### Lecture 1: Remembering the Masters: From Zeeman to Zavoisky

##### Lecture Details :

Principles and Applications of Electron Paramagnetic Resonance Spectroscopy by Prof. Ranjan Das, Department of Chemical Sciences, Tata Institute of Fundamental Research, Mumbai.For more details on NPTEL visit http://nptel.ac.in

##### Course Description :

Remembering the Masters: From Zeeman to Zavoisky:Zeemans observation of splitting of spectral lines; the difficulty of explaining the origin of Zeeman effect; Bohr model of hydrogen atom; Paulis exclusion principle; Stern-Gerlach experiment; Uhlenbeck and Goudsmits idea of spinning motion of electron and its initial dismissal by Pauli and Lorentz; Intrinsic magnetic moment and angular momentum of electron; Zavoiskys observation of electron paramagnetic resonance;Introduction to EPR spectroscopy:The Zeeman effect; Magnetic moment of an electron due its spin and orbital angular momenta; Combination of angular momenta and explanation of fine structures in atomic spectra; Magnetic moment in a magnetic field; Zeeman splitting of energy levels; Electron Zeeman vs nuclear Zeeman effect; Magnetic resonance spectroscopy; Resonance condition; Field-swept vs frequency-swept EPR spectra; Observation of hyperfine lines in several organic free radicals and transition metal complexes and the existence of electron-nuclear hyperfine interaction;Electron-Nuclear Hyperfine Interaction:Understanding the electron-nuclear hyperfine interaction; Hydrogen atom; Hydrogen molecule ion (H2+); Nuclear spin-degeneracy and relative intensity of hyperfine lines; EPR spectra of benzosemiquinone anion radical, methyl radical; Pascal triangle for several equivalent spin- nuclei; Hyperfine lines due nuclear spin I = 1; EPR spectrum of TEMPOL free radical - Hyperfine lines due nuclear spin I > ; EPR spectra of copper diethyl dithio-carbamate complex containing naturally abundant and isotopically pure 63Cu nucleus; Linewidths and intensities of various hyperfine lines; EPR spectrum of di-vanadyl complex; Pascal-like triangle for several equivalent nuclei with I > ; EPR vs ESR EPR spectrum of singlet oxygen molecule; splittings due to coupling of orbital angular momentum with rotational angular momentum;Magnetic Moment in Magnetic Field:Review of vector algebra: Right-hand Cartesian coordinate system, scalars and vectors, vector addition and multiplication; Motion of a bar magnet in a magnetic field; Oscillation; Relation between the magnetic moment and orbital angular momentum of an electron; Bohr magneton; Lorentz force; Tesla vs Gauss - Motion of a bar magnet in a magnetic field, contd.; Oscillation vs precession; Time-dependence of the magnetic moment in a magnetic field; Gyromagnetic ratio; Larmor frequency; Effect of a small rotating magnetic field applied perpendicular to the Zeeman field; Condition for magnetic resonance;EPR Instrumentation:Recapitulation of the requirements of EPR transition; Comparison between a basic EPR spectrometer and an optical spectrometer; Microwave components waveguides, bends, twist; Different microwave frequencies and EPR spectrometers; Source of microwave klystron and Gunn oscillator; Klystron mode; Microwave cavity transmission and reflection type; Modes in a microwave cavity; Microwave oven; Perturbation of modes due to a sample; TE102 modes in a rectangular cavity; TE011 modes in a cylindrical cavity; Fixed frequency EPR spectrometer; Quality factor (Q) of a cavity and its importance in sensitivity of the spectrometer - Magnetic field and electromagnet; Helmholtz coil; Requirements on the homogeneity; Measuring the magnetic field Hall-effect Gaussmeter and NMR Gaussmeter; Microwave detector; Non-linearity and biasing of the detector; Coupling of microwave from waveguide to the cavity role of an iris and a tuning screw; Describing microwave power in relative unit (dB) and absolute unit (dBm) - A transmission-cavity EPR spectrometer; Microwave circulator; A reflection-cavity EPR spectrometer; Matching the microwave frequency to the resonance frequency of the cavity; Coupling the microwave from the waveguide to the cavity role of an iris and a tuning screw; Undercoupling, overcoupling and critically coupling of the cavity; Biasing the detector using a directional coupler; Use of attenuators and phase shifters in the spectrometer; Balancing the microwave bridge analogous to a Wheatstone bridge; Appearance of the EPR spectra positive or negative; Direct-detection EPR spectrometer; Q value and the response time of a direct-detection EPR spectrometer - Improving the sensitivity of the EPR spectrometer; Signal-to-noise ratio; Signal averaging; Principle of lock-in or phase-sensitive detection; Magnetic field modulation and phase-sensitive detection; EPR spectrum in first-derivative form; Second-derivative form of EPR spectrum; Factors deciding the sense of the derivative spectrum; Magnetic field modulation and side bands; Effect on the response time of the spectrometer; Automatic frequency control of the microwave source;Quantum Mechanical Description of EPR:Recapitulation of the classical view of EPR transition; Basics of quantum mechanics wave function, time-dependent and time-independent Schrdinger equations; Angular momentum and its allowed values; Stationary states in quantum mechanics; Magnetic moment in a Zeeman magnetic field; Allowed states and energies; Rotating magnetic field in the xy plane; First-order time-dependent perturbation calculations - First-order time-dependent perturbation calculations, contd; Time-dependent evolution of states; Transition probability; Resonance condition.

