Quantum Mechanical Foundations of Molecular Spectroscopy

Professor Max Diem is based in the Department of Physical and Biophysical Chemistry at Northeastern University. He did his first degree at the University of Karlsruhe and then his PhD at the University of Toledo in OH. Until 2005 he was at the Central University of New York before moving to Northeastern University. His research interests are is centered on the development of physical / optical methods for medical diagnosis in tissue diagnostics.

• Preface xiIntroduction xv1 Transition from Classical Physics to Quantum Mechanics 11.1 Description of Light as an Electromagnetic Wave 21.2 Blackbody Radiation 31.3 The Photoelectric Effect 51.4 Hydrogen Atom Absorption and Emission Spectra 71.5 Molecular Spectroscopy 101.6 Summary 12References 12Problems 122 Principles of Quantum Mechanics 152.1 Postulates of Quantum Mechanics 162.2 The Potential Energy and Potential Functions 202.3 Demonstration of Quantum Mechanical Principles for a Simple, One-Dimensional, One-Electron Model System: The Particle in a Box 212.3.1 Definition of the Model System 212.3.2 Solution of the Particle-in-a-Box Schrödinger Equation 232.3.3 Normalization and Orthogonality of the PiB Wavefunctions 252.4 The Particle in a Two-Dimensional Box, the Unbound Particle, and the Particle in a Box with Finite Energy Barriers 272.4.1 Particle in a 2D Box 272.4.2 The Unbound Particle 282.4.3 The Particle in a Box with Finite Energy Barriers 292.5 Real-World PiBs: Conjugated Polyenes, Quantum Dots, and Quantum Cascade Lasers 312.5.1 Transitions in a Conjugated Polyene 312.5.2 Quantum Dots 332.5.3 Quantum Cascade Lasers 33References 34Problems 353 Perturbation of Stationary States by Electromagnetic Radiation 373.1 Time-Dependent Perturbation Treatment of Stationary-State Systems by Electromagnetic Radiation 373.2 Dipole-Allowed Absorption and Emission Transitions and Selection Rules for the Particle in a Box 403.3 Einstein Coefficients for the Absorption and Emission of Light 423.4 Lasers 45References 47Problems 474 The Harmonic Oscillator, a Model System for the Vibrations of Diatomic Molecules 494.1 Classical Description of a Vibrating Diatomic Model System 494.2 The Harmonic Oscillator Schrödinger Equation, Energy Eigenvalues, and Wavefunctions 514.3 The Transition Moment and Selection Rules for Absorption for the Harmonic Oscillator 564.4 The Anharmonic Oscillator 594.5 Vibrational Spectroscopy of Diatomic Molecules 624.6 Summary 65References 66Problems 665 Vibrational Infrared and Raman Spectroscopy of Polyatomic Molecules 695.1 Vibrational Energy of Polyatomic Molecules: Normal Coordinates and Normal Modes of Vibration 695.2 Quantum Mechanical Description of Molecular Vibrations in Polyatomic Molecules 735.3 Infrared Absorption Spectroscopy 765.3.1 Symmetry Considerations for Dipole-Allowed Transitions 765.3.2 Line Shapes for Absorption and Anomalous Dispersion 775.3.2.1 Line Shapes and Lifetimes 775.3.2.2 Anomalous Dispersion 795.4 Raman Spectroscopy 815.4.1 General Aspects of Raman Spectroscopy 815.4.2 Macroscopic Description of Polarizability 815.4.3 Quantum Mechanical Description of Polarizability 835.5 Selection Rules for IR and Raman Spectroscopy of Polyatomic Molecules 875.6 Relationship between Infrared and Raman Spectra: Chloroform 885.7 Summary: Molecular Vibrations in Science and Technology 90References 91Problems 916 Rotation of Molecules and Rotational Spectroscopy 936.1 Classical Rotational Energy of Diatomic and Polyatomic Molecules 946.2 Quantum Mechanical Description of the Angular Momentum Operator 976.3 The Rotational Schrödinger Equation, Eigenfunctions, and Rotational Energy Eigenvalues 996.4 Selection Rules for Rotational Transitions 1046.5 Rotational Absorption (Microwave) Spectra 1056.5.1 Rigid Diatomic and Linear Molecules 1056.5.2 Prolate and Oblate Symmetric Top Molecules 1086.5.3 Asymmetric Top Molecules 1106.6 Rot–Vibrational Transitions 110References 113Problems 1137 Atomic Structure: The Hydrogen Atom 1157.1 The Hydrogen Atom Schrödinger Equation 1167.2 Solutions of the Hydrogen Atom Schrödinger Equation 1187.3 Dipole Allowed Transitions for the Hydrogen Atom 1247.4 Discussion of the Hydrogen Atom Results 1247.5 Electron Spin 1267.6 Spatial Quantization of Angular Momentum 129References 130Problems 1308 Nuclear Magnetic Resonance (NMR) Spectroscopy 1318.1 General Remarks 1318.2 Review of Electron