This practical and unique textbook explains the core areas of molecular spectroscopy as a classical teacher would, from the perspective of both theory and experimental practice. Comprehensive in scope, the author carefully explores and explains each concept, walking side by side with the student through carefully constructed text, pedagogy, and derivations to ensure comprehension of the basics before approaching higher level topics. The author incorporates both electric resonance and magnetic resonance in the textbook.
Electromagnetic Wave Nature of Light
Gauss’s Law of Electrostatics
Gauss’s Law of Magnetism
Faraday’s Law of Induced Electric Field
Ampere’s Law of Induced Magnetic Field
Maxwell’s Equations
Wave Equation
Homogeneous Travelling Plane Wave
Wave Packet
Reference
Problems
2. Postulates of Quantum Mechanics
Stern-Gerlach Experiment
Postulates of Quantum Mechanics
Perturbation Theory
Perturbation of a Nondegenerate System
Perturbation of a Degenerate State
References
Problems
3. Semiclassical Theory of Spectroscopic Transition
Two-Level System
System-Radiation Interaction
Time Development of Eigenstate Probabilities
Probability Expressions
Rabi Oscillations
Transition Probability and Absorption Coefficient
Limitations of the Theory
Collisional Line Broadening
Line Broadening from Excited State Lifetime
Spectral Line Shape and Line Width
Homogeneous or Lorentzian Line Shape
Inhomogeneous or Gaussian Line Shape
Doppler Interpretation of Inhomogeneous Line Shape
General Reading
Problems
4. Hydrogen Atom Spectra
Free Hydrogen Atom
Eigenvalues, Quantum Numbers, Spectra, and Selection Rules
Hydrogen Atom in External Magnetic Field: Zeeman Effect and Spectral Multiplets
Magnetic Moment in External Magnetic Field
Larmor Precession
Eigenstate, Operator, and Eigenvalue in External Magnetic Field
Anomalous Zeeman Effect and Further Splitting of Spectra
Electron Spin and Spin Magnetic Moment
Lande -factor
Spin-Orbit Coupling
Spin-Orbit Coupling Energy
Spectroscopic Notation
Fine Structure of Atomic Spectra
Splitting of Degeneracy: Anomalous Zeeman Effect
Zeeman Effect in Weak Magnetic Field
Zeeman Splitting Changeover from Weak to Strong Magnetic Field
Electron-Nuclear Hyperfine Interaction
Zeeman Splitting of Hyperfine Energy Levels
Zeeman Splitting of Hyperfine States in Weak Magnetic Field
Hyperfine States of Hydrogen Atom in Strong Magnetic Field
Stark Effect
Hydrogen Atom in External Electric Field
Effect on the Level
Effect on the Level
References and Text
Problems
5. Molecular Eigenstates
Born-Oppenheimer Approximation
Solution of the Total Schrödinger Equation
States of Nuclear Motion
Adiabatic and Non-Adiabatic Processes
Molecular Potential Energy States
One-Electron Hydrogen-Like Atom States
Molecular Electronic States Derived from Atom States
LCAO-MO
Molecular Eigenstates of H2+
Molecular Eigenstates of H2
Singlet and Triplet Excited States of H2
Electric Dipole Transition in H2
Molecular Orbital Energy and Electronic Configuration
Molecular Orbitals of Heteronuclear Diatomic Molecule
Molecular Orbitals of Large Systems
LCAO-MO of Porphyrins
Free-Electron Orbitals of Porphyrin
References
Problems
6. Elementary Group Theory
Symmetry Operations
Rotation
Reflection
Improper Rotation
Inversion
Point Group
Properties of Point Groups
Representation of Symmetry Operators of a Group
Group Representations
Labels of Irreducible Representations
Reduction of Representations to Irreducible Representations
Direct Product of Irreducible Representations
Applications
Energy Eigenvalues of Molecular Orbitals
Removal of Energy Degeneracy by Perturbation
General Selection Rules for Electronic Transitions
Specific Transition Rules
References
Problems
7. Rotational Spectra
Rotational Spectra of Diatomic Molecules
Schrödinger Equation for Diatomic Rotation
Rotational Energy of Rigid Rotor
Rotational Energy of Non-Rigid Rotor
Stationary State Eigenfunctions and Rotational Transitions
Energy Levels and Representation of Pure Rotational Spectra
Rotational Spectra of Polyatomic Molecules
Rotational Inertia
Energy of Rigid Rotors
Wavefunctions of Symmetric Tops
Commutation of Rotational Angular Momentum Operators
Eigenvalues for Tops
Selection Rules for Polyatomic Rotational Transition
General Reading
Problems
8. Diatomic Vibrations, Energy, and Spectra
Classical Description of an Oscillator
Schrödinger Equation for Nuclear Vibration
Selection Rules for Vibrational Transitions
Rotational-Vibrational Combined Structure
General Reading
Problems
9. Polyatomic Vibrations and Spectra
A Simple Classical Model to Define a Normal Mode
Vibrational Energy from Classical Mechanics
Solution of Lagrange’s Equation
Vibrational Hamiltonian and Wavefunction
Symmetry of Normal Modes
Finding the Vibrational Frequencies
Activity of Normal Modes of Vibration
Secondary Band Manifold in Infrared Spectra
Overtone Band
Hot Band
Combination Band
Fermi Resonance Band
Vibrational Angular Momentum and Coriolis-Perturbed Band Structure
Rotational Band Structure in Vibrational Bands
Selection Rules for Vibrational Transition