Introduction to Spin Relaxation:Absorption, spontaneous emission and stimulated emission processes; Need for relaxation processes in magnetic resonance spectroscopy; Phenomenological derivation of spin-lattice relaxation as an exponential process; Physical meaning of the spin-lattice and spin-spin relaxation processes; Role of the relaxation process in the appearance of EPR spectra;Theory of First-order EPR Spectra:Hamiltonian of hydrogen atom; Magnetic interactions and spin hamiltonian; Hamiltonian for Zeeman interaction; Hamiltonian for electron-nuclear dipolar interaction and its directional dependence; Hamiltonian for electron-nuclear isotropic hyperfine interaction; Importance of s-type of orbitals; Separating the total hamiltonian into a main unperturbed Hamiltonian and a perturbation hamiltonian - Zeroth order wavefunctions and energies of hydrogen atom; Splitting of energy levels due to electron Zeeman, nuclear Zeeman and electron-nuclear hyperfine interactions; Selection rules and allowed transitions; Frequency-swept and field-swept EPR spectra; First-order perturbation calculations and EPR spectra;How to Analyse First-order EPR Spectra:Recapitulation of the characteristics of first-order EPR spectra; Measuring isotropic hyperfine splitting constants of several free radicals using a ruler and a divider; Identifying the number of equivalent nuclei and their spins; What to do when the outer hyperfine lines are buried in the noise level; Use of computer programs for analysing and simulating first-order EPR spectra;How to Record EPR Spectra:Solid, liquid or gaseous sample; EPR sample tubes; Sample preparation; Degassing and sealing of EPR samples; Choice of solvents; Polar solvents and use of capillary tubes and EPR flat cells; Sample placement inside the microwave cavity; Setting up the EPR spectrometer tuning the microwave frequency, coupling, and AFC; Optimizing the magnetic field position, scan range, modulation amplitude, microwave power, scan time and output filter time-constant, the phase of the microwave bias power and the reference phase of magnetic field modulation frequency;Second-order Effects on EPR Spectra:Why second-order calculations; Spin hamiltonian of hydrogen atom; Separation of unperturbed and perturbation hamiltonians; First-order wavefunctions and energies; Second-order calculation of energies; Transition energies; Fixed- magnetic field and fixed-frequency EPR spectra; Distinction between hyperfine splitting constant and hyperfine coupling constant; Second-order correction for calculating the g-values; EPR spectrum of CF3 radical; Second-order calculations of R-CH2 radical; Second-order effects on the EPR spectrum of a tri-nuclear Co complex;Photochemistry and EPR Spectroscopy:Formation of paramagnetic species by photoexcitation; Means to record EPR spectra of transient radicals; Modifications for in situ photolysis; Need for flowing the reactants; Temperature control; Steady-state EPR spectra under continuous photolysis; Photolysis of p-benzoquinone in alcohol; Photolysis of acetone in 2-propanol;Spin-trapping technique; PBN and DMPO as the trapping agents; Spin-trapping experiment on photolysis of p-benzoquinone in alcohol; Problems with spin-trapping EPR studies; Time-resolved EPR spectroscopy; Recording EPR spectra of transient species by time-resolved EPR technique; EPR spectrum at a given time; Time evolution of EPR signal at a given magnetic field; Photolysis of duroquinone in triethylamine; Photolysis of acetone in 2-propanol;Non-Boltzmann spin distribution and electron spin polarisation.

