CHEM2301: Physical Chemistry

Course Organizer:  Prof Helen Fielding

Lecturers:  Prof Helen Fielding, Prof Sally Price, Prof Francesco Gervasio, Dr Giorgio Volpe, Dr David Rowley

Normal prerequisite: CHEM1301

Units: 1


The aims of this course are to develop further quantum mechanics and thermodynamics and to extend the material of CHEM1301 to spectroscopy, kinetics, 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
  • explain the properties and behaviours of mixtures using thermodynamics
  • use the stationary state approximation to study unimolecular, linear and branched chain reactions

Course Structure

  • Lectures: 40
  • Tutorials: 20
  • Labs: 5 afternoons


  • Exam: 70% (3 hours)
  • Lab: 20%
  • Coursework: 10%

Practical course organizer:

Dr Matt Blunt

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 edition.
  • R. Chang and J. W. Thoman Jr., Physical Chemistry for the Chemical Sciences, University Science books.

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

Thermodynamics of mixing GV, 8 lectures

  • Introduction, motivation and refresher (phase; laws of thermodynamics; Gibbs free energy)
  • Thermodynamics of one component system (physical equilibrium; chemical potential; phase diagrams)
  • Thermodynamics of mixing in ideal two-component systems (partial molar quantities; extension of the fundamental equation of thermodynamics to mixtures; free energy, enthalpy and entropy of mixing ideal gases)  
  • The chemical potential of liquids (Raoult's law; mixing of ideal solutions; phase diagrams)
  • Colligative properties (boiling point elevation; freezing point depression; osmotic pressure; solubility) and chemical equilibrium
  • Thermodynamics of mixing in non-ideal systems (chemical potential of real gases; chemical reactions of real gas mixtures)
  • Non-ideal liquid mixtures (ideal dilute solutions; phase diagrams; positive and negative azeotropes; activity; colligative properties)
  • Non-ideal liquid mixtures (excess functions; regular mixtures; phase separation; immiscibility gaps; distillation)

Kinetics DMR, 8 lectures

  • Introduction, why kinetics. Definitions of parameters and terms. Experimental kinetics and their analysis.
  • Mechanisms: Concurrent/ opposing/ consecutive reactions.
  • The steady state approximation, its derivation and its usefulness.
  • The effect of temperature on reaction rates. The theoretical interpretation of this using simple models, a qualitative introduction to more complex theories for bimolecular processes.
  • Unimolecular reactions, how they occur and Lindemann theory to interpret them. Advances to the Lindemann theory.
  • Complex reactions: chain reactions, the definitions of linear and branched chain processes.
  • Hydrogen-halogen reactions, as an example of analysing (linear) chain processes using steady state theory.
  • Conclusions: Further case studies (eg pyrolysis of hydrocarbons). The importance of kinetics in applications: combustion, pyrolysis of hydrocarbons, atmospheric chemical change. Summary.