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Aromaticity of Polycyclic Conjugated Hydrocarbons

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Aromaticity of Polycyclic Conjugated Hydrocarbons Chem. Rev. 2003, 103, 3449−3605 3449 Aromaticity of Polycyclic Conjugated Hydrocarbons Milan Randic´* National Institute of Chemistry, Ljubljana, Slovenia Received December 13, 2001 Contents I. Prologue 3451 II. Introduction 3455 III. Dilemmas 3456 A. Qualitative versus Quantitative Approaches 3456 B. Observables versus Non-observables 3458 C. Structural Criteria versus Properties as Criteria 3459 D. Valence Bond Theory versus Molecular Orbital 3460 Theory E. On Interlocking of the MO and the VB 3461 Methods F. Chemical Graph Theory versus Quantum 3462 Chemistry G. Clar 6n Rule versus Hu¨ckel 4n + 2 Rule 3464 H. Hydrocarbons versus Heteroatomic Systems 3465 Milan Randic´ is a native of Croatia, born in 1930, and is a citizen of the IV. Hidden Treasures of Kekule´ Valence Structures 3466 United States and Croatia. He studied theoretical physics at the University A. Conjugated Circuits 3467 of Zagreb (1954) under Professor Ivan Supek (a student of Werner B. Innate Degree of Freedom 3470 Heisenberg). Supek introduced him to the book by Linus Pauling, The Nature of the Chemical Bond, with a request to get involved in quantum C. Clar Structures 3472 chemistry. He got his Ph.D. degree in Cambridge in 1958, studying high- V. Graph Theoretical Approach to Chemical Structure 3473 resolution infrared molecular spectra with Dr. Norman Sheppard. At the A. Metric 3473 Rudjer Bosˇkovic´ Institute in Zagreb, Croatia, in 1960, he founded the B. Chemical Graphs 3473 theoretical chemistry group. Since 1971, he has visited several U.S. universities. From 1980 to 2000, he was in the Department of Mathematics C. Isospectral Graphs 3473 and Computer Science at Drake University, Des Moines, Iowa. Among D. Embedded Graphs 3475 the awards he has received are the City of Zagreb Science Award, the E. Partial Ordering 3476 Boris Kidricˇ Science Award (of Republic of Slovenia), The Governor’s VI. On Enumeration of Benzenoid Hydrocarbons 3477 Science Award (Iowa), and the Skolnik Award (American Chemical Society). He is a member of the Croatian Academy of Sciences and Arts. VII. Kekule´ Valence Structures Count 3479 His continuing interest is to advance a better understanding of chemical A. Non-branched Cata-condensed Benzenoids 3481 graph theory. Since January 1, 2000, he is Professor Emeritus at Drake B. Branched Cata-condensed Benzenoids 3482 University, while continuing a three-months-a-year visitatation at the C. Benzenoid Lattices 3482 National Institute of Chemistry in Ljubljana, Slovenia. His other interests D. Peri-condensed Benzenoids 3483 include development of a universal language, NOBEL. E. Miscellaneous Benzenoids 3484 PHOTOGRAPH CAPTION: The author is in full agreement with Plutarch − s F. The Approach of Platt 3485 (46 119 A.D.), who characterized wine as, “Of drinks the most useful; Among medication s the most tasteful; Among food s the most G. Computer Programs for Calculating K 3485 enjoyable.” H. Transfer-Matrix Method 3486 X. Conjugated Circuits Model 3492 I. Use of Recursion Relations 3486 A. Monocyclic Conjugated Systems 3493 J. Use of Signed Matrices 3487 B. Polycyclic Conjugated Systems 3493 VIII. Enumeration of Conjugated Circuits 3488 XI. Expression for Molecular Resonance Energy 3494 IX. Approximate