Quantum Chemistry

PrefaceChapter 1 Classical Waves and the Time-Independent Schrödinger Wave Equation 1-1 Introduction 1-2 Waves 1-3 The Classical Wave Equation 1-4 Standing Waves in a Clamped String 1-5 Light as an Electromagnetic Wave 1-6 The Photoelectric Effect 1-7 The Wave Nature of Matter 1-8 A Diffraction Experiment with Electrons 1-9 Schrödinger's Time-Independent Wave Equation 1-10 Conditions on ψ 1-11 Some Insight into the Schrödinger Equation 1-12 Summary Problems Chapter 2 Quantum Mechanics of Some Simple Systems 2-1 The Particle in a One-Dimensional "Box" 2-2 Detailed Examination of Particle-in-a-Box Solutions 2-3 The Particle in a One-Dimensional "Box" with One Finite Wall 2-4 The Particle in an Infinite "Box" with a Finite Central Barrier 2-5 The Free Particle in One Dimension 2-6 The Particle in a Ring of Constant Potential 2-7 The Particle in a Three-Dimensional Box: Separation of Variables 2-8 Summary Problems Reference Chapter 3 The One-Dimensional Harmonic Oscillator 3-1 Introduction 3-2 Some Characteristics of the Classical One-Dimensional Harmonic Oscillator 3-3 The Quantum-Mechanical Harmonic Oscillator 3-4 Solution of the Harmonic Oscillator Schrödinger Equation 3-5 Quantum-Mechanical Average Value of the Potential Energy Problems Chapter 4 The Hydrogenlike Ion 4-1 The Schrödinger Equation and the Nature of Its Solutions 4-2 Separation of Variables 4-3 Solution of the R, Θ, and Φ Equations 4-4 Atomic Units 4-5 Angular Momentum and Spherical Harmonics 4-6 Summary Problems References Chapter 5 Many-Electron Atoms 5-1 The Independent Electron Approximation 5-2 Simple Products and Electron Exchange Symmetry 5-3 Electron Spin and the Exclusion Principle 5-4 Slater Determinants and the Pauli Principle 5-5 Singlet and Triplet States for the ls2s Configuration of Helium 5-6 The Self-Consistent Field, Slater-Type Orbitals, and the Aufbau Principle Problems References Chapter 6 Postulates and Theorems of Quantum Mechanics 6-1 Introduction 6-2 The Wavefunction Postulate 6-3 The Postulate for Constructing Operators 6-4 The Time-Dependent Schrödinger Equation Postulate 6-5 The Postulate Relating Measured Values to Eigenvalues 6-6 The Postulate for Average Values 6-7 Hermitian Operators 6-8 Proof That Eigenvalues of Hermitian Operators Are Real 6-9 Proof That Eigenfunctions of an Hermitian Operator Form an Orthonormal Set 6-10 Proof That Commuting Operators Have Simultaneous Eigenfunctions 6-11 Completeness of Eigenfunctions of an Hermitian Operator 6-12 The Variation Principle 6-13 Measurement, Commutators, and Uncertainty 6-14 Summary Problems ReferencesChapter 7 The Variation Method 7-1 The Spirit of the Method 7-2 Nonlinear Variation: The Hydrogen Atom 7-3 Nonlinear Variation: The Helium Atom 7-4 Linear Variation: The Polarizability of the Hydrogen Atom 7-5 Linear Combination of Atomic Orbitals: The H2+ Molecule-Ion 7-6 Molecular Orbitals of Homonuclear Diatomic Molecules 7-7 Basis Set Choice and the Variational Wavefunction 7-8 Beyond the Orbital Approximation Problems References Chapter 8 The Simple Hückel Method and Applications 8-1 The Importance of Symmetry 8-2 The Assumption of σ-π Separability 8-3 The Independent π-Electron Assumption 8-4 Setting up the Hückel Determinant 8-5 Solving the HMO Determinantal Equation for Orbital Energies 8-6 Solving for the Molecular Orbitals 8-7 The Cyclopropenyl System: Handling Degeneracies 8-8 Charge Distributions from HMOs 8-9 Some Simplifying Generalizations 8-10 HMO Calculations on Some Simple Molecules 8-11 Summary: The Simple HMO Method for Hydrocarbons 8-12 Relation between Bond Order and Bond Length 8-13 π-Electron Densities and Electron Spin Resonance Hyperfine Splitting Constants 8-14 Orbital Energies and Oxidation-Reduction Potentials 8-15 Orbital Energies and Ionization Potentials 8-16 π-Electron Energy and Aromaticity 8-17 Extension to