem. Rev. 2001, 101, 1115-1566.
5. (a) Elvidge, J. A.; Jackman, L. M. Studies of Aromaticity by Nuclear Magnetic Resonance Spectroscopy. Part I. 2-Pyridones and Related Systems. J. Chem. Soc. 1961, 859-866.
6. (b) Sondheimer, F. Recent Advances in the Chemistry of Large-Ring Conjugated Systems. Pure Appl. Chem. 1963, 7, 363-388.
7. (c) Dewar, M. J. S. A Molecular Orbital Theory of Organic Chemistry - VIII. Aromaticity and Electrocyclic Reactions. Tetrahedron Suppl. 1966, 8, 75-92.
8. (a) Katritzky, A. R.; Barczyñski, B.; Musumurra, G.; Pisano, D.; Szafran, M. Aromaticity as a Quantitative Concept. 1. A Statistical Demonstration of the Orthogonality of Classical and Magnetic Aromaticity in Five- and Six-Membered Heterocycles. J. Am. Chem. Soc. 1989, 111, 7-15.
9. (b) Jug, K.; Koster, A. Aromaticity as a Multi-Dimensional Phenomenon. J. Phys. Org. Chem. 1991, 4, 163-169.
10. (c) Krygowski, T. M.; Ciesielski, A.; Bird, C. W.; Kotschy, A. Aromatic Character of the Benzene Ring Present in Various Topological Environments in Benzenoid Hydrocarbons. Nonequivalence of Indices of Aromaticity. J. Chem. Inf. Comput. Sci. 1995, 35, 203-210.
11. (d) Katritzky, A. R.; Karelson, M.; Sild, S.; Krygowski, T. M.; Jug, K. Aromaticity as a Quantitative Concept. 7. Aromaticity Reaffirmed as a Multidimensional Characteristic. J. Org. Chem. 1998, 63, 5228-5231.
12. (e) Cyrański, M. K.; Krygowski, T. M.; Katritzky, A. R.; Schleyer, P. v. R. To What Extent Can Aromaticity Be Defined Uniquely. J. Org. Chem. 2002, 67, 1333-1338.
13. (f) Cyran̊ski, M. K.; Schleyer, P. v. R.; Krygowski, T. M.; Jiao, H. J.; Hohlneicher, G. Facts and Artifacts about Aromatic Stability Estimation. Tetrahedron 2003, 59, 1657-1665.
14. (g) Sadlej-Sosnowska, N. Mutual Relationships Between Magnetic Aromaticity Indices of Heterocyclic Compounds. J. Phys. Org. Chem. 2004, 17, 303-311.
15. Lazzaretti, P. Ring Currents. Prog. Nucl. Magn. Reson. Spectrosc. 2000, 36, 1-88.
16. (a) Katritzky, A. R.; Jug, K.; Onciu, D. C. Quantitative Measures of Aromaticity for Mono-, Bi-, and Tricyclic Penta- and Hexaatomic Heteroaromatic Ring Systems and Their Interrelationships. Chem. Rev. 2001, 101, 1421-1450.
17. (b) Balaban, A. T.; Oniciu, D.; Katritzky, A. R. Aromaticity as a Cornerstone of Heterocyclic Chemistry. Chem. Rev. 2004, 104, 2777-2812.
18. Schleyer, P. v. R.; Jiao, H. What Is Aromaticity. Pure Appl. Chem. 1996, 68, 209-218.
19. (a) Shaik, S. S.; Hiberty, P. C.; Ohanessian, G.; Lefour, J. M. Allylic Resonance is Forced Upon the π-System by the α-Framework. Nouv. J. Chim. 1985, 9, 385-388.
20. (b) Shaik, S. S.; Hiberty, P. C.; Ohanessian, G.; Lefour, J. M. Is the Delocalized π-System of Benzene a Stable Electronic System. J. Org. Chem. 1985, 50, 4657-4659.
21. (c) Shaik, S. S.; Hiberty, P. C.; Ohanessian, G.; Lefour, J. M. When Does Electronic Derealization Become a Driving Force of Chemical Bonding. J. Phys. Chem. 1988, 92, 5086-5094.
22. (d) Jug, K.; Köster, A. M. Influence of α and π Electrons on Aromaticity. J. Am. Chem. Soc. 1990, 112, 6772-6777.
23. (e) Shaik, S. S.; Shurki, A.; Danovich, D.; Hiberty, P. C. A Different Story of π-Delocalization - The Distortivity of π-Electrons and Its Chemical Manifestations. Chem. Rev. 2001, 101, 1501-1539.
