Topological approach to the chemistry of conjugated molecules
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Bibliographic Information
Topological approach to the chemistry of conjugated molecules
（Lecture notes in chemistry, 4）
Springer-Verlag, c1977
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Note
Bibliography: p. [115]-120
Includes index
Description and Table of Contents
Description
"The second step is to determine constitution, Le. which atoms are bonded to which and by what types of bond. The result is ex pressed by a planar graph (or the corresponding connectivity mat rix) **** In constitutional formulae, the atoms are represented by letters and the bonds by lines. They describe the topology of the molecule." VLADIMIR PRELOG, Nobel Lecture, December l2;h 1975. In the present notes we describe the topological approach to the che mistry of conjugated molecules using graph-theoretical concepts. Con jugatedstructures may be conveniently studied using planar and connec ted graphs because they reflect in the simple way the connectivity of their pi-centers. Connectivity is important topological property of a molecule which allows a conceptual qualitative understanding, via a non numerical analysis, of many chemical phenomena or at least that part of phenomenon which depends on topology. This would not be possible sole ly by means of numerical (molecular orbital) analysis.
Table of Contents
1. Introduction.- 2. Graphs in Chemistry.- 2.1. Basic Definitions and Concepts of Graph Theory.- 2.1.1. Definition of a Graph.- 2.1.2. The Adjacency Matrix of a Graph.- 2.1.3. Isomorphism of the Graphs.- 2.1.4. Further Characterization of a Graph.- 2.2. Graphs and Topology.- 2.2.1. Path, Length and Distance.- 2.2.2. Neighbours. The Invariants of a Graph.- 2.2.3. Ring and Oriented Ring. Regular and Complete Graphs. The Ring and the Edge Components of a Graph.- 2.2.4. Sachs Graphs with N Vertices.- 2.3. Graphs Representing Conjugated Molecules.- 2.3.1. Planar Graphs. Colouring of Graphs.- 2.3.2. Huckel Graphs.- 2.3.3. Trees. Benzenoid Graphs.- 2.4. Graph Spectrum. Sachs Theorem.- 2.4.1. Graph Spectrum.- 2.4.2. Graph Spectral Properties of Particular Classes of Graphs.- 2.4.3. Sachs Theorem.- 2.5. Topology and Simple Molecular Orbital Model.- 2.6. Application of the Coulson-Sachs Graphical Method.- 2.7. Extension of Graph-Theoretical Considerations to Moebius Structures.- 3. Total Pi-Electron Energy.- 3.1. Introduction.- 3.2. Identities And Inequalities.- 3.2.1. The Fundamental Identity.- 3.2.2. Relations Between Epi The Adjacency Matrix and the Density Matrix.- 3.2.3. The Loop Rule.- 3.2.4. Inequalities for Epi.- 3.3. The Coulson Integral Formula.- 3.3.1. The First Integral Formula.- 3.3.2. Further Coulson-Type Formulas. I.- 3.3.3. An Application of the Coulson Integral Formula: The Tree with Maximal Energy.- 3.3.4. Further Coulson-Type Formulae. II.- 3.3.5. A Class of Approximate Topological Formulas for Epi.- 3.4. Topological Factors Determining the Gross Part of Epi.- 3.5. The Influence of Cycles: The Huckel Rule.- 3.5.1. General Considerations.- 3.5.2. The Huckel Rule.- 3.5.3 An Application: The Huckel Rule for Annulenes.- 3.5.4. Extension of the Huckel Rule to Nonalternant Systems.- 3.6. The Influence of KekulE Structures.- 3.6.1. Structure Count and Algebraic Structure Count.- 3.6.2. The Basic Postulate of Resonance Theory.- 3.7. The Influence of Branching.- 3.7.1. Violation of the Basic Postulate of Resonance Theory.- 3.8. Summary.- 4. Resonance Energy.- 4.1. Introduction.- 4.2. Classical and Dewar Resonance Energies.- 4.3. Topological Resonance Energy.- 4.3.1. The Mathematical Basis.- 4.3.2. The Computation of the Acyclic Polynomial.- 4.4. Tre as a Criterion of Aromatic Stability. Correlation with Experimental Findings.- 4.5. Concluding Remarks.- 5. Reactivity of Conjugated Structures.- 5.1. Localization Energy.- 5.2. Dewar Number.- 5.3. Topological Approach to Localization Energy.- 5.4. Topological Aspect of Dewar Number.- 5.5. Nonbonding Molecular Orbitals.- 6. Conclusions.- 7. Literature.
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