Physical Chemistry 3

Overview

1. APPLICATIONS OF GROUP THEORY TO MOLECULAR STRUCTURE AND SPECTROSCOPY

8 Lectures, 1 Seminar + 1 revision class

Lecturer: Prof. Bell, Room 0G.124 E-mail: s.bell@qub.ac.uk

Elements of Group Theory
Symmetry elements and symmetry operations, including revision of material from module CHM2002 and CHM2005; representation of symmetry operations; group multiplication tables. Symmetry classification of molecules: molecular point groups. Reducible and irreducible representations; degenerate and non-degenerate representations. Normal modes of molecular vibration as bases for representations.
The structure and information content of character tables.

Use of Group Theory in the Analysis of Molecular Vibrations
Generation of a reducible representation from the 3N basis set of Cartesian vectors on the N atoms of a polyatomic molecule.
Symmetries of translation and rotation; symmetries of the normal modes of vibration.
Group theoretical basis for determining the infrared and Raman activity of normal modes.

Application of Group Theory to Chemical Bonding & Spectroscopy
Atomic orbitals as bases for irreducible representations; derivation of spectroscopic states from electron configurations; symmetry basis of spectroscopic selection rules. Symmetry considerations as a guide to construction of molecular orbitals; bond vectors as bases for discussion of sigma-bonding; brief introduction to use of character projection operators for derivation of symmetry-adapted linear combinations of orbitals; orbital correlation diagrams.


2. INTERMOLECULAR FORCES

9 Lectures, 2 Seminars + 1 revision class

Lecturer: Prof. Mills E-mail: andrew.mills@qub.ac.uk

This course will look at the physical processes associated with the major intermolecular forces, such as: the orientation, distortion and dispersion effects, as well as hydrogen bonding, which are responsible for much of the non-ideal behaviour of gases, liquids and solids.


3. MATHEMATICAL METHODS IN PHYSICAL CHEMISTRY*

9 lectures + 1 seminar

Lecturer: Dr Lane, Room OG.123 E-mail: i.lane@qub.ac.uk

Part 1: Mathematical methods
Background revision of quantum theory and classical physics: the commutator; complex numbers; angular momentum operators and the ladder operators; introduction to matrices; determining eigenvalues of operators using matrix methods; the electronic structure of atoms and molecules; the wave function and matrix versions of quantum mechanics; the Pauli Principle and the use of matrix (Slater) determinants in quantum chemistry; the epistemic and ontological interpretations of a wavefunction; hyperfine structure.

Part 2: Application: light-matter interactions
The classical model of light including polarisation, the mathematical description of waves, Malus’ law and the vector potential; the quantum model including ladder operators; the matrix elements of quantum mechanical operators; the transition dipole and origin of the selection rules; rotational levels of diatomic molecules and angular-momentum coupling in terms of Hund’s cases.


*The final examination will not include material from the mathematical methods in physical chemistry component.

Learning Objectives

Learning outcomes: Upon completion of this module students should:

have a working understanding of the group theoretical basis for the classification of molecules into symmetry point groups and have a working knowledge of the use of character tables to deduce symmetry classifications of normal modes of vibration and of the electronic states of molecules;
be able to apply such information to consideration of selection rules for vibrational and electronic transitions and for the construction of molecular orbitals;
display a general knowledge of quantum mechanics and the use of angular momentum operators;
understand the importance of the Pauli Principle and the use of a matrix determinant to represent a many-electron wavefunction;
understand the basic properties of light and the interaction with atoms and molecules from a classical and quantum perspective;
have an appreciation of the role of internuclear forces, such as hydrogen bonding, in molecular behaviour.

Skills

Skills associated with module:
The module focuses on cognitive abilities relating in particular to numerical problem solving, specifically in the areas of spectroscopy, quantum mechanics and chemistry, photodynamics and statistical thermodynamics. Problem solving in these areas is practiced.

Assessment

Assessment
• 70% Final examination
exam time: 2 hrs
co-examined with: N/A
• 20% Mid-term exam (Mathematical methods lectures only)
• 10% Tutorial (four classes)


Course Requirements: Compulsory element of tutorials, 40% veto on exam and coursework