1st Edition

Fundamental Concepts of Molecular Spectroscopy

By Abani Bhuyan Copyright 2023
    322 Pages 319 B/W Illustrations
    by CRC Press

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    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



    2. Postulates of Quantum Mechanics

    Stern-Gerlach Experiment

    Postulates of Quantum Mechanics

    Perturbation Theory

    Perturbation of a Nondegenerate System

    Perturbation of a Degenerate State



    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


    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


    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


    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



    6. Elementary Group Theory

    Symmetry Operations



    Improper Rotation


    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


    Energy Eigenvalues of Molecular Orbitals

    Removal of Energy Degeneracy by Perturbation

    General Selection Rules for Electronic Transitions

    Specific Transition Rules



    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


    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


    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



    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



    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


    Diffused Molecular Spectra

    Stark Effect in Rotational Transitions: Observation and Selection Rules

    Zeeman Effect on Rotational Energy Levels and Selection Rules

    Magnetooptic Rotational Effect



    12. Vibrational and Rotational Coherence Spectroscopy

    Ultrashort Time of Spectroscopy

    Wave Packet


    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



    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


    Triple-Resonance 3D Spectroscopy

    Calculation of 3D Molecular Structure




    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.