Topological Approach to the Chemistry of Conjugated Molecules

ISBN-13: 9783540084310 / Angielski / Miękka / 1977 / 124 str.

A. Graovac; I. Gotman; N. Trinajstic

Opis

"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.

Spis treści

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. Hückel 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 Möbius 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 Hückel Rule.- 3.5.1. General Considerations.- 3.5.2. The Hückel Rule.- 3.5.3 An Application: The Hückel Rule for Annulenes.- 3.5.4. Extension of the Hückel Rule to Nonalternant Systems.- 3.6. The Influence of KekulÉ 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.