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, σr
		13.13.2 Electric Field Effect, σe
		13.13.3 Bond Magnetic Anisotropy, σm
		13.13.4 Shielding By Hydrogen Bonding, σH
		13.13.5 Hyperfine Shielding, σhfs
		13.13.6 Shielding From Solvent Effect, σs
		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