This course will explore the application of quantum mechanics to understanding chemical phenomena, with special emphasis on atomic structure and properties. The postulates of quantum mechanics will be introduced and applied to simple systems. Examination of the simple, yet practically useful, harmonic oscillator and rigid rotor systems will lead into discussion of hydrogenic atoms and hybridization.
Intended Outcomes for the course:
• Apply the postulates of quantum mechanics to simple systems of chemical interest, such as the particle-in-a-box, harmonic oscillator, rigid rotor, hydrogenic atoms, hybrid orbitals.
• Students shall be able to visualize atomic orbitals of hydrogenic atoms
• Shall have ability to solve introductory problems in quantum mechanics
• Shall have ability to identify various molecular symmetry elements and their operations and construct group multiplication table and character table.
Unit I: Blackbody radiation - photoelectric effect - Hydrogen emission and Rydberg formula - Louis de Broglie postulate - Bohr theory - Heisenberg Uncertainty
Unit II: Classical wave equation - oscillating string - superposition of normal modes - vibrating membrane - Schrodinger equation and particle in a box – - Eigen values - quantized energy values and quantum number - uncertainty principle - probabilistic interpretation of wave function - free particles – particle in rectangular well – tunnelling
Unit III: Postulates and General principles in quantum mechanics - properties of operators, Eigen functions, Eigen values, normalization, orthogonality, commuting and non-commuting operators
Unit IV: Solution to Harmonic Oscillator - solution to rigid rotor - solution to hydrogen atom - quantum numbers - atomic orbitals - Hybrid atomic orbitals - construction and visualization of hybrid atomic orbitals - sp, sp2, sp3, dsp2, dsp3, d2sp3 - shape and directional behaviour
Unit V: Symmetry elements and Operations, point groups, non-degenerate representations
Physical Chemistry, A molecular approach, Donald A McQuarrie and John D Simon, 1998, Viva Books Limited
For Unit 5: Molecular symmetry and Group Theory, A programmed introduction to chemical applications, Alan Vincent, 2ed, John Wiley, 2001