Fundamental Concepts of Molecular Spectroscopy

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
About the Author
1 Electromagnetic Wave Nature of Light
1.1 Gauss’s Law of Electrostatics
1.2 Gauss’s Law of Magnetism
1.3 Faraday’s Law of Induced Electric Field
1.4 Ampere’s Law of Induced Magnetic Field
1.5 Maxwell’s Equations
1.6 Wave Equation
1.7 Homogeneous Traveling Plane Wave
1.8 Wave Packet
Problems
Bibliography
2 Postulates of Quantum Mechanics
2.1 Stern-Gerlach Experiment
2.2 Postulates of Quantum Mechanics
2.2.1 Postulate 1
2.2.2 Postulate 2
2.2.3 Postulate 3
2.2.4 Postulate 4
2.2.5 Postulate 5
2.2.6 Postulate 6
2.3 Perturbation Theory
2.3.1 Perturbation of a Nondegenerate System
2.3.2 Perturbation of a Degenerate State
Problems
Bibliography
3 Semiclassical Theory of Spectroscopic Transition
3.1 Two-Level System
3.2 System-Radiation Interaction
3.3 Time Development of Eigenstate Probabilities
3.4 Probability Expressions
3.5 Rabi Oscillations
3.6 Transition Probability and Absorption Coefficient
3.7 Limitations of the Theory
3.8 Collisional Line Broadening
3.9 Line Broadening From Excited State Lifetime
3.10 Spectral Line Shape and Line Width
3.10.1 Homogeneous Or Lorentzian Line Shape
3.10.2 Inhomogeneous Or Gaussian Line Shape
3.10.3 Doppler Interpretation of Inhomogeneous Line Shape
Problems
Further Reading
4 Hydrogen Atom Spectra
4.1 Free Hydrogen Atom
4.2 Eigenvalues, Quantum Numbers, Spectra, and Selection Rules
4.3 Hydrogen Atom in External Magnetic Field: Zeeman Effect and Spectral Multiplets
4.3.1 Magnetic Moment in External Magnetic Field
4.3.2 Larmor Precession
4.3.3 Eigenstate, Operator, and Eigenvalue in External Magnetic Field
4.4 Anomalous Zeeman Effect and Further Splitting of Spectra
4.4.1 Electron Spin and Spin Magnetic Moment
4.4.2 Lande -Factor
4.4.3 Spin-Orbit Coupling
4.4.4 Spin-Orbit Coupling Energy
4.4.5 Spectroscopic Notation
4.4.6 Fine Structure of Atomic Spectra
4.4.7 Splitting of Degeneracy: Anomalous Zeeman Effect
4.5 Zeeman Effect in Weak Magnetic Field
4.6 Zeeman Splitting Changeover From Weak to Strong Magnetic Field
4.7 Electron-Nuclear Hyperfine Interaction
4.8 Zeeman Splitting of Hyperfine Energy Levels
4.8.1 Zeeman Splitting of Hyperfine States in Weak Magnetic Field
4.8.2 Hyperfine States of Hydrogen Atom in Strong Magnetic Field
4.9 Stark Effect
4.9.1 Hydrogen Atom in External Electric Field
4.9.2 Effect On the Level
4.9.3 Effect On the Level
Problems
Bibliography
5 Molecular Eigenstates
5.1 Born-Oppenheimer Approximation
5.2 Solution of the Total Schrödinger Equation
5.3 States of Nuclear Motion
5.4 Adiabatic and Nonadiabatic Processes
5.5 Molecular Potential Energy States
5.5.1 One-Electron Hydrogen-Like Atom States
5.5.2 Molecular Electronic States Derived From Atom States
5.6 LCAO-MO
5.7 Molecular Eigenstates of H₂+
5.8 Molecular Eigenstates of H₂
5.9 Singlet and Triplet Excited States of H₂
5.10 Electric Dipole Transition in H₂
5.11 Molecular Orbital Energy and Electronic Configuration
5.12 Molecular Orbitals of Heteronuclear Diatomic Molecule
5.13 Molecular Orbitals of Large Systems
5.13.1 LCAO-MO of Porphyrins
5.13.2 Free-Electron Orbitals of Porphyrins
Problems
Bibliography
6 Elementary Group Theory
6.1 Symmetry Operations
6.1.1 Rotation
6.1.2 Reflection
6.1.3 Improper Rotation
6.1.4 Inversion
6.2 Point Group
6.2.1 Properties of Point Groups
6.2.2 Representation of Symmetry Operators of a Group
6.3 Group Representations
6.4 Labels of Irreducible Representations
6.5 Reduction of Representations to Irreducible Representations
6.6 Direct Product of Irreducible Representations
