Quantum Mechanics For Organic Chemists

ContentsPrefaceChapter 1 Delineation of the Methods and Results of the LCAO-MO Hiickel Approach 1.1 Some Preliminary Basic Definitions and Introductory Material 1.2 Basic Procedure for Quantum Mechanical Mixing of Atomic Orbitals; Solution for Molecular Orbital Energies 1.3 Elucidation of the Electronic Nature of Molecular Orbitals; Determination of LCAO-MO Coefficients 1.4 Choice of the Basis Set of Atomic Orbitals in LCAO-MO Calculations 1.5 Cases Where Negative Overlap Is Enforced in the Basis Set 1.6 The Hückel and Möbius Rules 1.7 Relation between the LCAO-MO Coefficients and the Molecular Orbital Energies Problems References Chapter 2 Introduction to Some Concepts of Quantum Mechanics and the Theoretical Basis of the LCAO-MO Method 2.1 Fundamental Concepts of Quantum Mechanics 2.2 The Variation Method; Minimization of LCAO-MO Energy to Give the Secular Equation and Secular Determinant 2.3 Justification of the Method of Cofactors for Determining LCAO Coefficients 2.4 The Hermitian Character of the Molecular Orbital Operators 2.5 Rank of Secular Determinants as Affecting Determination of Coefficients Suggested Reading Chapter 3 The Use of Molecular Symmetry for Simplification of Secular Determinants; Introduction to Group Theory 3.1 Conversion of Secular Determinants Expressed in Terms of Atomic Orbitals into Secular Determinants Expressed in Terms of Group (Symmetry) Orbitals 3.2 Matrix Methods for Diagonalizing Secular Determinants and Matrices; The Heisenberg Formulation of Quantum Mechanics 3.3 Matrix Methods for Perturbation Calculations 3.4 The Jacobi Method for Diagonalization of Matrices 3.5 More Formal Use of Symmetry by Means of Group Theory 3.6 Complex Characters in Deriving the Hückel and Möbius Solutions 3.7 Use of Moiety Eigenfunctions in Construction of Molecular Orbitals Problems Suggested ReadingChapter 4 Extensions, Modifications, and Applications of the Hückel Approach 4.1 Calculations for Molecules Containing Heteroatoms 4.2 Inclusion of Overlap 4.3 Treatment of Hybrid and Unusually Oriented Orbitals 4.4 Properties of Alternant Hydrocarbons 4.5 The Dewar Nonbonding MO Method 4.6 Nonbonding MOs in Möbius Systems 4.7 Uses of the NBMO Coefficients 4.8 The Mulliken-Wheland-Mann and Omega Techniques 4.9 Correlation Diagrams; Reaction Allowedness and Forbiddenness Problems References Chapter 5 More Advanced Methods; Three-Dimensional Treatments and Polyelectron Wavefunctions 5.1 Polyelectron Wavef unctions; Slater Determinants 5.2 Energy of a Single Slater Determinantal Wavefunction 5.3 Evaluation of MO Repulsion Integrals 5.4 Energy of a Slater Determinant for a Closed Shell in Terms of Atomic Orbital Integrals 5.5 Minimization of the Energy of a Slater Determinant; Roothaan's SCF Equations 5.6 Pople's SCF Equations 5.7 Configuration Interaction 5.8 General Expressions for Use in Configuration Interaction 5.9 Three-Dimensional Hückel Theory; The Extended Hückel Treatment 5.10 Three-Dimensional SCF Methods Problems References Answers to Problems Index