Approaches versus Ambitious 3490 + Computations XII. Benzenoids: Systems with Only 4n 2 3494 Conjugated Circuits A. Semi-empirical Valence Bond Approaches for 3490 Benzenoid Hydrocarbons XIII. Non-benzenoid Systems 3504 1. Pauling−Wheland Valence Bond Approach 3490 A. Biphenylene and Related Non-benzenoid 3506 Systems 2. Pauling−Wheland Resonance Theory 3491 − B. Non-benzenoid Systems with Odd Rings 3507 3. Herndon Simpson Model 3491 Having Only 4n + 2 Conjugated Circuits 4. Hierarchical VB Schemes 3491 C. Non-benzenoid Systems with Odd Rings 3508 Having 4n Conjugated Circuits * Professor Emeritus, Department of Mathematics and Computer Science, Drake University, Des Moines, IA 50311. Permanent D. Summary on Applications of the Conjugated 3508 address: 3225 Kingman Rd., Ames, IA 50311. Fax: (515) 292- Circuits Method to Hydrocarbon and Carbon 8629. Chemistry 10.1021/cr9903656 CCC: $44.00 © 2003 American Chemical Society Published on Web 07/29/2003 3450 Chemical Reviews, 2003, Vol. 103, No. 9 Randic´ XIV. Quantum Chemical Justification of the Conjugated 3509 D. Canonical Clar Structures 3563 Circuits Model E. Resonant Clar Structures 3564 XV. On a Diagnostic Use of Conjugated Circuits 3512 F. Graphical Construction of Clar Structures 3565 XVI. Resonance Graphs 3512 XXXIV. Fullerenes 3566 XVII. Aromaticity versus Anti-aromaticity 3516 XXXV. Challenges and Unsolved Problems 3570 XVIII. On Classification of Polycyclic Conjugated 3517 A. Challenges 3570 Hydrocarbons B. Unsolved Problems 3571 XIX. Fully Aromatic Hydrocarbons 3520 XXXVI. Concluding Remarks 3572 XX. Less than Fully Aromatic Hydrocarbons 3522 XXXVII. Epilogue 3573 A. Degree of Aromaticity 3523 A. Quantum Chemical and Graph Theoretical 3574 B. On the Boundary of Aromaticity 3524 Analysis of [n]Phenylenes C. Degree of Anti-aromaticity 3525 B. Clar Structures for Non-benzenoid Hydrocarbons 3576 s D. Clar Valence Structures and Aromaticity 3526 XXXVIII.Chemical Graph Theory Prospects and Retrospect 3577 XXI. Biphenylenes 3527 XXXIX. Tribute to Experimental Chemistry 3579 XL. Apologies 3581 XXII. Fully Anti-aromatic Hydrocarbons 3528 XLI. Acknowledgments 3584 XXIII. Aromaticity/Anti-aromaticity 3529 XLII. Appendix 1. Biographical Notes 3584 XXIV. ABC of Aromaticity 3530 Arthur Cayley (1821−1895) 3584 A. A of Aromaticity 3530 James Joseph Sylvester (1814−1897) 3585 B. B of Aromaticity 3531 August Kekule´ (1829−1896) 3585 C. C of Aromaticity 3532 Charles A. Coulson (1910−1974) 3586 XXV. Local Aromaticity 3532 Erich Clar (1902−1987) 3586 A. The Approach of Polansky and Derflinger 3532 Oskar E. Polansky (1919−1989) 3587 B. Approaches Based on Bond Orders 3533 Michael J. S. Dewar (1918−1997) 3587 C. Graph Theoretical Approach to “Benzene 3535 XLIII. Appendix 2. Short Historical Comments on Graph 3588 Character” of Fused Benzene Rings Theory in Mathematics and Chemistry D. On Quantitative Interpretation of Clar Valence 3535 A. Graph Theory in Mathematics 3588 Structures B. Graph Theory in Chemistry 3589 E. On Neglect of Local Aromaticity 3536 C. Further Readings 3589 F. Alternative Ring Indices 3537 D. Personal Note 3589 XXVI. Ring Currents 3539 XLIV. Appendix 3. ErrorssOmissions 3590 s A. Ring Currents as Ring Descriptors 3539 XLV. Appendix 4. Errors Prevention 3591 B. Nuclear-Independent Chemical Shifts (NICS) 3540 XLVI. Note Added in Proof 3594 C. A Graph Theoretical View on Ring Currents 3541 A. Clar Structures of C60 3594 B. Benzenoid [10]Cyclophenacene