Quantum Mechanical Foundations of Molecular Spectroscopy

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Title Page Copyright Preface Introduction References 1 Transition from Classical Physics to Quantum Mechanics 1.1 Description of Light as an Electromagnetic Wave 1.2 Blackbody Radiation 1.3 The Photoelectric Effect 1.4 Hydrogen Atom Absorption and Emission Spectra 1.5 Molecular Spectroscopy 1.6 Summary References Problems 2 Principles of Quantum Mechanics 2.1 Postulates of Quantum Mechanics 2.2 The Potential Energy and Potential Functions 2.3 Demonstration of Quantum Mechanical Principles for a Simple, One‐Dimensional, One‐Electron Model System: The Particle in a Box 2.4 The Particle in a Two‐Dimensional Box, the Unbound Particle, and the Particle in a Box with Finite Energy Barriers 2.5 Real‐World PiBs: Conjugated Polyenes, Quantum Dots, and Quantum Cascade Lasers References Problems 3 Perturbation of Stationary States by Electromagnetic Radiation 3.1 Time‐Dependent Perturbation Treatment of Stationary‐State Systems by Electromagnetic Radiation 3.2 Dipole‐Allowed Absorption and Emission Transitions and Selection Rules for the Particle in a Box 3.3 Einstein Coefficients for the Absorption and Emission of Light 3.4 Lasers References Problems Note 4 The Harmonic Oscillator, a Model System for the Vibrations of Diatomic Molecules 4.1 Classical Description of a Vibrating Diatomic Model System 4.2 The Harmonic Oscillator Schrödinger Equation, Energy Eigenvalues, and Wavefunctions 4.3 The Transition Moment and Selection Rules for Absorption for the Harmonic Oscillator 4.4 The Anharmonic Oscillator 4.5 Vibrational Spectroscopy of Diatomic Molecules 4.6 Summary References Problems 5 Vibrational Infrared and Raman Spectroscopy of Polyatomic Molecules 5.1 Vibrational Energy of Polyatomic Molecules: Normal Coordinates and Normal Modes of Vibration 5.2 Quantum Mechanical Description of Molecular Vibrations in Polyatomic Molecules 5.3 Infrared Absorption Spectroscopy 5.4 Raman Spectroscopy 5.5 Selection Rules for IR and Raman Spectroscopy of Polyatomic Molecules 5.6 Relationship between Infrared and Raman Spectra: Chloroform 5.7 Summary: Molecular Vibrations in Science and Technology References Problems 6 Rotation of Molecules and Rotational Spectroscopy 6.1 Classical Rotational Energy of Diatomic and Polyatomic Molecules 6.2 Quantum Mechanical Description of the Angular Momentum Operator 6.3 The Rotational Schrödinger Equation, Eigenfunctions, and Rotational Energy Eigenvalues 6.4 Selection Rules for Rotational Transitions 6.5 Rotational Absorption (Microwave) Spectra 6.6 Rot–Vibrational Transitions References Problems 7 Atomic Structure: The Hydrogen Atom 7.1 The Hydrogen Atom Schrödinger Equation 7.2 Solutions of the Hydrogen Atom Schrödinger Equation 7.3 Dipole Allowed Transitions for the Hydrogen Atom 7.4 Discussion of the Hydrogen Atom Results 7.5 Electron Spin 7.6 Spatial Quantization of Angular Momentum References Problems Note 8 Nuclear Magnetic Resonance (NMR) Spectroscopy 8.1 General Remarks 8.2 Review of Electron Angular Momentum and Spin Angular Momentum 8.3 Nuclear Spin 8.4 Selection Rules, Transition Energies, Magnetization, and Spin State Population 8.5 Chemical Shift 8.6 Multispin Systems 8.7 Pulse FT NMR Spectroscopy References Problems 9 Atomic Structure: Multi‐electron Systems 9.1 The Two‐electron Hamiltonian, Shielding, and Effective Nuclear Charge 9.2 The Pauli Principle 9.3 The Aufbau Principle 9.4 Periodic Properties of Elements 9.5 Atomic Energy Levels 9.6 Atomic Spectroscopy 9.7 Atomic Spectroscopy in Analytical Chemistry References Problems 10 Electronic States and Spectroscopy of Polyatomic Molecules 10.1 Molecular Orbitals and Chemical Bonding in the H2+ Molecular Ion 10.2 Molecular Orbital Theory for Homonuclear Diatomic Molecules 10.3 Term Symbols and Selection Rules for Homonuclear Diatomic Molecules 10.4 Electronic Spectra of Diatomic Molecules 10.5 Qualitative Description of Electronic Spectra of Polyatomic Molecules 10.6 Fluorescence Spectroscopy 10.7 Optical Activity: Electronic Circular Dichroism and Optical Rotation References Problems Note 11 Group Theory and Symmetry 11.1 Symmetry Operations and Symmetry Groups 11.2 Group Representations 11.3 Symmetry Representations of Molecular Vibrations 11.4 Symmetry‐Based Selection Rules for Dipole‐Allowed Processes 11.5 Selection Rules for Raman Scattering 11.6 Character Tables of a Few Common Point Groups References Problems Appendix 1: Constants and Conversion Factors Appendix 2: Approximative Methods: Variation and Perturbation Theory A2.1 General Remarks A2.2 Variation Method A2.3 Time‐independent Perturbation Theory for Nondegenerate Systems A2.4 Detailed Example of Time‐independent Perturbation: The Particle in a Box with a Sloped Potential Function A2.5 Time‐dependent Perturbation of Molecular Systems by Electromagnetic Radiation Reference Appendix 3: Nonlinear Spectroscopic Techniques A3.1 General Formulation of Nonlinear Effects A3.2 Noncoherent Nonlinear Effects: Hyper‐Raman Spectroscopy A3.3 Coherent Nonlinear Effects A3.4 Epilogue References Appendix 4: Fourier Transform (FT) Methodology A4.1 Introduction to Fourier Transform Spectroscopy A4.2 Data Representation in Different Domains A4.3 Fourier Series A4.4 Fourier Transform A4.5 Discrete and Fast Fourier Transform Algorithms A4.6 FT Implementation in EXCEL or MATLAB References Appendix 5: Description of Spin Wavefunctions by Pauli Spin Matrices A5.1 The Formulation of Spin Eigenfunctions α and β as Vectors A5.2 Form of the Pauli Spin Matrices A5.3 Eigenvalues of the Spin Matrices Reference Index End User License Agreement