6.7 Applications
6.7.1 Energy Eigenvalues of Molecular Orbitals
6.7.2 Removal of Energy Degeneracy By Perturbation
6.7.3 General Selection Rules for Electronic Transitions
6.7.4 Specific Transition Rules
Problems
Bibliography
7 Rotational Spectra
7.1 Rotational Spectra of Diatomic Molecules
7.1.1 Schrödinger Equation for Diatomic Rotation
7.1.2 Rotational Energy of Rigid Rotor
7.1.3 Rotational Energy of Non-Rigid Rotor
7.1.4 Stationary State Eigenfunctions and Rotational Transitions
7.1.5 Energy Levels and Representation of Pure Rotational Spectra
7.2 Rotational Spectra of Polyatomic Molecules
7.2.1 Rotational Inertia
7.2.2 Energy of Rigid Rotors
7.2.3 Wavefunctions of Symmetric Tops
7.2.4 Commutation of Rotational Angular Momentum Operators
7.2.5 Eigenvalues for Tops
7.2.6 Selection Rules for Polyatomic Rotational Transition
Problems
8 Diatomic Vibrations, Energy, and Spectra
8.1 Classical Description of an Oscillator
8.2 Schrödinger Equation for Nuclear Vibration
8.3 Selection Rules for Vibrational Transitions
8.4 Rotational–Vibrational Combined Structure
Problems
9 Polyatomic Vibrations and Spectra
9.1 A Simple Classical Model to Define a Normal Mode
9.2 Vibrational Energy From Classical Mechanics
9.3 Solution of Lagrange’s Equation
9.4 Vibrational Hamiltonian and Wavefunction
9.5 Symmetry of Normal Modes
9.6 Finding the Vibrational Frequencies
9.7 Activity of Normal Modes of Vibration
9.8 Secondary Band Manifold in Infrared Spectra
9.8.1 Overtone Band
9.8.2 Hot Band
9.8.3 Combination Band
9.8.4 Fermi Resonance Band
9.8.5 Vibrational Angular Momentum and Coriolis-Perturbed Band Structure
9.9 Rotational Band Structure in Vibrational Bands
9.10 Selection Rules for Vibrational Transition
Problems
10 Raman Spectroscopy
10.1 Light Scattering
10.2 Frequencies of Rayleigh and Raman-Scattered Light
10.3 Limitation of the Classical Theory of Raman Scattering
10.4 Brillouin Scattering
10.5 Raman Tensor
10.5.1 Polarizability Tensor Ellipsoid
10.5.2 Nomenclature of the Polarizability Tensor
10.5.3 Anisotropy of Polarizability
10.5.4 Isotropic Average of Scattered Intensity
10.6 Semi-Classical Theory of Raman Scattering
10.6.1 Rotational Raman Spectra
10.6.2 Vibration-Rotation Raman Spectra
10.7 Raman Tensor and Vibrational Symmetry
10.8 Secondary Or Coupled Bands in Raman Spectra
10.9 Solution Phase Raman Scattering
10.10 Resonance Raman Scattering
10.11 Sundries and Outlook
Problems
11 Electronic Spectra
11.1 Energy Term-Value Formulas for Molecular States
11.2 Dipole Transitions in the Electronic-Vibrational-Rotational Spectra
11.3 Electronic Transition Dipole With Nuclear Configurations
11.4 Franck-Condon Factor
11.5 Progression of Vibrational Absorption in an Electronic Band
11.6 Analysis of Vibrational Bands
11.7 Analysis Rotational Bands
11.8 Electron-Nuclear Rotational Coupling and Splitting of Rotational Energy Levels
11.8.1 Hund’s Cases
11.8.2 -Type Doubling
11.9 Selection Rules for Electronic Transitions in Diatomic Molecules
11.9.1 Symmetry-Based General Rules for Electronic Transitions
11.9.2 Selection Rules
11.9.3 Selection Rules Pertaining to Hund’s Coupling Cases
11.10 Perturbation Manifests in Vibronic Spectra
11.10.1 Rotational Perturbation and Kronig’s Selection Rules
11.10.2 Frequency Shift and Λ-Doubling in Rotational Perturbation
11.10.3 Vibrational Perturbation
11.10.4 Predissociation
11.10.5 Diffused Molecular Spectra
11.11 Stark Effect in Rotational Transitions: Observation and Selection Rules
11.12 Zeeman Effect On Rotational Energy Levels and Selection Rules
11.13 Magnetooptic Rotational Effect
Problems
