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Max Diem. Quantum Mechanical Foundations of Molecular Spectroscopy
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Quantum Mechanical Foundations of Molecular Spectroscopy
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
2.3.1 Definition of the Model System
2.3.2 Solution of the Particle‐in‐a‐Box Schrödinger Equation
2.3.3 Normalization and Orthogonality of the PiB Wavefunctions
2.4 The Particle in a Two‐Dimensional Box, the Unbound Particle, and the Particle in a Box with Finite Energy Barriers. 2.4.1 Particle in a 2D Box
2.4.2 The Unbound Particle
2.4.3 The Particle in a Box with Finite Energy Barriers
2.5 Real‐World PiBs: Conjugated Polyenes, Quantum Dots, and Quantum Cascade Lasers. 2.5.1 Transitions in a Conjugated Polyene
2.5.2 Quantum Dots
2.5.3 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
5.3.1 Symmetry Considerations for Dipole‐Allowed Transitions
5.3.2 Line Shapes for Absorption and Anomalous Dispersion. 5.3.2.1 Line Shapes and Lifetimes
5.3.2.2 Anomalous Dispersion
5.4 Raman Spectroscopy. 5.4.1 General Aspects of Raman Spectroscopy
5.4.2 Macroscopic Description of Polarizability
5.4.3 Quantum Mechanical Description of Polarizability
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. 6.5.1 Rigid Diatomic and Linear Molecules
6.5.2 Prolate and Oblate Symmetric Top Molecules
6.5.3 Asymmetric Top Molecules
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
8.4.1 Electric Dipole Selection Rules for a One‐Spin Nuclear System
8.4.2 Transition Energies
8.4.3 Magnetization
8.4.4 Spin State Population Analysis
8.5 Chemical Shift
8.6 Multispin Systems. 8.6.1 Noninteracting Spins
8.6.2 Interacting Spins: Spin–Spin Coupling
8.6.3 Interaction of Multiple Spins
8.7 Pulse FT NMR Spectroscopy. 8.7.1 General Comments
8.7.2 Description of NMR Event in Terms of the “Net Magnetization”
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
9.5.1 Good and Bad Quantum Numbers and Term Symbols
9.5.2 Selection Rules for Transitions in Atomic Species
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. 10.4.1 The Vibronic Absorption Spectrum of Oxygen
10.4.2 Vibronic Transitions and the Franck–Condon Principle
10.5 Qualitative Description of Electronic Spectra of Polyatomic Molecules
10.5.1 Selection Rules for Electronic Transitions
10.5.2 Common Electronic Chromophores
10.5.2.1 Carbonyl Chromophore
10.5.2.2 Olefins
10.5.2.3 Benzene
10.5.2.4 Other Aromatic Molecules
10.5.2.5 Transition Metals in the Electrostatic Field of Ligands
10.6 Fluorescence Spectroscopy
10.6.1 Fluorescence Energy Level (Jablonski) Diagram
10.6.2 Intersystem Crossing and Phosphorescence
10.6.3 Two‐Photon Fluorescence
10.6.4 Summary of Mechanisms for Raman, Resonance Raman, and Fluorescence Spectroscopies
10.7.1 Circularly Polarized Light and Chirality
10.7.2 Manifestation of Optical Activity: Optical Rotation, Optical Rotatory Dispersion and Circular Dichroism
10.7.3 Optical Activity of Asymmetric Molecules: The Magnetic Transition Moment
10.7.4 Optical Activity of Dissymmetric Molecules: Transition Coupling and the Exciton Model
10.7.5 Vibrational Optical Activity
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
A3.3.1 Second Harmonic Generation
A3.3.2 Coherent Anti‐Stokes Raman Scattering (CARS)
A3.3.3 Stimulated Raman Scattering (SRS) and Femtosecond Stimulated Raman Scattering (FSRS)
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. a
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