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

Units: 1/2


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

Course Structure

  • 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%

Recommended Texts

  • 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

Further Reading

  • I N Levine, "Quantum Chemistry", 4th ed, Prentice Hall, 1991
  • J M Hollas, Modern Spectroscopy", 2nd ed, Wiley, 1992

Course Outline

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