S.J. Cyvin, J. Brunvoll, R.S. Chen

Theory of Coronoid Hydrocarbons II

Mitwirkender: Cyvin, Sven J.; Chen, R. S.; Brunvoll, J.

• Broschiertes Buch

Produktbeschreibung

The present monograph is a continuation of Cyvin SJ, Brunvoll J and Cyvin (1991c), a reference to be found in Bibliography. Naturally, the previous volume is cited frequently here. For the sake of brevity, it is referred to as "Volume I". References to different chapters, sections or paragraphs are given like Vol. 1-1, 1-1.2 or 1-1.2.2, respectively. Also tables and equations in "Volume I" are cited; the very last equation therein, for instance, is Vol. I-{9.9). The present text spans from references to organic syntheses or attempted organic syntheses - - to stringent mathematical theorems proved by graph-theoretical methods. Enumerations of coronoid systems is a substantial part of the work. Algebraic methods involving combinatorics and generating functions are employed on one hand, and computer programming on the other. The whole book is supposed to demonstrate a piece of mathematical chemistry, which can be characterized as lying on the "interfaces between mathematics, chemistry and computer science", a formulation used for the MATH/CHEM/COMP Conferences; d. Cyvin SJ, Brunvoll and Cyvin (1989d) in Bibliography. Financial support to BNC from the Norwegian Council for Science and the Humanities is gratefully acknowledged.

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Produktdetails

• Lecture Notes in Chemistry 62
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 10128834, 978-3-540-58138-3
• Softcover reprint of the original 1st ed. 1994
• Seitenzahl: 316
• Erscheinungstermin: 28. Juli 1994
• Englisch
• Abmessung: 235mm x 155mm x 18mm
• Gewicht: 422g
• ISBN-13: 9783540581383
• ISBN-10: 3540581383
• Artikelnr.: 26160037

Inhaltsangabe

1 Introduction and Chemical Relevance.- 1.1 Reiteration.- 1.2 Motivation.- 1.2.1 General Viewpoints.- 1.2.2 Alkane Isomers.- 1.3 Cycloarenes.- 1.3.1 The Story of Kekulene Revisited.- 1.3.2 Other Cycloarenes.- 1.3.3 The Story of Kekulene Continues.- 1.4 Annulenes, Annulenoannulenes, and Annulene Derivatives.- 1.5 Antikekulene.- 1.6 Corannulene.- 1.7 Cyclacenes.- 1.8 Buckminsterfullerene.- 1.9 Nomenclature and Coding.- 1.10 Conclusion.- 2 Classification of Polygonal Systems, and Some Aspects of KekulÉ Structures.- 2.1 Introduction.- 2.2 Classification of Single Coronoids in Relation to Kekulé Structures.- 2.3 Degenerate and Generalized Single Coronoids.- 2.4 Examples of Single Coronoids, and Their Kekulé Structure Counts.- 2.4.1 Regular Single Coronoids.- 2.4.2 Essentially Disconnected Single Coronoids.- 2.4.3 Additional Instructive Examples.- 2.4.4 Irregular Single Coronoids With Isolated Internal Vertices.- 2.5 Survey of Kekulé Structure Counts for Single Coronoids.- 2.5.1 Combinatorial Formulas.- 2.5.2 Algorithm and Annulenoid Kekulé Structures for Primitive Coronoids.- 2.5.3 General Solution Convenient for Computer Programming.- 2.5.4 Supplementary References.- 2.6 Isospectral Single Coronoids.- 2.7 Some Main Classes of Polyhexes.- 2.7.1 Introduction.- 2.7.2 Hexagonal and Trigonal Lattices, and the Dualist.- 2.7.3 Helicenes and Corohelicenes.- 2.7.4 Planarity and Nonplanarity.- 2.8 Examples of Graph Theoretically Nonplanar Polyhexes.- 2.8.1 Cyclohelicenes.- 2.8.2 Möbius-Polyhexes.- 2.9 Polygonal Systems.- 2.9.1 Introduction.- 2.9.2 Mono q Polyhexes.- 2.9.3 Holes and Polygons.- 2.9.4 Cluster Systems.- 3 Benzenoids, Single Coronoids and Multiple Coronoids.- 3.1 General Considerations, Basic Definitions, and Terminology.- 3.2 Invariants and Relations Between Them.- 3.2.1 Specifications.- 3.2.2 Relations.- 3.2.3 Outer and Inner Perimeters.- 3.3 Additional Definitions, Terminology and Relations.- 3.3.1 Corona Holes.- 3.3.2 Associated Benzenoid and Perforated Benzenoid.- 3.3.3 Naphthalenic Coronoid.- 3.3.4 Extremal Coronoid.- 3.4 First Enumeration Results for Benzenoids and Coronoids.- 3.5 Smallest Multiple Coronoids.- 3.5.1 Introduction.- 3.5.2 Basic Assumptions.- 3.5.3 Algorithm for Construction of Smallest Multiple Coronoids.- 3.5.4 Discussion and Depiction of Forms.- 3.5.5 Pericondensed Smallest Multiple Coronoids.- 3.6 Perfect and Imperfect Extremal Coronoids.- 3.6.1 Introduction.- 3.6.2 Numbers of Hexagons and of Internal Vertices.- 3.6.3 Catacondensed Extremal Coronoids.- 3.6.4 Extension to Pericondensed Extremal Coronoids.- 3.7 Chemical Formulas.- 3.7.1 Introduction and Notation.- 3.7.2 Inequalities for the Formula Coefficients.- 3.7.3 Table of Formulas.- 3.8 Numbers of Isomers.- 3.8.1 Definition and Notation.- 3.8.2 Numerical Values.- 4 Invariants of Single Coronoids.- 4.1 Introduction.- 4.2 Summary of Invariants and Relations Between Them.- 4.2.1 Summary of Relations.- 4.2.2 Connectivity and the Dias Parameter.- 4.3 Maximum Number of Internal Vertices, and Minimum Number of Hexagons.- 4.3.1 Maximum Number of Internal Vertices, and Extremal Single Coronoids.- 4.3.2 Minimum Number of Hexagons.- 4.3.3 Spiral Walk.- 4.3.4 Perforated Polycircumcoronenes.- 4.4 Possible Values of Invariants.- 4.5 Upper and Lower Bounds for Some Invariants.- 4.5.1 General.- 4.5.2 Functions of the Number of Hexagons and of the Number of Internal Vertices.- 4.5.3 Functions of Invariants Other Than the Number of Hexagons and the Number of Internal Vertices.- 4.6 Minimum Number of Vertices of Degree Two, and Maximum Number of Hexagons.- 4.6.1 Minimum Number of Vertices of Degree Two.- 4.6.2 Maximum Number of Hexagons, and Circular Single Coronoids.- 4.6.3 Spiral Walk.- 4.6.4 Detailed Analysis.- 5 Chemical Formulas of Single Coronoids.- 5.1 Introduction.- 5.2 Terminology.- 5.3 Inequalities in Terms of the Formula Coefficients.- 5.3 1 When is a Given Formula Compatible With a Single Coronoid?.- 5.3.2 Supplementary Inequalities.- 5.4 Circumscribi