Physical Chemistry IV: Quantum Chemistry & Spectroscopy

Postulates of quantum mechanics, quantum mechanical operators, Schrödinger equation and its application to free particle and “particle-in-a-box” (rigorous treatment), quantization of energy levels, zero-point energy and Heisenberg uncertainty principle, wavefunctions, probability distribution functions, nodal properties, extension to two and three dimensional boxes, separation of variables, degeneracy.

Qualitative treatment of simple harmonic oscillator model of vibrational motion: setting up of Schrödinger equation and discussion of solution and wavefunctions, vibrational energy of diatomic molecules and zero-point energy.

Angular momentum: commutation rules, quantization of square of total angular momentum and z-component.

Rigid rotator model of rotation of diatomic molecule, Schrödinger equation, transformation to spherical polar coordinates, separation of variables, spherical harmonics, discussion of solution.

Qualitative treatment of hydrogen atom and hydrogen-like ions: setting up of Schrödinger equation in spherical polar coordinates, radial part, quantization of energy (only final energy expression), average and most probable distances of electron from nucleus.

Setting up of Schrödinger equation for many-electron atoms (He, Li), need for approximation methods, statement of variation theorem and application to simple systems (particle-in-a-box, harmonic oscillator, hydrogen atom).

Chemical bonding: Covalent bonding, valence bond and molecular orbital approaches, LCAO-MO treatment of H₂⁺,bonding and antibonding orbitals, qualitative extension to H₂, comparison of LCAO-MO and VB treatments of H₂ (only wavefunctions, detailed solution not required) and their limitations, refinements of the two approaches (configuration interaction for MO, ionic terms in VB),qualitative description of LCAO-MO treatment of homonuclear and heteronuclear diatomic molecules (HF, LiH), localised and non-localised molecular orbitals treatment of triatomic (BeH₂, H₂O) molecules, qualitative MO theory and its application to AH₂ type molecules.

Interaction of electromagnetic radiation with molecules and various types of spectra; Born- Oppenheimer approximation.

Rotational spectroscopy: Selection rules, intensities of spectral lines, determination of bond lengths of diatomic and linear triatomic molecules, isotopic substitution.

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, vibration-rotation spectroscopy: diatomic vibrating rotator, P, Q, R branches.

Raman spectroscopy: Qualitative treatment of rotational Raman effect, effect of nuclear spin, vibrational Raman spectra, stokes and anti-stokes lines, their intensity difference, rule of mutual exclusion.

Electronic spectroscopy: Franck-Condon principle, electronic transitions, singlet and triplet states, fluorescence and phosphorescence, dissociation and predissociation, calculation of electronic transitions of polyenes using free electron model.

Nuclear magnetic resonance (NMR) spectroscopy: Principles of NMR spectroscopy, Larmor precession, chemical shift and low resolution spectra, different scales, spin-spin coupling and high resolution spectra, interpretation of PMR spectra of simple organic molecules.

Electron spin resonance (ESR) spectroscopy: Principle, hyperfine structure, ESR of simple radicals.

Characteristics of electromagnetic radiation, Lambert-Beer’s law and its limitations, physical significance of absorption coefficients, laws of photochemistry, quantum yield, actinometry, examples of low and high quantum yields, photochemical equilibrium and the differential rate of photochemical reactions, photosensitised reactions, quenching, role of photochemical reactions in biochemical processes, photostationary states, chemiluminescence.