24. (f) Maksić, Z. B.; Muller, T. Clar's Sextet Rule Is a Consequence of the α-Electron Framework. J. Phys. Chem. A 2006, 110, 10135-10147.
25. (g) Barić, D.; Kovacević, B.; Maksić, Z. B.; Muller, T. A Novel Approach in Analyzing Aromaticity by Homo- and Isostructural Reactions: An ab Initio Study of Fluoroben-zenes. J. Phys. Chem. A 2005, 109, 10594-10606.
26. Jug, K.; Hiberty, P. C.; Shaik, S. α-π Energy Separation in Modern Electronic Theory for Ground States of Conjugated Systems. Chem. Rev. 2001, 101, 1477-1500.
27. (a) Anet, F. A. L.; Yavari, I. Force-field Calculations for some Unsaturated Cyclic Hydrocarbons. Tetrahedron 1978, 34, 2879-2886.
28. (b) Lipkowitz, K. B.; Peterson, M. A. Benzene Is Not Very Rigid. J. Comput. Chem. 1993, 14, 121-125.
29. (a) Bodwell, G. J.; Miller, D. O.; Vermeij, R. Nonplanar Aromatic Compounds. 6. [2]Paracyclo[2](2,7)pyrenophane. A Novel Strained Cyclophane and a First Step on the Road to a "Vogtle" Belt. Org. Lett. 2001, 3, 2093-2096.
30. (b) Bickelhaupt, F. Small Cyclophanes: The Bent Benzene Business. Pure Appl. Chem. 1990, 62, 373-382.
31. (c) Pascal, R. A., Jr. Twisted Acenes. Chem. Rev. 2006, 106, 4809-4819.
32. (a) Jenneskens, W.; Klammer, J. C.; de Boer, H. J. R.; de Wolf, W. H.; Bickelhaupt, F.; Stam, C. H. Molekiilstruktur von 8,11-Dichlor[5]metacyclophan: Ein stark verbogener Benzolring. (Molecular structure of 8,11-dichlor[5] metacyclophane: a strongly bent benzene ring). Angew. Chem. 1984, 96, 236-237.
33. (b) Dijsktra, F.; van Lenthe, J. H. Aromaticity of bent benzene rings: A VBSCF study. Int. J. Quantum Chem. 1999, 74, 213-221.
34. (c) Ma, B.; Sulzbach, H. M.; Remington, R. B.; Schaefer, H. F., III. Structure, Strain Energy, and Magnetic Susceptibility of [4]Paracyclophane and the Activation Energy for Its Interconversion with 1,4-Tetramethylene Dewar Benzene. J. Am. Chem. Soc. 1995, 117, 8392-8400.
35. (d) Bodwell, G. J.; Fleming, J. J.; Mannion, M. R.; Miller, D. O. Nonplanar Aromatic Compounds. 3. A Proposed New Strategy for the Synthesis of Buckybowls. Synthesis, Structure and Reactions of [7-], [8-], and [9](2,7)Pyrenophanes. J. Org. Chem. 2000, 65, 5360-5370.
36. (e) Bodwell, G. J.; Bridson, J. N.; Cyrański, M. K.; Kennedy, J. W. J.; Krygowski, T. M.; Mannion, M. R.; Miller, D. O. Nonplanar Aromatic Compounds. 8. Synthesis, Crystal Structures, and Aromaticity Investigations of the l,n-Dioxa[n](2,7)pyrenophanes. How Does Bending Affect the Cyclic π-Electron Derealization of the Pyrene System. J. Org. Chem. 2003, 68, 2089-2098.
37. (f) Dobrowolski, M. A.; Cyranski, M. K.; Merner, B. L.; Bodwell, G. J.; Wu, J. I.; Schleyer, P. v. R. Interplay of π-Electron Dercalization and Strain in [n](2,7)Pyrenophanes. J. Org. Chem. 2008, 73, 8001-8009.
38. Jeffrey, G. A.; Ruble, J. R.; McMullan, R. K.; Pople, J. A. The Crystal Structure of Deuterated Benzene. Proc. R. Soc, London 1987, 414, 47-57.
39. (a) Krygowski, T. M.; Cyrański, M. K.; Häfelinger, G.; Katritzky, A. R. Aromaticity: a Theoretical Concept of Immense Practical Importance. Tetrahedron 2000, 56, 1783-1796.