12 Vibrational and Rotational Coherence Spectroscopy
12.1 Ultrashort Time of Spectroscopy
12.2 Wave Packet
12.3 Coherence
12.3.1 Linear Superposition and Interference
12.3.2 Vibrational Coherence
12.3.3 Rotational Coherence
12.3.4 Coherence Decay
12.4 Wave Packet Oscillation
12.5 Frequency Spectrum of Time-Domain Coherence
12.6 Assignment of Vibrational Bands
12.7 Pure Rotational Coherence
12.8 Density Operator, Coherence, and Coherence Transfer
12.8.1 Homogeneous and Statistical Mixture of States of a System
12.8.2 Density Operator
12.8.3 Time Evolution of the Density Operator
12.8.4 Matrix Representation of the Unitary Transformation Superoperator
12.8.5 Matrix Representation of the Commutator Superoperator
12.8.6 Partial Density Matrix
12.8.7 Density Operator Expression Using Irreducible Tensor Operator
12.9 Density Matrix Treatment of an Optical Experiment
Problems
13 Nuclear Magnetic Resonance Spectroscopy
13.1 Nuclear Spin of Different Elements
13.2 Excited-State Nuclear Spin
13.3 Nuclear Spin Angular Momentum and Magnetic Moment
13.4 Zeeman Splitting of Nuclear Energy Levels
13.5 Larmor Precession of Angular Momentum
13.6 Transition Torque Mechanics
13.7 Spin Population and NMR Transition
13.7.1 Static Field Dependence of Signal Intensity
13.7.2 Nuclear Receptivity
13.7.3 Macroscopic Magnetization
13.8 Bloch Equations and Relaxation Times
13.9 The Rotating Frame
13.10 Bloch Equations in the Rotating Frame
13.11 RF Pulse and Signal Generation
13.12 Origin of Chemical Shift: Local Shielding
13.13 Long-Range Shielding
13.13.1 Ring Current Effect, σ_r
13.13.2 Electric Field Effect, σ_e
13.13.3 Bond Magnetic Anisotropy, σ_m
13.13.4 Shielding By Hydrogen Bonding, σ_H
13.13.5 Hyperfine Shielding, σ_hfs
13.13.6 Shielding From Solvent Effect, σ_s
13.13.7 Chemical Shift Scale
13.14 Spin-Spin Coupling
13.15 Basic Theory of the Origin of Nuclear Spin Relaxation
13.16 Mechanism of Spin Relaxation
13.16.1 Shielding Anisotropy
13.16.2 Spin-Rotation Interaction
13.16.3 Scalar Interaction
13.16.4 Paramagnetic Effect
13.16.5 Dipole-Dipole Interaction
13.17 Dipolar Interaction and Cross-Relaxation
13.18 Effect of Dipolar Interaction On Nuclear Relaxation
13.19 Spin Cross-Relaxation: Solomon Equations
13.20 Nuclear Overhauser Effect (NOE)
13.20.1 Positive and Negative NOE
13.20.2 Direct and Indirect NOE Transfer
13.20.3 Rotating Frame Overhauser Effect
13.20.4 Transient NOE
13.21 Chemical Exchange
13.21.1 Effect of Chemical Exchange On Line Shape
13.21.2 One-Sided Chemical Reaction
13.22 Hahn Echo and Double Resonance
13.23 Echo Modulation and J-Spectroscopy
13.24 Heteronuclear J-Spectroscopy
13.25 Polarization Transfer (INEPT and Refocused INEPT)
13.26 Two-Dimensional -Resolved Spectroscopy
13.26.1 Absence of Coherence Transfer in 2D J-Spectroscopy
13.26.2 2D J-Spectroscopy in Strong Coupling Limit
13.27 Density Matrix Method in NMR
13.27.1 Outline of the Density Matrix Apparatus in NMR
13.27.2 Expression of Nuclear Spin Density Operators
13.27.3 Transformations of Product Operators
13.28 Homonuclear Correlation Spectroscopy (COSY)
13.29 Relayed Correlation Spectroscopy (Relay COSY)
13.30 Total Correlation Spectroscopy (TOCSY)
13.31 2D Nuclear Overhauser Enhancement Spectroscopy (NOESY)
13.32 Pure Exchange Spectroscopy (EXSY)
13.33 Phase Cycling, Spurious Signals, and Coherence Transfer
13.34 Coherence Transfer Pathways
13.35 Magnetic Field Gradient Pulse
13.36 Heteronuclear Correlation Spectroscopy
13.37 3D NMR
13.37.1 Dissection of a 3D Spectrum
13.37.2 NOESY-[1H-15N]HSQC
13.37.3 Triple-Resonance 3D Spectroscopy
13.38 Calculation of 3D Molecular Structure
Problems
Index