Unit 1:
Quantum Chemistry Introduction [6 h]Mechanics as a means for study of systemic characteristics. Limitations of classical mechanics while dealing with quantum entities – black body radiation, UV-catastrophe. Quantization of energy, dual behaviour of quantum entities, photoelectric effect, principle of uncertainty. Postulates of quantum mechanics – postulate I wave functions, postulate II – operators in quantum mechanics, operator algebra, postulate III eigen values, eigen value equations, postulate IV expectation value, postulate V time dependent and time independent Schrodinger equation.
Unit 2:
Applying Schrodinger Equation to Various General Systems [12 h]Translational motion of a quantum entity – particle in a box, quantum mechanical tunneling. Vibrational motion – harmonic oscillator. Rotational motion – rigid rotator, particle on a ring and particle on a sphere. Basic ideas on angular momentum.
Unit 3:
Variation and Perturbation Methods [10 h]One electron atomic system – hydrogen atom wave function, orbitals. Multielectron atomic systems – the variation method variation theorem, extension of the variation method, determinants, simultaneous linear equations and linear variation functions. Perturbation theory- nondegenerate perturbation theory, perturbation treatment of helium atom ground state, perturbation theory for a degenerate energy level, perturbation treatment of first excited states of helium. Time dependent perturbation theory – interaction of radiation with matter.
Unit 4:
Angular Momentum and Electron spin [7 h]Angular momentum – operators, ladder operators, orbital and spin angular momenta, angular momentum in many electron atoms. Atomic states, term symbols, splitting of term levels into atomic levels, spin-orbit interaction. Electron spin eigen values and eigen functions of spin operator – matrix methods – spin-orbitals. Pauli principle – antisymmetric wave function.
Unit 5:
Chemical Bonding – Quantum Mechanical Approach [10 h]Hydrogen molecule ion and hydrogen molecule – molecular orbital and valence bond theory – homo and hetero nuclear diatomic molecules. The concept of directed valences and hybridization. Quantum mechanics in band theory of metallic solids. The virial theorem and chemical bonding.