40. (b) Chen, Z.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R. Nucleus-Independent Chemical Shifts (NICS) as an Aromaticity Criterion. Chem. Rev. 2005, 105, 3842-3888.
41. Ingold, C. K. Structure and Mechanism in Organic Chemistry; Cornell University Press: Ithaca, U.S.A., 1953; Chapter 4.
42. Muller, E. Neuere Anschauungen der organischen Chemie (New views in organic chemistry); Springer Verlag: Berlin, Germany, 1957; Chapter 3.
43. (a) Pauling, L.; Wheland, G. W. The Nature of the Chemical Bond. V. The Quantum-Mechanical Calculation of the Resonance Energy of Benzene and Naphthalene and the Hydrocarbon Free Radicals. J. Chem. Phys. 1933, 1, 362-374.
44. (b) Pauling, L.; Sherman, J. The Nature of the Chemical Bond. VI. The Calculation from Thermo-chemical Data of the Energy of Resonance of Molecules Among Several Electronic Structures. J. Chem. Phys. 1933, 1, 606-617.
45. Kistiakowsky, G. B.; Ruhoff, J. R.; Smith, H. A.; Vaughan, W. E. Heats of Organic Reactions. IV. Hydrogenation of Some Dienes and of Benzene. J. Am. Chem. Soc. 1936, 58, 146-153.
46. Wheland, G. W. The Theory of Resonance and its Application to Organic Chemistry; Wiley: New York, U.S.A., 1944.
47. (a) George, P.; Trachtman, M.; Bock, C. W.; Brett, A. M. Homodes-motic Reactions for the Assessment of Stabilization Energies in Benzenoid and Other Conjugated Cyclic Hydrocarbons. J. Chem. Soc, Perkin Trans. 2 1976, 1222-1227.
48. (b) George, P.; Trachtman, M.; Bock, C. W.; Brett, A. M. The use of 90°-1,3-butadiene as a reference structure for the evaluation of stabilization energies for benzene and other conjugated cyclic hydrocarbons. Tetrahedron 1976, 32, 1357-1362.
49. (a) Schaad, L. J.; Hess, B. A. Dewar Resonance Energy. Chem. Rev. 2001, 101, 1465-1476.
50. (b) Slayden, W. S.; Liebman, J. F. The Energetics of Aromatic Hydrocarbons: An Experimental Thermo-chemical Perspective. Chem. Rev. 2001, 101, 1541-1566.
51. (c) Cyrański, M. K. Energetic Aspects of Cyclic Pi-Electron Dercalization: Evaluation of the Methods of Estimating Aromatic Stabilization Energies. Chem. Rev. 2005, 105, 3773-3811.
52. Julg, A.; Françoise, P. Recherches sur la Géométrie de Quelques Hydrocarbures Non-alternants: Son Influence sur les Energies de Transition, une Nouvelle Définition de L'aromaticité (Research on geometry of Some Non-alternant Hydrocarbons Its Influence on Transition Energy, a New Definition of Aromaticity). Theor. Chim. Acta 1967, 8, 249-259.
53. (a) Kruszewski, J.; Krygowski, T. M. Definition of aromaticity basing on the harmonic oscillator model. Tetrahedron Lett. 1972, 13, 3839-3842.
54. (b) Krygowski, T. M. Crystallographic Studies of Inter- and Intramolecular Interactions Reflected in Aromatic Character of π-Elec-tron Systems. J. Chem. Inf. Comput. Sci. 1993, 33, 70-78.
55. Krygowski, T. M.; Cyrański, M. K. Structural Aspects of Aromaticity. Chem. Rev. 2001, 101, 1385-1419.
56. Dauben, H. J.; Wilson, J. D.; Laity, J. L. Diamagnetic Susceptibility Exaltation as a Criterion of Aromaticity. J. Am. Chem. Soc. 1968, 90, 811-813.
57. Flygare, W. H. Magnetic Interactions in Molecules and an Analysis of Molecular Electronic Charge Distribution from Magnetic Parameters. Chem. Rev. 1974, 74, 653-687.
58. (a) Gomes, J. A. N. F.; Mallion, R. B. Aromaticity and Ring Currents. Chem. Rev. 2001, 10 , 1349-1384.
59. (b) Mallion, R. B. Topological Ring-Currents in Condensed Benzenoid Hydrocarbons. Croat. Chem. Acta 2008, 81, 227-246.