Belt D. Conjugated Circuits Currents 3542 3594 C. Historical Remark on Clar π-Sextets 3595 XXVII. Graph Theoretical Ring Resonance Energies 3544 D. More Support for Clar’s π-Aromatic Sextets 3595 XXVIII. The Most Aromatic Aromatic Compounds 3544 XLVII. References 3595 A. Fully Benzenoid Hydrocarbons 3544 B. Giant Benzenoids 3545 XXIX. Clar’s Aromatic Sextets 3547 A. Geometrical Definition of Clar’s Valence 3547 PRACTICAL POINTS: Molecular structures are Formulas numbered according to the figure in which they are B. Mathematical Definition of Clar’s Valence 3549 shown by a fraction x/X, where x is the number of Formulas the molecule and X is the number of the figure XXX. Quantum Chemical Justification for Clar’s 3549 showing its skeleton. In the list of references, in the Structures case of review articles we have given the title of each XXXI. On Interpretation of Molecular Resonance Energy 3552 article as this offers some information on the par- XXXII. Other Points 3552 ticular content of the review. In addition, we may have indicated the length of the review by listing the A. Benzenoid Hydrocarbons Revisited 3553 full page range of such articles. B. Biphenylenes Revisited 3556 1. Parity of Kekule´ Valence Structures 3556 2. Degrees of Freedom of Kekule´ Valence 3557 If a man can preach a better sermon, write a Structures of Non-benzenoids better book, or make a better mouse-trap than C. Dilemma: Kekule´ Structures or Clar 3558 his neighbor, though he build his house in the Structures? woods, the world will make a beaten path to his D. On Kekulene and Superaromaticity 3560 door. XXXIII. Clar Structures Revisited 3561 R. W. Emerson (1803-1882), A. Exceptions to the Rule 3561 American essayist and poet, B. Generalized Clar Structures 3562 a leading figure in C. Sextet Polynomial 3563 American literary history. 3530 Chemical Reviews, 2003, Vol. 103, No. 9 Randic´ a molecule. That the presence of 4n conjugated Table 39. ABC’s of Aromaticity circuits is detrimental to molecular stability has been RE(4n + 2) - RE(4n) A ) aromaticity witnessed already for aromatic compounds in which RE(4n + 2) + RE(4n) 4n + 2 conjugated circuits dominate and enforce the RE(R ) - RE(R * ) planar geometry for the systems in which 4n conju- B ) 1 n 1 benzene character RE(R ) + RE(R ) gatedcircuitsarealsopresent.HafnerandSchneider553 1 n*1 RRE(R ) - RRE(R * ) considered alkyl derivatives of aceheptylene and C ) 1 n 1 Clar index + observed that these compounds depart somewhat in RRE(R1) RRE(Rn*1) their properties from the “standard” non-benzenoid conjugated systems. Clearly this “departure” is due anti-aromaticity that was for the most part “ficti- to the presence of anti-aromatic 4n contributing tious” is becoming “factual”. conjugated circuits. An indirect “proof” that anti-aromatic compounds For a compound to qualify as anti-aromatic, how- are elusive comes from data on inter-stellar com- ever, we must have a dominant anti-aromatic con- pounds.660-662 In view of the low density of matter tribution. Hafner and co-workers655 designed a clever and extremely low temperatures in outer space, way to arrive at anti-aromatic compounds by “forc- structures that would be difficult to observe in the ing” a molecule that has undergone the Jahn-Teller laboratory may have long enough life in the inter- distortion back into a more symmetrical geometric stellar space to be detected.
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