SPECTROSCOPY AND STATISTICAL THERMODYNAMICS

Pre requisite- interaction of electromagnetic radiation with matter, characterization of electromagnetic radiation, quantisation of energy, regions of the spectrum, representation of spectra, basic elements of practical spectroscopy, signal-to-noise ratio – resolving power, line width – natural line broadening, Doppler broadening, Heisenberg uncertainty principle, intensity of spectral lines –transition probability, population of states, path length of sample, Born-Oppenheimer approximation, rotational, vibrational and electronic energy levels in molecules, transition moment, selection rules, Fourier Transform methods (IR and NMR)

Rotational spectroscopy- diatomic molecule, energy levels of a rigid rotor (semi-classical principles), selection rules, intensities of spectral lines, determination of bond lengths of diatomic and linear triatomic molecules, qualitative description of non-rigid rotor, isotopic effect.
Vibrational spectroscopy- classical equation of vibration, computation of force constant, amplitude of diatomic molecular vibrations, anharmonicity, Morse potential, dissociation energies, fundamental frequencies, overtones, hot bands, degrees of freedom for polyatomic molecules, modes of vibration, concept of group frequencies, rotational-vibrational spectrum.

Raman spectroscopy- concept of polarizability, pure rotational Raman and pure vibrational Raman spectra of diatomic molecules, selection rules, effect of nuclear spin.
Electronic spectroscopy- concept of potential energy curves for bonding and antibonding molecular orbitals, qualitative description of s, p and n molecular orbitals, electronic transitions, selection rules, Franck-Condon principle, Jablonski diagram, singlet and triplet states, fluorescence and phosphorescence, dissociation and predissociation.

Introduction, quantum mechanical aspects, common terms- canonical ensemble, occupation number, statistical weight factor, configuration, phase space, macroscopic state, microscopic, state, system, assembly and ensemble, statistical equilibrium, Boltzmann distribution law, type of statistics, Bose-Einstein statistics, Fermi-Dirac statistics.

Partition function- molecular partition function for an ideal gas, translational partition function, rotational partition function, vibrational partition function, electronic partition function, nuclear partition function.
Calculation of thermodynamics properties in terms of partition function- internal energy, enthalpy, entropy, Helmholtz function, pressure, Gibbs functions, residual entropy, chemical potential, heat capacity of monoatomic gases.