CHEM2304: Quantum Mechanics and Spectroscopy
Note: available only as a Natural Science or Affiliate course - chemists take CHEM2301
Course Organizer: Prof Helen Fielding
Lecturers: Prof Helen Fielding, Prof Sally Price, Prof Francesco Gervasio
Normal prerequisite: CHEM1301
The aims of this course are to develop further quantum mechanics and to extend the material of CHEM1301 to spectroscopy and statistical mechanics.
Students will be able to
- analyse chemical systems using rotational, vibrational and electronic spectroscopy
- apply the fundamental postulates of quantum mechanics to problems with exact and approximate solutions
- use molecular orbital theory with diatomic molecules and Hückel theory with π electron systems
- use the principles of statistical mechanics to derive thermodynamic quantities using rotational, vibrational and electronic energy level expressions
- Lectures: 24
- Tutorials: 12
- Labs: 0
- Exam: 80% (2 hours). The exam is held at the same tome as CHEM2301 exam.
- Lab: 0%
- Coursework: 20%
- R Silbey, R A Alberty and M G Bawendi Physical Chemistry 4th Edition John Wiley. Earlier editions of Ailbey and Alberty are equally useful.
An acceptable alternative is:
- P W Atkins and J de Paula Atkins' Physical Chemistry 8th edition, Oxford 2006; or earlier editions
- I N Levine, "Quantum Chemistry", 4th ed, Prentice Hall, 1991
- J M Hollas, Modern Spectroscopy", 2nd ed, Wiley, 1992
Spectroscopy of diatomic molecules HHF, 8 lectures
- Basics: electromagnetic spectrum, absorption and emission of radiation, transition moment and selection rules. Rotational spectroscopy: rigid rotor energy levels, reduced mass, rotation spectroscopy selection rules, intensities of transitions in rotational spectroscopy
- Vibrational spectroscopy: harmonic oscillator, Morse potential, anharmonic oscillator energy levels, selection rules, dissociation energies, Birge-Sponer extrapolation
- Rovibrational spectroscopy: combination differences
- Rovibrational spectroscopy workshop
- Electronic spectroscopy: principles, term symbols of diatomic molecules, selection rules
- Vibrational structure of electronic transitions, progressions and sequences, vibronic transition wavenumbers, Deslandres tables, intensities of vibrational components of electronic transitions (Franck-Condon principle)
- Vibronic spectroscopy: dissociation energies, rotational fine structure
- Electronic spectroscopy workshop
Quantum Mechanics SLP, 8 lectures
- Fundamental principles and postulates: probability interpretation of Ψ, operators and Hamiltonians, eigenvalue equations, Schrödinger equation, expectation values, Variation principle, more dimensions and particles.
- Exact solutions to the Schrödinger equation: harmonic oscillator, particle on a ring, particle on a sphere (rigid rotor), hydrogen atom.
- Beyond exact solutions: helium atom.
- Molecular orbitals: Born-Oppenheimer approximation, linear combination of atomic orbitals, secular equations, two-orbital systems.
- Hückel theory for π‑electron systems.
Statistical Mechanics FLG, 8 lectures
- Scope of statistical mechanics
- Ensembles. (a) microcanonical ensemble; (b) canonical ensemble; (c) grand canonical ensemble
- Distributions and arrangements in an ensemble
- Boltzmann distribution
- Canonical ensemble and thermodynamics
- Partition functions: canonical and molecular
- Electronic contributions to the partition function
- Rotational contribution
- Nuclear spin