Chemistry 331 Introduction to Quantum Chemistry
Instructor: D. G. Leaist, Office PSC3072, Lab PSC 3020
Telephone: 867-5372
General Description: Chemistry 331 introduces the basic ideas and applications of quantum theory, quantum chemistry, and statistical mechanics, emphasizing energy levels and how they are occupied. The postulates of quantum mechanics will be developed and used to solve a variety of problems, including blackbody radiation, free particles, barrier penetration and tunnelling, the particle in a box, harmonic oscillators, rigid rotators, atoms, and molecules. The methodology and interpretive nature of quantum mechanics will be stressed and the connection between theory and experiment will be emphasized. The relationship between the properties of individual atoms, molecules, and matter made up of atoms and molecules will be discussed and illustrated.
Prerequisite: Chemistry 232
Followed by: Chemistry 332
Assignments: Five problem sets will be assigned to cover the course material.
Course Mark:
Course Outline
1. Brief Summary of Classical Mechanics: Newton's Laws. Hamilton's equations of motion in Cartesian coordinates. Other
coordinate systems.
2. The Need for Quantum Mechanics: Quantization of energy. Wave nature of matter. The uncertainty principle. Failure of
classical mechanics for blackbody radiation, low-temperature heat capacities, photoelectric effect, atomic spectra.
3. Postulates of Quantum Mechanics: Connection between classical and quantum mechanics. The postulates or laws
of quantum mechanics. Stationary states.
4. Some One-Dimensional Systems: The free particle problem. Beam-potential barrier problems. Quantum mechanical
tunnelling. Energy levels for a particle in a box. Applications.
5. Important Theorems: Commutators. Self-adjoint or Hermitian operators. Quantum numbers. Examples.
6. One-Dimensional Harmonic Oscillator: Raising and lowering operators. Energy levels and wave functions. Properties of the
harmonic oscillator. Transition selection rules. Zero-point energy. A model for a vibrating molecule. Vibrational
spectroscopy and diatomic molecules. Other applications.
7. Multi-Dimensional Problems: Three-dimensional free particle, particle in a box, and harmonic oscillator problems. Degenerate
energy levels. Applications.
8. Multi-Dimensional Problems with Spherical Symmetry: Quantum numbers. The rigid rotator. Rotational spectroscopy of
diatomic molecules. Selection rules. Bond lengths. Vibrational-rotational spectra. The radial and angular parts of the wave
functions for one-electron atom and ion: energies, spectra and selection rules. Average values of properties. Probability
density plots. Directed atomic orbitals.