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Molecular Orbital Calculations Using Chemical Graph Theory - Jerry Ray Dias

Molecular Orbital Calculations Using Chemical Graph Theory


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This text is directed toward senior undergraduate and beginning graduate students as well as practicing chemists. It provides conceptual tools for understanding chemical phenomena with HMO theory. The author demonstrates that one can use graph theory to streamline HMO calculations without the aid of group theory or computer programmes. The merging of graph theory and chemical theory is intuitive to chemists. Chemical graph theory provides simple descriptive interpretations of complicated quantum mechanical calculations. The author provides practical applications on numerous HMO energy levels (eigenvalues) and corresponding wave functions (eigenvectors).

1. Small Conjugated Polyenes.- 1.1 Introduction.- 1.2 Huckel 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 Kekule 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 Mobius 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.

ISBN: 9783540561347
ISBN-10: 354056134X
Audience: General
Format: Paperback
Language: English
Number Of Pages: 115
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 0.71
Weight (kg): 0.2