Electron Spin Polarisation:Example of spin-polarised EPR spectra photolysis of acetone in 2-propanol; Definition of polarisation; The first observation of spin-polarised EPR spectra of H and D atoms; Evidence of electron spin polarisation in steady-state EPR spectra; Comparison of steady-state and time-resolved EPR spectra during the photolysis of p-benzoquinone in 2-propanol; Spin-polarised NMR spectra; CIDEP, CIDNP, CIMP and Electron spin polarisation (ESP); Types of spin-polarised EPR spectra; Mechanism of single-phase hyperfine-independent electron spin polarisation the triplet mechanism (TM); Conditions for TM to operate; Characteristics of EPR spectra arising from TM - Mechanism of mix-phase hyperfine dependent electron spin polarisation; Importance of a pair of radicals and their evolution; Radical pair mechanism (RPM); Overall spin states of the radical pair and interconversion of singlet and triplet radical pairs; Importance of the difference in the frequencies of precession; Conditions for RPM to operate; Characteristics of EPR spectra due to RPM; Dominance of TM or RPM in observed time-resolved EPR spectra; Insight into the detailed dynamics of photophysical and photochemical pathways from spin-polarised time-resolved EPR spectra;Anisotropic Interactions in EPR Spectroscopy:Common examples of anisotropic properties; Averaging of anisotropic properties due to rapid tumbling motions; Need for restricted motion; Origin of g-anisotropy; g-matrix; g2-matrix; Principal axes and principal values of the g-matrix; Effective g-values; Symmetry of crystals; Examples of anisotropic EPR spectra of vacancies in single crystals; EPR lineshapes from powder samples or frozen solutions; Examples of powder EPR spectra; Electron-nuclear dipolar interaction; Anisotropic hyperfine coupling constants; Principal values of the hyperfine coupling constants; Powder patterns due to anisotropic hyperfine coupling; Lineshapes due to combined effects of g-anisotropy and hyperfine anisotropy;Theoretical Basis of isotropic Hyperfine Coupling:Hamiltonian of the isotropic hyperfine interaction; Role of the wavefunction in determining the isotropic hyperfine coupling constant; Concepts of electron density, spin density and spin population; Meaning of negative spin density; Determinantal wavefunction; Atomic spin population; Relation between spin population of C-atom and the hyperfine splitting due to the H-atom in >CH radical; Configuration mixing;Spin Relaxation and Bloch Equations:Magnetisation; Boltzmann distribution of spins at thermal equilibrium; Magnetic susceptibility and Curie law; Non-equilibrium magnetisation and electron spin relaxation process; Blochs proposal of longitudinal (spin-lattice) and transverse (spin-spin) relaxation processes; Time dependence of magnetization in the presence of relaxation Bloch equations - Time dependence of magnetization in the presence of relaxation Bloch equations in the laboratory coordinate system. Rotating coordinates; Time dependence of a vector in a rotating coordinate system; Bloch equations in a rotating coordinate system; Physical meaning; Steady-state solutions of Bloch equations in the rotating coordinate system; EPR lineshapes absorption and dispersion EPR signals; Measuring the relaxation times from the EPR lineshapes, and problems associated with that; Bloch equations as a function of magnetic field