Quantum Chemistry

Quantum Chemistry: An Introduction provides information pertinent to the fundamental aspects of quantum mechanics. This book presents the theory of partial differentiation equations by using the classical theory of vibrations as a means of developing physical insight into this essential branch of mathematics.

Organized into five parts encompassing 16 chapters, this book begins with an overview of how quantum mechanical deductions are made. This text then describes the achievements and limitations of the application of quantum mechanics to chemical problems. Other chapters provide a brief survey of some essential properties of the associated Legendre functions. The final chapter deals with the Franck-Condon principle, which states that transitions tend to occur between vibrational levels of two different electronic states for which either the minimum or maximum values of the internuclear distance in the potential energy diagram occur with the same nuclear configuration.

This book is a valuable resource for chemists.

Contenu

Preface
Suggested Plan of Study

1. Introduction
   A. Chemistry as a Branch of Mechanics
   B. The Structure and Aims of Scientific Theories
   C. Quantum Mechanics as a Tool and as a Language
   References
   Part I Mathematical Background
2. Some Basic Mathematical Concepts
   A. Operators
   B. Complex Numbers
   C. Well Behaved Functions
   D. Vectors
   E. Probability Functions and Average Values
   F. Series Expansions of Functions
   G. Ordinary Differential Equations
   H. Partial Differential Equations
   I. Determinants
   References
3. The Classical Theory of Vibrations I Some Typical Vibrating Systems
   A. Vibrations in One Dimension
   B. Vibrations of Two-Dimensional Systems
   C. Vibrations of Three-Dimensional Systems
   References
4. The Classical Theory of Vibrations II Approximate Methods for Complex Systems
   A. The Sturm-Liouville Theory
   B. The Variation Method
   C. The Perturbation Method
   D. The Use of Symmetry and Commutation Properties in the Variation and Perturbation Methods
   E. The Interaction of Vibrating Systems
   References
   Part II General Principles Of Quantum Mechanics
5. The Schroedinger Formulation of Quantum Mechanics
   A. Some Fundamental Concepts Used in Quantum Mechanics
   B. The Laws of Quantum Mechanics
   C. Some Important Corollaries of the Laws of Quantum Mechanics
   D. The Quantum Mechanical Treatment of Chemical Systems
   E. Atomic Units
   References
6. Some Solutions of the Steady State Schroedinger Equation
   I. Systems with Constant Potential Energy
   A. Free Particles
   B. Particles in Boxes
   C. Systems Involving Potential Walls of Finite Height
   D. Rotating Bodies
   II. Systems for which the Potential Energy is not Constant
   E. The One-Dimensional Harmonic Oscillator
   F. The Sinusoidal Potential
   G. The Hydrogen Atom and Hydrogen-Like Ions
   H. The Hydrogen Molecular Ion, H2+
   I. The Morse Potential
   J. The Virial Theorem
   References
7. The Uncertainty Relations
   A. Limitations on the Simultaneous Measurement of Position and Momentum
   B. Limitations on the Measurement of Energy in an Observation of Limited Duration
   C. Relationship of Zero-Point Energies to the Uncertainty Principle
   D. Zero-Point Energies and the Formation of Molecules
   References
8. Angular Momentum in Quantum Mechanics
   A. The Angular Momentum of a Single Particle
   B. The Angular Momentum of Systems Composed of Many Particles
   C. Spectroscopic Notation Based on Angular Momentum
   D. Use of Magnetic Fields in Studying the Angular Momentum of Charged Particles
   References
   Part III Atomic Systems
9. Atomic Structure I Hydrogen, Helium, and Electron Spin
   A. The Experimental Determination of the Energy Levels of Atoms
   B. The Energy Levels, Wave Functions, and Spectrum of Hydrogen
   C. The Energy Levels, Wave Functions, and Spectrum of Helium
   D. Electron Spin and the Pauli Principle
   References
10. Atomic Structure II Elements Other than Hydrogen and Helium
    A. The Energies of Orbitals in Elements Beyond Helium; the Periodic System
    B. Multiplet Structure
    C. Spin-Orbit Interaction (Fine Structure)
    D. The Magnetic Properties of Atoms
    References
    Part IV Molecular Systems
11. Molecules and the Chemical Bond I The First Approximation
    A. The Hydrogen Molecular Ion, H2+
    B. The Hydrogen Molecule, H2
    C. Other Diatomic Molecules
    D. Directed Valence Bonds in H2O and NH3
    E. Hybridization and Directed Valence Bonds
    F. Multiple Bonds
    G. Aromatic Compounds
    References
12. Molecules and the Chemical Bond II Difficulties in Developing Satisfactory Quantitative Theories
    A. Criteria for the Reliability of Approximate Wave Functions
    B. Some Problems in Constructing Accurate Molecular Wave Functions
    C. The Quantitative Treatment of Aromatic Hydrocarbons
    D. The Quantitative Comparison of Chemical Bonds Between Different Pairs of Atoms
    References
13. Van der Waals Forces
    A. General Discussion of Intermolecular Forces Not Involving Chemical Bonds
    B. The Interaction of a Pair of Dipoles
    C. The London Forces Between a Pair of Oscillating Dipoles
    D. London Forces Between Two Hydrogen Atoms
    E. London Forces Between More Complex Atoms and Molecules
    References
    Part V Systems In Non-Stationary States
14. Time-Dependent Processes
    A. The Behavior of Localized Clusters of Free Particles
    B. Perturbation Theory for Time-Dependent Processes
    C. Resonance and the Rate of Electronic Tautomerism
    D. Nonadiabatic Transitions
    References
15. The Interactions of Matter with Light I The Classical Electron Theory of Optics
    A. The Basic Assumptions in the Classical Electron Theory of Optics
    B. The Emission of Light by Excited Atoms and Molecules
    C. The Widths and Shapes of Spectral Lines
    D. The Response of Bound Electrons to Light
    E. The Scattering of Light and Some of its Consequences
    F. Other Modes of Producing Radiation
    G. Optical Rotatory Power
    References
16. The Interactions of Matter with Light II Quantum Mechanical Aspects
    A. General Theory
    B. Selection Rules for Dipole Transitions
    C. Absorption Spectra and Color
    D. The Relationship of Absorption and Dispersion
    E. The Return of Excited Molecules to their Ground States
    F. The Quantum Mechanical Basis of Optical Rotatory Power
    References
    Appendixes
    I. Atomic Units
    II. Conversion Factors for Energy Units
    III. Hydrogen Atom Wave Functions
    Index of Symbols
    Subject Index