Heteroatomic Molecules 8-18 Self-Consistent Variations of α and ß 8-19 HMO Reaction Indices 8-20 Conclusions Problems References Chapter 9 Matrix Formulation of the Linear Variation Method 9-1 Introduction 9-2 Matrices and Vectors 9-3 Matrix Formulation of the Linear Variation Method 9-4 Solving the Matrix Equation 9-5 Summary Problems ReferencesChapter 10 The Extended Hückel Method 10-1 The Extended Hückel Method 10-2 Mulliken Populations 10-3 Extended Hückel Energies and Mulliken Populations 10-4 Extended Hückel Energies and Experimental Energies Problems References Chapter 11 The SCF-LCAO-MO Method and Extensions 11-1 Ab Initio Calculations 11-2 The Molecular Hamiltonian 11-3 The Form of the Wavefunction 11-4 The Nature of the Basis Set 11-5 The LCAO-MO-SCF Equation 11-6 Interpretation of the LCAO-MO-SCF Eigenvalues 11-7 The SCF Total Electronic Energy 11-8 Basis Sets 11-9 The Hartree-Fock Limit 11-10 Correlation Energy 11-11 Koopmans' Theorem 11-12 Configuration Interaction 11-13 Examples of Ab Initio Calculations 11-14 Approximate SCF-MO Methods Problems References Chapter 12 Time-Independent Rayleigh-Schrödinger Perturbation Theory 12-1 An Introductory Example 12-2 Formal Development of the Theory for Nondegenerate States 12-3 A Uniform Electrostatic Perturbation of an Electron in a "Wire" 12-4 The Ground-State Energy to First Order of Heliumlike Systems 12-5 Perturbation at an Atom in the Simple Hückel MO Method 12-6 Perturbation Theory for a Degenerate State 12-7 Polarizability of the Hydrogen Atom in the n = 2 States 12-8 Interaction between Two Orbitals: An Important Chemical Model 12-9 Connection between Time-Independent Perturbation Theory and Spectroscopic Selection Rules Problems References Chapter 13 Group Theory 13-1 Introduction 13-2 An Elementary Example 13-3 Symmetry Point Groups 13-4 The Concept of Class 13-5 Symmetry Elements and Their Notation 13-6 Identifying the Point Group of a Molecule 13-7 Representations for Groups 13-8 Generating Representations from Basis Functions 13-9 Labels for Representations 13-10 Some Connections between the Representation Table and Molecular Orbitals 13-11 Representations for Cyclic and Related Groups 13-12 Orthogonality in Irreducible Inequivalent Representations 13-13 Characters and Character Tables 13-14 Using Characters to Resolve Reducible Representations 13-15 Identifying Molecular Orbital Symmetries 13-16 Determining in Which Molecular Orbital an Atomic Orbital Will Appear 13-17 Generating Symmetry Orbitals 13-18 Hybrid Orbitals and Localized Orbitals 13-19 Symmetry and Integration Problems References Chapter 14 Qualitative Molecular Orbital Theory 14-1 The Need for a Qualitative Theory 14-2 Hierarchy in Molecular Structure and in Molecular Orbitals 14-3 H2+ Revisited 14-4 H2: Comparisons with 2+ 14-5 Rules for Qualitative Molecular Orbital Theory 14-6 Application of QMOT Rules to Homonuclear Diatomic Molecules 14-7 Shapes of Polyatomic Molecules: Walsh Diagrams 14-8 Frontier Orbitals 14-9 Qualitative Molecular Orbital Theory of Reactions Problems References Appendix 1 Useful Integrals Appendix 2 Determinants Appendix 3 Evaluation of the Coulomb Repulsion Integral over Is AOs Appendix 4 Some Characteristics of Solutions of the Linear Variation ProcedureAppendix 5 The Pairing Theorem Appendix 6 Hückel Molecular Orbital Energies, Coefficients, Electron Densities, and Bond Orders for Some Simple Molecules Appendix 7 Derivation of the Hartree-Fock Equation Appendix 8 The Virial Theorem for Atoms and Diatomic Molecules Appendix 9 Details of the Solution of the Matrix Equation HC=SCE Appendix 10 Computer Program Listings Appendix 11 Bra-Ket Notation Appendix 12 Values of Some Useful Constants and Conversion Factors Appendix 13 Group Theoretical Charts and Tables Appendix 14 Hints for Solving Selected Problems Appendix 15 Answers to Selected Problems Index