CHEM2304: Quantum Mechanics and Spectroscopy

Course Organizer: Dr Simon T. Banks

Lecturers: Dr K Holt, Dr D M Rowley

and Prof N Kaltsoyannis

Normal prerequisite: CHEM1301

Units: 1/2


The aims of this course are to develop further quantum mechanics and 

and kinetics and to extend the material of CHEM1301 to spectroscopy.

Assessment is based on Quantum Mechanics, Kinetics and one other section.


Students will be able to

  • 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 pi electron systems
  • use the stationary state approximation to study unimolecular, linear and branched chain reactions
  • analyse chemical systems using atomic, rotational, vibrational and electronic spectroscopy
  • discuss the fates of electronically excited molecules

Course Structure

  • Lectures: 27
  • Tutorials: 9
  • Labs: 0


  • Exam: 80% (2 hours)
  • 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
  • A Gilbert and J Baggott, "Essentials of Molecular Photochemistry", Blackwells,1991

Course Outline

Quantum Mechanics NK, 9 lectures

  • Fundamental postulates: the wavefunction, operators, expectation values, the Hamiltonian, the Schrödinger equation, eigenfunctions and eigenvalues.
  • Exact solutions: the particle in a box, simple harmonic oscillator, rigid rotor, hydrogen atom.
  • The helium atom: electron spin, ground and excited states of the helium atom.
  • Many-electron atoms.
  • Molecular orbitals: the Born-Oppenheimer approximation, potential energy surfaces, linear combination of atomic orbitals, the secular equations.
  • The two-orbital problem: bonding and antibonding orbitals, zero and non-zero overlap.
  • Homonuclear diatomics: molecular orbitals, parity, energy levels, bond-order.
  • Hückel Theory for p electrons: Secular equations, electron populations, bond-order, example of the allyl radical.

Kinetics, Photochemistry and Atmospheric Chemistry DMR, 9 lectures

  • Gas-phase kinetics: stationary state approximation; unimolecular reactions; Lindemann mechanism; introduction to RRKM theor.
  • Linear chain reactions: classification of elementary steps; pyrolysis of ethanal and ethane.
  • Excitation and the fate of electronically excited states of molecules; fluorescence, phosphorescence, non-radiative processes, vibrational relaxation, Stokes shift, dissociation, predissociation, quenching.

Spectroscopy KH, 9 lectures

  • Atomic Spectroscopy: The H atom, term symbols, selection rules, absorption and emission spectra for Na, the Helium atom, spectra of many electron atoms.
  • Molecular Spectroscopy: Born-Oppenheimer approximation, experimental techniques, rotational spectroscopy: selection rules, energy level expressions, intensities, centrifugal distortion, deriving bond lengths.
  • Vibrational Spectroscopy: harmonic and anharmonic oscillators, selection rules, force constants, vibration-rotation spectra, dissociation energies, hot bands.