60. Mitchell, R. H. Measuring Aromaticity by NMR. Chem. Rev. 2001, 101, 1301-1315.
61. Schleyer, P. v. R.; Maerker, C.; Dransfeld, H.; Jiao, H.; van Eikemma Hommes, N. J. R. Nucleus-Independent Chemical Shifts: A Simple and Efficient Aromaticity Probe. J. Am. Chem. Soc. 1996, 118, 6317-6318.
62. (a) Taylor, R. Electrophilic Aromatic Substitution; Wiley: New York, U.S.A., 1990.
63. (b) De la Mare, P. B. D.; Ridd, J. H. Aromatic Substitution, Nitration and Halogenation; Butterworths: London, U.K., 1959.
64. Balaban, A. T.; Biermann, D.; Schmidt, W. Chemical Graphs. 42. Dualist Graph Approach for Correlating Diels-Alder Reactivites of Polycyclic Aromatic Hydrocarbons. Nouv. J. Chim. 1985, 9, 443-449.
65. Our approach is based on chemical graph theory; therefore, we do not consider systems (or their fragments) in which the canonical structures involve ions. Note that the number of canonical structures K for a given benzenoid hydrocarbon corresponds to all valence states, and it can be derived in a simple way from the connectivity matrix of the molecule as the square root of the absolute value of the matrix determinant. Even though the ionic structures are included (which needs a completely different approach than presented in this paper) their contribution to stability of a given benzenoid hydrocarbon is small and should not significantly influence our findings.
66. Morikawa, T.; Narita, S.; Klein, D. J. Molecular Electric Conductance and Long-bond Structure Counting for Conjugated-carbon Nano-structures. Chem. Phys. Lett. 2005, 402, 554-558.
67. Randić, M. Aromaticity of Polycyclic Conjugated Hydrocarbons. Chem. Rev. 2003, 103, 3449-3605.
68. (a) Keith, T. A.; Bader, R. F. W. Calculation of Magnetic Response Properties using a Continuous Set of Gauge Transformations. Chem. Phys. Lett. 1992, 194, 1-8.
69. (b) Keith, T. A.; Bader, R. F. W. Calculation of Magnetic Response Properties using a Continueous Set of Gauge Transformations. Chem. Phys. Lett. 1993, 210, 223-231.
70. (c) Cheeseman, J. R.; Trucks, G. W.; Keith, T. A.; Frisch, M. J. A comparison of Models for Calculating Nuclear Magnetic Resonance Shielding Tensors. J. Chem. Phys. 1996, 104, 5497-5509.
71. (a) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648-5652.
72. (b) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785-789.
73. Hoarau, J.; Joussot-Dubien, J.; Lemanceau, B.; Lumbroso, N.; Pacault, A. Cah. Phys. 1956, 74, 34.
74. Gupta, R. R. Landolt-Börnstein, Numerical Data and Functional Relationship in Science and Technology, New Series, 11/16, Diamagnetic Susceptibility; Springer: Berlin, Germany, 1986.
75. Krishnan, K. S.; Guha, B. C.; Banerjee, S. Investigations on Magne-Crystallic Action. Part I: Diamagnetics. Phil. Trans. R. Soc. London A 1933, 231, 235-262.
76. Poquet, E. J. Chim. Phys. 1963, 60, 566.
77. Abrahams, R. J.; Robertson, J. M.; White, J. G. The Crystal and Molecular Structure of Naphthalene. I. X-ray Measurements. Acta Crystallogr. 1949, 2, 233-238.
78. Abrahams, R. J.; Robertson, J. M.; White, J. G. The Crystal and Molecular Structure of Naphthalene. II. Structure Investigation by the Triple Fourier Series Method. Acta Crystallogr. 1949, 2, 238-244.
79. Lonsdale, K.; Krishnan, K. S. Diamagnetic Anisotropy of Crystals in Relation to Their Molecular Structure. Proc. R. Soc. London A 1936, 156, 597-613.
80. Robertson, J. M. The Crystalline Structure of Anthracene. A Quantitative X-Ray Investigation. Proc. R. Soc. London A 1933, 140, 79-98.
81. Robertson, J. M.; White, J. G. The Crystal Structure of Pyrene. A Quantitative X-ray Investigation. J. Chem. Soc. 1947, 358-368.
82. (a) Krishnan, K. S.; Banerjee, S. Investigations on Magne-Crystallic Action. III. Further Studies on Organic Crystals. Phil. Trans. R. Soc. London A 1935, 234, 265-298.
83. (b) Dhar, J.; Guha, A. Z Kristallogr. 1935, 91, 123.
