Molecular Orbital Calculations Using Chemical Graph Theory
Professor John D. Roberts published a highly readable book on Molecular Orbital Calculations directed toward chemists in 1962. That timely book is the model for this book. The audience this book is directed toward are senior undergraduate and beginning graduate students as well as practicing bench chemists who have a desire to develop conceptual tools for understanding chemical phenomena. Although, ab initio and more advanced semi-empirical MO methods are regarded as being more reliable than HMO in an absolute sense, there is good evidence that HMO provides reliable relative answers particularly when comparing related molecular species. Thus, HMO can be used to rationalize electronic structure in 1t-systems, aromaticity, and the shape use HMO to gain insight of simple molecular orbitals. Experimentalists still into subtle electronic interactions for interpretation of UV and photoelectron spectra. Herein, it will be shown that one can use graph theory to streamline their HMO computational efforts and to arrive at answers quickly without the aid of a group theory or a computer program of which the experimentalist has no understanding. The merging of mathematical graph theory with chemical theory is the formalization of what most chemists do in a more or less intuitive mode. Chemists currently use graphical images to embody chemical information in compact form which can be transformed into algebraical sets. Chemical graph theory provides simple descriptive interpretations of complicated quantum mechanical calculations and is, thereby, in-itself-by-itself an important discipline of study.
- Paperback | 115 pages
- 155 x 235 x 7.11mm | 215g
- 24 Jun 1993
- Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Berlin, Germany
- Softcover reprint of the original 1st ed. 1993
- XI, 115 p.
Table of contents
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 Moebius 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.