This book presents detailed aspects of different fields of molecular spectroscopy. It consists of eleven chapters starting from the Born–Oppenheimer approximation and its relevance to various spectra to some topics on nonlinear spectroscopy through rotational, vibrational, Raman, and electronic spectroscopy, group theoretical application, nuclear magnetic resonance, electron spin resonance, nuclear quadrupole resonance, and Mossbauer spectroscopy. The intention is to present a good background of the theoretical aspects of the concerned fields which will help the readers to understand the subject firmly and apply them to their own fields according to their needs. For this purpose, several problems have been worked out to make the readers understand how the theories are applied in the relevant practical cases. In this book, it is presumed that the readers are well acquainted with the fundamentals of the basic subjects of physics, for example, mathematical methods, classical mechanics, quantum mechanics, statistical mechanics, and electrodynamics. The purpose of writing is not only to bring a wider field in a single book but also to develop the theories starting from the fundamentals and also from the simple to the final forms through fairly elaborate powerful techniques so that the readers become self-sufficient and apply them accordingly. Since this book covers most of the major fields of molecular spectroscopy, it reduces the work of searching several publications and serves the purpose of getting detailed deductive pictures of various aspects of the subject in a single publication.
Author(s): Prabal Kumar Mallick
Publisher: Springer
Year: 2023
Language: English
Pages: 495
City: Singapore
Preface
Contents
List of Figures
List of Tables
1 Introduction
1.1 Introduction
1.1.1 Born–Oppenheimer Approximation
1.1.2 Validity of Born–Oppenheimer Approximation
1.1.3 Estimation of Different Energies in Molecules
1.1.4 Energy-level Diagram
1.1.5 Breakdown of Born–Oppenheimer Approximation
References and Suggested Reading
2 Rotational Spectra
2.1 Nuclear Wave Equation in Diatomic Molecules
2.2 Diatomic Molecule as a Rigid Rotator
2.3 Selection Rules and the Spectral Structure
2.4 Isotopic Effect in Rotational Spectra
2.5 Intensities of Rotational Lines
2.6 Non-rigid Rotator (A Semiclassical Approach)
2.7 Rotational Spectra of Polyatomic Molecules
2.7.1 Hamiltonian in Terms of Angular Momentums
2.7.2 Different Types of Rotating Molecules
2.8 Stark Effect
2.9 Quadrupole Hyperfine Structure in Molecules
References and Suggested Reading
3 Infrared Spectra
3.1 Vibrational Energy Levels of a Diatomic Molecule Considered as a Simple Harmonic Oscillator
3.1.1 Selection Rules
3.2 Rotational-Vibrational Spectrum of a Diatomic Molecule with the Potential Function of a Simple Harmonic Oscillator
3.3 Anharmonic Oscillator and Morse Potential Function
3.4 Dissociation Energy
References and Suggested Reading
4 Raman Spectroscopy
4.1 Classical Explanation of Raman Scattering
4.1.1 Polarizability Ellipsoid and Raman Activity
4.2 Quantum Theoretical Explanation
4.3 Selection Rules of Rotational Raman Spectra
4.3.1 Rotational Raman Spectra of Diatomic Molecules
4.3.2 Rotational Raman Spectra of Polyatomic Molecules
4.4 Symmetry Properties of Wave Functions
4.4.1 Effect of Nuclear Spins
4.5 Selection Rules and Characteristics of Vibrational Raman Spectra of Diatomic Molecules
4.5.1 Rotational Vibrational Raman Spectra
4.6 Raman Intensities
4.7 Surface Enhanced Raman Scattering (SERS)
References and Suggested Reading
5 Vibrational Spectra of Polyatomic Molecules
5.1 Normal Coordinates (Classical Description)
5.2 Normal Coordinates (Quantum Mechanical Description)
5.3 Selection Rules
5.3.1 Selection Rules for the Infrared Spectra
5.3.2 Selection Rules for the Raman Spectra
5.4 Normal Modes of a Linear Symmetric Triatomic Molecule
5.4.1 Parallel Bands
5.4.2 Perpendicular Bands
5.5 Normal Modes of an Asymmetric Linear Triatomic Molecule
5.6 Normal Coordinate Calculation by the Method of Wilson
5.6.1 Internal Coordinate
5.6.2 Determination of s-vectors
5.6.3 G-Matrix and Kinetic Energy
5.6.4 Potential Energy in Terms of Internal Coordinates and the Secular Equation
5.7 Molecular Symmetry and Vibrational Problems