84. 2, and of Related Compounds. Proc. R. Soc. London A 1941, 177, 272-280.
85. (a) Banerjee, S. Z Kristallogr. 1939, 100, 316-355.
86. (b) Hertel, E.; Romer, G. H. Der Strukturelle Feinbau der Strukturisomeren Kohlen-wasserstoffe Quaterphenyl und Triphenylbenzol. (The fine structure of the structural isomers of hydrocarbons: quaterphenyle and triph-enylbenzene). Z Phys. Chem. B 1933, 23, 226-234.
87. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. GAUSSIAN03; Gaussian Inc.: Wallingford, CT, 2004.
88. Hess, B. A.; Schaad, L. J. Hückel Molecular Orbital π Resonance Energies. The Benzenoid Hydrocarbons. J. Am. Chem. Soc. 1971, 93, 2413-2416.
89. Dewar, M. J. S.; Mole, T.; Urch, D. S.; Warford, E. W. T. 689. Electrophilic Substitution. Part IV. The Nitration of Diphenyl, Chry-sene, Benzo[a]pyrene, and Anthanthrene. J. Chem. Soc. 1956, 3572-3575.
90. Streitwieser, A., Jr. Molecular Orbital Theory for Organic Chemists; Wiley: New York, U.S.A., 1961; p 322 ff.
91. Table 11.1 in ref 53.
92. (a) Krygowski, T. M.; Stencel, M.; Galus, Z. Polarographic and Voltametric Study of Mono-nitro Derivatives of Benzenoid Hydrocarbons in DMF - Interpolation within Hammett-Streitwieser Equation and HMO-Theory. J. Electroanal. Chem. 1972, 39, 395-405.
93. (b) Kamieński, B.; Krygowski, T. M. Application of the Hammett-Streitwieser Equation to Interpretation of the Chemical Shifts of Nonaromatic Protons in Substituted Arenes. Tetrahedron Lett. 1972, 681-684.
94. (c) Krygowski, T. M.; Kruszewski, J. Application of the Hammett-Streitwieser Equation to Predictions of Paraband Location in UV and VIS Spectra of Benzelogues of Perylene and Fluoranthrene. Bull. Acad. Polon. Sci., Ser. Sci. Chim. 1974, 22, 1059-1064.
95. Krygowski, T. M. Towards the Unification of the Substituent (Position) Constants in Hammett-Streitwieser Equation. Tetrahedron 1972, 28, 4981-4987.
96. (a) Zhou, Z.; Parr, R. G.; Garst, J. F. Absolute Hardness as a Measure of Aromaticity. 1988, 29, 4843-4846.
97. (b) De Proft, F.; Geerlings, P. Relative Hardness as a Measure of Aromaticity. Phys. Chem. Chem. Phys. 2004, 6, 242-248.
98. Isoarithmic catafusenes (cata-condensed benzenoids) have the same numbers of Kekule structures, which are in 1-to-l correspondence; they differ only in the direction of the "kink" condensation, and in their 3-digit code this difference is reflected in permutations between digits 1 and 2 of the code. See: (a) Balaban, A. T.; Harary, F. Chemical graphs. V. Enumeration and proposed nomenclature of benzenoid cata-condensed polycyclic aromatic hydrocarbons. Tetrahedron 1968, 24, 2505-2516.
99. (b) Balaban, A. T. Chemical graphs. VII. Proposed nomenclature of branched cata-condensed benzenoid polycyclic hydrocarbons. Tetrahedron 1969, 25, 2949-2956.
100. (c) Balaban, A. T. Chemical graphs. Part 50. Symmetry and enumeraton of fibonacenes (unbranched catacondensed benzenoids isoarithmic with helicenes and zigzag catafusenes). Math. Chem. (MATCH) 1989, 24, 29-38.
101. Balaban, A. T.; Tomescu, I. Algebraic Expressions for the Number of Kekule Structures of Isoarithmic Cata-Condensed Benzenoid Polycyclic Hydrocarbons. Match Commun. Math. Comput. Chem. 1983, 14, 155-182.
102. Steiner, E.; Fowler, P. W.; Jenneskens, I. W. Counter-Rotating Ring Currents in Coronene and Corannulene. Angew. Chem., Int. Ed. 2001, 40, 362-366.
103. Havenith, R. W. A. Electric and Magnetic Properties Computed for Valence Bond Structures: Is There a Link between Pauling Resonance Energy and Ring Current. J. Org. Chem. 2006, 71, 3559-3563.