Kekulé Structures in Benzenoid Hydrocarbons
This text is an attempt to outline the basic facts concerning Kekul€ structures in benzenoid hydrocarbons: their history, applica tions and especially enumeration. We further pOint out the numerous and often quite remarkable connections between this topic and various parts of combinatorics and disc...
Main Authors: | , |
---|---|
Format: | eBook |
Language: | English |
Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1988, 1988
|
Edition: | 1st ed. 1988 |
Series: | Lecture Notes in Chemistry
|
Subjects: | |
Online Access: | |
Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 11.1 Introduction
- 11.2 Pentagons
- 11.3 Triangles
- 11.4 Streamers and Goblets
- 12 — Classes of Basic Benzenoids (IV): Rectangles
- 12.1 Definitions
- 12.2 Prolate Rectangle
- 12.3 Oblate Rectangle
- 12.4 Auxiliary Benzenoid Classes
- 12.5 Modified Oblate Rectangles
- 12.6 Some General Formulations Concerning Oblate Rectangles
- 13 — Regular Six-Tier Strips and Related Systems
- 13.1 Introduction
- 13.2 Six-Tier Strips
- 13.3 Supplement to the Methods of Derivation of K Formulas For t-Tier Strips
- 13.4 Auxiliary Benzenoid Classes
- 13.5 Two-Parameter K Formulas for Some Multiple Chains
- 13.6 Generalized Auxiliary Class
- 13.7 Étagère
- 13.8 Some Seven-Tier Strips: A Summing UP
- 14 — Determinant Formulas
- 14.1 Introduction
- 14.2 Hexagon
- 14.3Chevron
- 14.4 Ribbon
- 14.5 Parallelogram
- 14.6 Zigzag Chains
- 14.7 Pentagons
- 14.8 Oblate Rectangle
- 15 — Algorithm: A Generalization
- 15.1 Introduction
- 15.2 General Principles
- 1 — Introduction
- 1.1 Benzenoid Hydrocarbons
- 1.2 Historical Remarks
- 1.3 Importance of Kekulé Structures in the Theory of Benzenoid Hydrocarbons
- 2 — Benzenoid Systems: Basic Concepts
- 2.1 Introduction
- 2.2 Definitions and Relations
- 2.3 Classifications of Benzenoids
- 3 — Kekulé Structures and Their Numbers: General Results
- 3.1 Introduction
- 3.2 Theorems About K Numbers
- 3.3 Vertices and Edges in Kekulé Structures
- 3.4 Lower and Upper Bounds of K
- 3.5 Benzenoids with Extremal K
- 3.6 Generation of Normal Benzenoids
- 3.7 Isoarithmicity
- 4 — Introduction to the Enumeration of Kekulé Structures
- 4.1 Schematic Survey
- 4.2 Empirical Methods
- 4.3 Combinatorial Formulas, Especially for the Single Linear Chain
- 4.4 Recurrence Relations for Single Linear and Zigzag Chains
- 4.5 Summation Formulas for Single Linear and Zigzag Chains
- 4.6 Algorithms for Single Linear and Zigzag Chains
- 4.7 Combinatorial Formula for the Single Zigzag Chain
- 4.8 Treatment of a Pericondensed Benzenoid: The Parallelogram
- 4.9 General Remarks
- 4.10 Other Methods
- 5 — Non-Kekuléan and Essentially Disconnected Benzenoid Systems
- 5.1 Introduction
- 5.2 Introductory Examples
- 5.3 The Müller-Muller-Rodloff Rule
- 5.4 Characterization of Concealed Non-Kekuléan Benzenoid Systems
- 5.5 Segmentation
- 6 — Catacondensed Benzenoids
- 6.1 Previous Work
- 6.2 Single Unbranched Chain
- 6.3 Branched Chain
- 6.4 Catacondensed Ladder
- 6.5 Catacondensed All-Benzenoids and Related Systems
- 6.6 Limit Values Involving K Numbers
- 7 — Annelated Benzenoids
- 7.1 Definitions
- 7.2 Previous Work
- 7.3 Annelation to a Linear Chain
- 7.4 Annelation to a Zigzag Chain
- 7.5 Further Developments
- 7.6 Discussion of the Formulas
- 7.7 Algorithm
- 7.8 Dictionary of K Numbers withRelevance to Annelation
- 7 9 Annelation of Two Single Chains
- 7.10 Annelations of Special Benzenoids
- 8 — Classes of Basic Benzenoids (I)
- 8.1 Introduction
- 8.2 Hexagon
- 8.3 Chevron
- 8.4 Ribbon
- 8.5 Parallelogram
- 9 — Classes of Basic Benzenoids (II): Multiple Zigzag Chain
- 9.1 Definition
- 9.2 Previous Work
- 9.3 Auxiliary Benzenoid Class
- 9.4 Recurrence Relations for A (n,m) with Fixed Values of n
- 9.5 Combinatorial K Formulas for A (n,m,l) With Fixed Values of m
- 9.6 Combinatorial K Formulas for Z (m,n) With Fixed Values of m
- 9.7 The Polynomial Pm(n) = K{Z(m,n)}
- 9.8 Algorithm
- 9.9 Some General Formulations
- 10 — Regular Three-, Four- and Five-Tier Strips
- 10.1 Previous Work
- 10.2 Definitions
- 10.3 Classification of Regular t-Tier Strips
- 10.4 Examples of Non-Regular t-Tier Strips
- 10.5 Dictionary of K Formulas For Regular 3-, 4- and 5-Tier Strips
- 10.6 Methods of Derivation of K Formulas for t-Tier Strips
- 10.7 The 4-Tier Zigzag Chain
- 11 — Classes of Basic Benzenoids (III)
- 15.3 Multiple Chains
- 15.4 Multiple Chains with Truncated Rows
- 15.5 Parallelogram with Truncated and Augmented Rows
- 15.6 Constructable Benzenoids
- 16 — Pericondensed All-Benzenoids and Related Classes
- 16.1 Introductory Remarks
- 16.2 All-Benzenoid Classes Including Modifications
- 16.3 Reticular All-Benzenoids
- 17 — Benzenoids with Repeated Units
- 17.1 Introduction
- 17.2 Fused Repeated Units
- 17.3 Condensed Repeated Units
- 17.4 Benzenoids with Hexagonal and Trigonal Symmetries
- 18 — Distribution of K, and Kekulé Structure Statistics
- 18.1 Introduction and Previous Work
- 18.2 Distribution of K
- 18.3 Average Values of K, and Related Quantities
- 18.4 Number of Normal Benzenoids with a Given K.