Recognize the fundamental principles of optical and magnetic resonance through both theory and examples drawn from molecular literature, Derive the Fermi’s Golden Rule and simple relations between experimentally observable spectroscopic quantities and molecule dependent parameters by introducing time dependent quantum mechanics and show that spectroscopy connects matter with molecules through interaction of electromagnetic radiation.
Learning Outcomes: At the end of the course, the learners should be able to:
Connect the spectroscopic line positions (frequencies), line intensities and line widths with a single approximate formula given by Enrico Fermi.
Apply principles of microwave, infrared and electronic spectroscopies to identify the fingerprint region of small molecules in gas and solution phases.
Apply the concept of chemical shift and spin-spin coupling in both NMR and EPR spectroscopy to identify high resolution spectra of small organic molecules.
Apply the concepts learnt in the course to the general study of spectra of a large class of inorganic and organic compounds given in other courses in M.Sc.
Interaction of radiation with matter, Einstein coefficients, time dependent perturbation theory, transition probability, transition dipole moments and selection rules, factors that control spectral linewidth and lineshape. Beer-Lambert law and absorbance.
The rigid diatomic rotor, energy eigenvalues and eigenstates, selection rules, intensity of rotational transitions, the role of rotational level degeneracy, the role of nuclear spin in determining allowed rotational energy levels. Classification of polyatomic rotors and the non-rigid rotor.
Vibrational spectroscopy, harmonic and anharmonic oscillators, Morse potential, mechanical and electrical anharmonicity, selection rules. The determination of anharmoncity constant and equilibrium vibrational frequency from fundamental and overtones. Normal modes of vibration, G and F matrices, internal and symmetry coordinates.
Electronic transitions, Franck-Condon principle. Vertical transitions. Selection rules, parity, symmetry and spin selection rules. Polarization of transitions. Fluorescence and phosphorescence.
Raman spectroscopy, polarizability and selection rules for rotation and vibrational Raman spectra.
Expression for Hamiltonian/Energy – Zeeman interaction, torque exerted by a magnetic field on spins, equation, its solution and the physical picture of precession. Thermal equilibrium, Curie susceptibility. Expressions for MR spectral sensitivity. Approach to equilibrium, Bloch equations, the rotating frame, Steady state (continuous wave) and Transient (pulsed) experiments, solutions of classical master equation. Absorption and dispersion in cw and pulse experiments, the complex Fourier transform. Field modulation in cw MR and derivative EPR lineshapes. The spin Hamiltonian, isotropic and anisotropic interactions.
The EPR Hamiltonian. Theory of g-factors in EPR, transition metal complexes, rare earth complexes. Theory of hyperfine interactions in π−type free radicals, McConnell relation. The NMR Hamiltonian, shifts and couplings. The Solomon equations and cross-relaxation, the Overhauser effect, steady state NOE, sensitivity enhancement, transient NOE, interatomic distance information.
The spin echo. Vector picture and algebraic expressions for effect on spin evolution under field inhomogeneities, chemical shifts and homonuclear/heteronuclear couplings, the basis of heteronuclear decoupling.
Polarization transfer. Selective Population Inversion, INEPT and RINEPT, sensitivity enhancement and spectral editing.