References
Problems
10. Raman Spectroscopy
Light Scattering
Frequencies of Rayleigh and Raman-Scattered Light
Limitation of the Classical Theory of Raman Scattering
Brillouin Scattering
Raman Tensor
Polarizability Tensor Ellipsoid
Nomenclature of the Polarizability Tensor
Anisotropy of Polarizability
Isotropic Average of Scattered Intensity
Semi-Classical Theory of Raman Scattering
Rotational Raman Spectra
Vibration-Rotation Raman Spectra
Raman Tensor and Vibrational Symmetry
Secondary or Coupled Bands in Raman Spectra
Solution Phase Raman Scattering
Resonance Raman Scattering
Sundries and Outlook
References
Problems
11. Electronic Spectra
Energy Term-Value Formulas for Molecular States
Dipole Transitions in the Electronic-Vibrational-Rotational Spectra
Electronic Transition Dipole with Nuclear Configurations
Franck-Condon Factor
Progression of Vibrational Absorption in an Electronic Band
Analysis of Vibrational Bands
Analysis Rotational Bands
Electron-Nuclear Rotational Coupling and Splitting of Rotational Energy Levels
Hund’s Cases
-type Doubling
Selection Rules for Electronic Transitions in Diatomic Molecules
Symmetry-Based General Rules for Electronic Transitions
Selection Rules
Selection Rules Pertaining to Hund’s Coupling Cases
Perturbation Manifests in Vibronic Spectra
Rotational Perturbation and Kronig’s Selection Rules
Frequency Shift and -doubling in Rotational Perturbation
Vibrational Perturbation
Predissociation
Diffused Molecular Spectra
Stark Effect in Rotational Transitions: Observation and Selection Rules
Zeeman Effect on Rotational Energy Levels and Selection Rules
Magnetooptic Rotational Effect
References
Problems
12. Vibrational and Rotational Coherence Spectroscopy
Ultrashort Time of Spectroscopy
Wave Packet
Coherence
Linear Superposition and Interference
Vibrational Coherence
Rotational Coherence
Coherence Decay
Wave Packet Oscillation
Frequency Spectrum of Time-Domain Coherence
Assignment of Vibrational Bands
Pure Rotational Coherence
Density Operator, Coherence, and Coherence Transfer
Homogeneous and Statistical Mixture of States of a System
Density Operator
Time Evolution of the Density Operator
Matrix Representation of the Unitary Transformation Superoperator
Matrix Representation of the Commutator Superoperator
Partial Density Matrix
Density Operator Expression Using Irreducible Tensor Operator
Density Matrix Treatment of an Optical Experiment
References
Problems
13. Nuclear Magnetic Resonance Spectroscopy
Nuclear Spin of Different Elements
Excited-State Nuclear Spin
Nuclear Spin Angular Momentum and Magnetic Moment
Zeeman Splitting of Nuclear Energy Levels
Larmor Precession of Angular Momentum
Transition Torque Mechanics
Spin Population and NMR Transition
Static Field Dependence of Signal Intensity
Nuclear Receptivity
Macroscopic Magnetization
Bloch Equations and Relaxation Times
The Rotating Frame
Bloch Equations in the Rotating Frame
RF Pulse and Signal Generation
Origin of Chemical Shift: Local Shielding
Long-Range Shielding
Ring Current Effect,
Electric Field Effect,
Bond Magnetic Anisotropy,
Shielding by Hydrogen Bonding,
Hyperfine Shielding,
Shielding from Solvent Effect,
Chemical Shift Scale
Spin-Spin Coupling
Basic Theory of the Origin of Nuclear Spin Relaxation
Mechanism of Spin Relaxation
Shielding Anisotropy
Spin-Rotation Interaction
Scalar Interaction
Paramagnetic Effect
Dipole-Dipole Interaction
Dipolar Interaction and Cross Relaxation
Effect of Dipolar Interaction on Nuclear Relaxation
Spin Cross Relaxation: Solomon Equations
Nuclear Overhauser Effect (NOE)
Positive and Negative NOE
Direct and Indirect NOE Transfer
Rotating Frame Overhauser Effect
Transient NOE
Chemical Exchange
Effect of Chemical Exchange on Line Shape
One-Sided Chemical Reaction
Hahn Echo and Double Resonance
Echo Modulation and -spectroscopy
Heteronuclear -spectroscopy
Polarization Transfer (INEPT and Refocused INEPT)
Two-Dimensional -resolved Spectroscopy
Absence of Coherence Transfer in 2D -spectroscopy
2D -spectroscopy in Strong Coupling Limit
Density Matrix Method in NMR
Outline of the Density Matrix Apparatus in NMR
Expression of Nuclear Spin Density Operators
Transformations of Product Operators
Homonuclear Correlation Spectroscopy (COSY)
Relayed Correlation Spectroscopy (Relay COSY)
Total Correlation Spectroscopy (TOCSY)
2D Nuclear Overhauser Enhancement Spectroscopy (NOESY)
Pure Exchange Spectroscopy (EXSY)
Phase Cycling, Spurious Signals, and Coherence Transfer
Coherence Transfer Pathways
Magnetic Field Gradient Pulse
Heteronuclear Correlation Spectroscopy
3D NMR
Dissection of a 3D Spectrum
NOESY-[1H-15N]HSQC
Triple-Resonance 3D Spectroscopy
Calculation of 3D Molecular Structure
References
Problems
Biography
Abani K. Bhuyan has been in the Chemistry faculty at the University of Hyderabad since 2000, and is currently a Senior Professor of Physical Chemistry. He received his PhD in Molecular Biophysics from the University of Pennsylvania in 1995 and was a Visiting Fellow at Tata Institute of Fundamental Research from 1995 to 2000.
