Molecular Orbital Calculations Using Chemical Graph Theory

ISBN-13: 9783540561347 / Angielski / Miękka / 1993 / 115 str.

Jerry Ray Dias

Opis

This study provides conceptual tools for understanding chemical phenomena by the use of HMO theory. The author demonstrates how graph theory can be used to streamline HMO calculations without the aid of group theory or computer programs.

Spis treści

1. Small Conjugated Polyenes.- 1.1 Introduction.- 1.2 Hückel Molecular Orbital Calculations.- 1.2.1 The Wave Equation.- 1.2.2 The LCAO Method.- 1.3 Graph Theoretical Terminology.- 1.3.1 Molecular Graph Notation.- 1.3.2 1-Factor Subgraphs and Kékulé Structures.- 1.3.3 Common Molecular Graphs.- 1.4 Determining Characteristic Polynomials.- 1.4.1 Characteristic Polynomials.- 1.4.2 Sachs graphs.- 1.4.3 The Fourth and Sixth Coefficients.- 1.4.4 Odd Coefficients.- 1.4.5 The Tail Coefficient.- 1.5 Determining Select Eigenvalues by Embedding.- 1.5.1 Introduction.- 1.5.2 Descriptive Embedding Rules.- 1.5.3 The Pairing Theorem.- 1.5.4 Relationships Between the Zero Roots and Coefficient of a Polynomial.- 1.6 Eigenvectors.- 1.6.1 Introduction.- 1.6.2 Path Deleting Procedure for Determining Eigenvectors.- 1.6.3 Vertex Deleting Procedure for Determining Eigenvectors.- 1.6.4 Determination of Bond Order.- 1.6.5 Example Applications.- 1.7 References.- 1.8 Problems.- 2. Decomposition of Molecules with n-Fold Symmetry.- 2.1 Introduction.- 2.2 Decomposition of Molecules with 2-Fold Symmetry.- 2.2.1 Mirror Plane Fragmentation.- 2.2.2 Common Right-Hand Mirror Plane Fragments.- 2.2.3 Factorization of Molecules with a Twofold Axis of Rotation.- 2.3 Molecules with n-Fold Symmetry.- 2.3.1 Introduction.- 2.3.2 Factorization of Molecular Graphs with 3-Fold Symmetry.- 2.3.3 Factorization of Molecular Graphs with 4-Fold Symmetry.- 2.3.4 A General Method for Factorization of n-Fold Symmetrical Molecular Graphs.- 2.3.5 Spectroscopic Evidence for Electronic Degeneracy in Molecules with Greater than 2-Fold Symmetry.- 2.4 References.- 2.5 Problems.- 3. Heterocyclic and Organometallic Molecules.- 3.1 Introduction.- 3.2 Heterocyclic and Related Molecules.- 3.2.1 Characteristic Polynomials of Small Molecular Graphs with one Heteroatom.- 3.2.2 Characteristic Polynomials of Small Molecular Garphs with Multiple Heteroatoms.- 3.2.3 Eigenvectors corresponding to heterocyclic molecules.- 3.2.4 3-Fold Polyazaheterocyclic Molecules.- 3.3 Characteristic Polynomials of ?-Hydrocarbon-Iron Tricarbonyl Complexes.- 3:3.1 Basis Orbitals for ?-Hydrocarbonyl-Iron Tricarbonyl Complexes.- 3.3.2 Determining Characteristic Polynomials and Eigenvalues.- 3.3.3 Eigenvalues by Embedding.- 3.3.4 ?E? as a Relative Measure of Reaction Spontaniety.- 3.3.5 Other Examples of Möbius Circuits.- 3.4 References.- 3.5 Problems.- 4. Large Conjugated Polyenes.- 4.1 Introduction.- 4.2 Molecular Orbital Solution of Buckminsterfullerene.- 4.2.1 Introduction.- 4.2.2 Eigenvalues of Buckminsterfullerene.- 4.3 MO Solution of 3-Fold Coronene Derivatives.- 4.3.1 Factorization of 3-Fold Coronene Derivatives.- 4.4 Embedding of Benzenoid Hydrocarbons.- 4.4.1 Examples of Embedding of Allyl, Butadiene, Benzene, Naphthalene, Pentadienyl, and Styrene on Large Benzenoids..- 4.5 References.- 4.6 Problems.- Appendix A. BASIC Program for Finding the Real Roots of a Monic Polynomial.- Compound Index.- General Index.