5.8 Fourier Transform Spectroscopy
Appendix
s-Vectors for Torsional Vibrations
References and Suggested Reading
6 Electronic Spectra of Diatomic Molecules
6.1 Vibrational Coarse Structure of Electronic Bands of a Diatomic Molecule
6.2 Isotope Effect
6.3 Rotational Fine Structure of Vibronic Bands in Diatomic Molecules
6.4 Intensity Distribution in the Vibrational Bands of the Electronic Spectra (Franck–Condon Principle) of Diatomic Molecule
6.4.1 Quantum Mechanical Formulation of Franck–Condon Principle
6.5 Quantum Numbers of Electronic States in Diatomic Molecules
6.5.1 Coupling of Angular Momenta
6.5.2 Selection Rules
6.6 Determination of Heat of Dissociation of a Diatomic Molecule from the Observed Electronic Spectra
6.7 Predissociation
6.8 Quantum Theory of Valence
6.8.1 Hydrogen Molecule Ion
6.8.2 Hydrogen Molecule
6.9 Electronic Structure of Diatomic Molecules
6.9.1 Homonuclear Diatomic Molecules
6.9.2 Heteronuclear Diatomic Molecules
Appendix
References and Suggested Reading
7 Electronic Spectra of Polyatomic Molecules
7.1 Hybridization
7.2 Conjugated System of Molecules
7.2.1 Free Electron Model
7.2.2 Molecular Orbital Method
7.3 Relaxation Mechanism
7.3.1 Lifetime and Quantum Yield
7.3.2 Vibronic and Spin–Orbit Interactions and N → π* Transitions in Organic Molecules
7.3.3 Radiative Sources for T1 → S0 Transition (Phosphorescence Decay)
7.3.4 Radiation Less Transition
7.4 Molecular Interaction
7.4.1 Charge Transfer Process
7.4.2 Hydrogen Bonding
7.4.3 Excimers and Exciplexes
7.4.4 Energy Transfer Phenomena
7.4.5 Electron Transfer Phenomena
7.5 Photoelectron Spectroscopy (PES)
7.5.1 Experimental Set-up
7.5.2 Few Examples of Photoelectron Spectra and Their Interpretation
Appendix 7.1
Einstein Coefficients
Molar Extinction Coefficient and Fluorescence Quantum Spectrum
References and Suggested Reading
8 Application of Group Theory to Molecular Spectroscopy
8.1 Definition of a Group
8.2 Multiplication Table and Other Properties of a Group
8.3 Representations and Their Characteristics
8.4 Determination of the Point Group of a Molecule
8.5 Selection Rules
8.5.1 Electronic Spectra
8.5.2 Vibrational Spectra
8.6 Symmetry Coordinates
8.7 Vibronic Coupling
8.8 Spin–Orbit Coupling
8.9 Depolarization Ratio (ρ) in Raman Spectra
References and Suggested Reading
9 Nuclear Magnetic Resonance (NMR), Electron Spin or Paramagnetic Resonance (ESR/EPR) and Nuclear Quadrupole Resonance (NQR) Spectroscopy
9.1 Nuclear Magnetic Resonance (NMR)
9.1.1 Basic Principle
9.1.2 Experimental Set-Up
9.1.3 Relaxation
9.1.4 Bloch Equations
9.1.5 Chemical Shift
9.1.6 Spin–Spin Interaction (High-Resolution NMR Spectra)
9.1.7 Solid-State NMR
9.1.8 Nuclear Magnetic Resonance Imaging (NMRI)
9.2 Electron Spin or Paramagnetic Resonance (ESR/EPR)
9.2.1 Basic Principle
9.2.2 ESR Spectrometer
9.2.3 Effect of Nuclear Spin (Hyperfine and Super Hyperfine Interactions)
9.2.4 Anisotropic Systems
9.2.5 Zero Field Splitting
9.2.6 ESR Spectra of Transition Metal Ion
9.3 Nuclear Quadrupole Resonance (NQR)
9.3.1 Basic Principle of NQR
9.3.2 Axially Symmetric System
9.3.3 Non-axially Symmetric System
Appendix 1
Appendix 2
Appendix 3
References and Suggested Reading
10 Mossbauer Spectroscopy
10.1 Nuclear Recoil and Doppler Effect
10.2 Earlier Experiments on Resonance Absorption
10.3 Principal of Mossbauer Spectroscopy
10.4 Experimental Set-up of Mossbauer Spectroscopy
10.5 Isomer Shift (Chemical Shift)
10.6 Nuclear Quadrupole Interaction
10.7 The Effect of Magnetic Field
References and Suggested Reading
11 Some Nonlinear Processes
11.1 Nonlinear Raman Effect
11.1.1 Normal, Hyper and Second Hyper Rayleigh and Raman Scattering
11.1.2 Stimulated Raman Scattering (SRS)
11.1.3 Coherent Antistokes Raman Scattering (CARS)
11.1.4 Inverse Raman Scattering
11.1.5 Two Photon and Multiphoton Absorption and Ionization
11.1.6 Multiphoton Dissociation and Laser Isotope Separation
11.2 Theoretical Description
11.2.1 First-Order Effect and Linear Susceptibility
11.2.2 Second-Order Effect and Second-Order Susceptibility
11.2.3 Third-Order Effect and Third-Order Susceptibility
11.3 Sum Frequency and Second Harmonics Generation
11.4 Stimulated Raman Scattering
11.5 Coherent Antistokes Raman Scattering (CARS)
References and Suggested Reading
Index
