Quantum Chemistry

Quantum Chemistry

1st Edition - September 28, 1978

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  • Author: John Lowe
  • eBook ISBN: 9780323141161

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Description

Quantum Chemistry covers the basic principles, methods, and results of quantum chemistry, providing insights on electron behavior. This book is organized into 14 chapters that focus on ground state molecular orbital theory. After briefly dealing with some of the concepts of classical physics, the book goes on describing some simple but important particle systems. It then examines several systems with discontinuous potential energies, such as the simple harmonic oscillator and the hydrogen-like ion system. A chapter presents a set of postulates and theorems that form the formal foundation of quantum mechanics. Considerable chapters are devoted to various quantum chemical methods, as well as their basic features and application to molecular orbital evaluation. These methods include Huckel molecular orbital, variation, linear variation, extended Huckel, and SCF-LCAO-MO. The concluding chapters deal with the development of theories for molecular orbital, including time-independent Rayleigh-Schrodinger perturbation, group, and qualitative molecular orbital theories. Supplemental texts of the more complicated derivations or proofs and problems encountered in quantum chemistry are also provided. This book is an introductory text intended for organic, inorganic, and physical chemists, as well as for graduate and undergraduate students.

Table of Contents


  • Preface

    Chapter 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

    References

    Chapter 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

    References

    Chapter 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 Procedure

    Appendix 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


Product details

  • No. of pages: 618
  • Language: English
  • Copyright: © Academic Press 1978
  • Published: September 28, 1978
  • Imprint: Academic Press
  • eBook ISBN: 9780323141161

About the Author

John Lowe

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