Angular Momentum and Spin Angular Momentum 1328.3 Nuclear Spin 1348.4 Selection Rules, Transition Energies, Magnetization, and Spin State Population 1378.4.1 Electric Dipole Selection Rules for a One-Spin Nuclear System 1378.4.2 Transition Energies 1388.4.3 Magnetization 1388.4.4 Spin State Population Analysis 1398.5 Chemical Shift 1408.6 Multispin Systems 1418.6.1 Noninteracting Spins 1418.6.2 Interacting Spins: Spin–Spin Coupling 1438.6.3 Interaction of Multiple Spins 1448.7 Pulse FT NMR Spectroscopy 1468.7.1 General Comments 1468.7.2 Description of NMR Event in Terms of the “Net Magnetization” 147References 148Problems 1499 Atomic Structure: Multi-electron Systems 1519.1 The Two-electron Hamiltonian, Shielding, and Effective Nuclear Charge 1519.2 The Pauli Principle 1529.3 The Aufbau Principle 1539.4 Periodic Properties of Elements 1559.5 Atomic Energy Levels 1569.5.1 Good and Bad Quantum Numbers and Term Symbols 1569.5.2 Selection Rules for Transitions in Atomic Species 1599.6 Atomic Spectroscopy 1609.7 Atomic Spectroscopy in Analytical Chemistry 161References 162Problems 16210 Electronic States and Spectroscopy of Polyatomic Molecules 16310.1 Molecular Orbitals and Chemical Bonding in the H2 + Molecular Ion 16310.2 Molecular Orbital Theory for Homonuclear Diatomic Molecules 16810.3 Term Symbols and Selection Rules for Homonuclear Diatomic Molecules 17110.4 Electronic Spectra of Diatomic Molecules 17310.4.1 The Vibronic Absorption Spectrum of Oxygen 17310.4.2 Vibronic Transitions and the Franck–Condon Principle 17510.5 Qualitative Description of Electronic Spectra of Polyatomic Molecules 17710.5.1 Selection Rules for Electronic Transitions 17810.5.2 Common Electronic Chromophores 17810.5.2.1 Carbonyl Chromophore 17810.5.2.2 Olefins 17910.5.2.3 Benzene 18010.5.2.4 Other Aromatic Molecules 18010.5.2.5 Transition Metals in the Electrostatic Field of Ligands 18110.6 Fluorescence Spectroscopy 18110.6.1 Fluorescence Energy Level (Jablonski) Diagram 18210.6.2 Intersystem Crossing and Phosphorescence 18310.6.3 Two-Photon Fluorescence 18310.6.4 Summary of Mechanisms for Raman, Resonance Raman, and Fluorescence Spectroscopies 18410.7 Optical Activity: Electronic Circular Dichroism and Optical Rotation 18510.7.1 Circularly Polarized Light and Chirality 18510.7.2 Manifestation of Optical Activity: Optical Rotation, Optical Rotatory Dispersion and Circular Dichroism 18710.7.3 Optical Activity of Asymmetric Molecules: The Magnetic Transition Moment 18810.7.4 Optical Activity of Dissymmetric Molecules: Transition Coupling and the Exciton Model 19110.7.5 Vibrational Optical Activity 192References 193Problems 19411 Group Theory and Symmetry 19911.1 Symmetry Operations and Symmetry Groups 20011.2 Group Representations 20411.3 Symmetry Representations of Molecular Vibrations 21111.4 Symmetry-Based Selection Rules for Dipole-Allowed Processes 21411.5 Selection Rules for Raman Scattering 21711.6 Character Tables of a Few Common Point Groups 218References 219Problems 219Appendix 1 Constants and Conversion Factors 221Appendix 2 Approximative Methods: Variation and Perturbation Theory 223A2.1 General Remarks 223A2.2 Variation Method 224A2.3 Time-independent Perturbation Theory for Nondegenerate Systems 225A2.4 Detailed Example of Time-independent Perturbation: The Particle in a Box with a Sloped Potential Function 226A2.5 Time-dependent Perturbation of Molecular Systems by ElectromagneticRadiation 230Reference 231Appendix 3 Nonlinear Spectroscopic Techniques 233A3.1 General Formulation of Nonlinear Effects 233A3.2 Noncoherent Nonlinear Effects: Hyper-Raman Spectroscopy 234A3.3 Coherent Nonlinear Effects 235A3.3.1 Second Harmonic Generation 236A3.3.2 Coherent Anti-Stokes Raman Scattering (CARS) 237A3.3.3 Stimulated Raman Scattering (SRS) and Femtosecond Stimulated Raman Scattering (FSRS) 240A3.4 Epilogue 242References 242Appendix 4 Fourier Transform (FT) Methodology 243A4.1 Introduction to Fourier Transform Spectroscopy 243A4.2 Data Representation in Different Domains 244A4.3 Fourier Series 244A4.4 Fourier Transform 247A4.5 Discrete and Fast Fourier Transform Algorithms 248A4.6 FT Implementation in EXCEL or MATLAB 249References 251Appendix 5 Description of Spin Wavefunctions by Pauli Spin Matrices 253A5.1 The Formulation of Spin Eigenfunctions ;; and ;; as Vectors 254A5.2 Form of the Pauli Spin Matrices 255A5.3 Eigenvalues of the Spin Matrices 256Reference 257Index 259