Physical Chemistry 3

Overview

Summary of lecture content


1. APPLICATIONS OF GROUP THEORY 8 Lectures, 1 Seminar + 1 revision class


Lecturer: Prof. Bell (Room LG.432A) 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 (Room 01.401) 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* 10 lectures + 1 seminar


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


Part 1: Mathematics in Physical Chemistry (6 lectures)

The classical model of light including polarisation. The use of vectors and vector products (dot and cross). A brief introduction to vector calculus: the divergence and the curl. Maxwell’s equations of light and the mathematical description of waves including Euler’s formula. Magnetic and electric fields: the (probably fictitous) magnetic vector potential. Selection rules of electric dipole transitions in atoms and molecules.

Background revision of quantum theory: angular momentum operators and the ladder operators; 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: The science of NMR (4 lectures)

The minimal coupling model of electromagnetic interactions. The introducing of the Pauli vector and matrices to include spin. The idea of a magnetic moment and it’s relationship to the spin. The definition of the g-factor and gyromagnetic ratio. The Zeeman shift in a magnetic field. The discovery of nuclear spin and the Pauli principle for identical nuclei: nuclear spin statistics. Effect on spectroscopy of homonuclear diatomics and the liquefaction of molecular hydrogen. Calculating the magnetic vector potential of a magnetic moment and the internal magnetic field. The Dirac delta function and the Fermi contact potential. Origin of scalar (Fermi) coupling. Hydrogen atom in a magnetic field. Creating a matrix Hamiltonian. 1st and 2nd order effects in NMR. Diamagnetic shielding as a 2nd order response to an external field.

Mathematical topics covered include: the commutator; complex numbers; complex conjugates; Levi-Civita symbol; introduction to matrices; the adjoint; matrix operations; matrix determinants; differentiation (product rule); Dirac delta function; the curl of a vector field; diagonalising a matrix.


*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 mathematical theory and it’s application to general problems in classical physics (electromagnetic fields including waves) and quantum mechanics (in particular the use of angular momentum operators);
 understand the importance of the Pauli Principle both in quantum chemistry (the use of a matrix determinant to represent a many-electron wavefunction) and nuclear spin statistics;
 understand the basic science behind NMR (Nuclear Magnetic Resonance) and the interaction of external magnetic fields with quantum mechanical spin;
 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

• 70% Final examination - 1.5 hrs
• 20% Mid-term exam (Mathematical methods lectures only)
• 10% Tutorial (three classes)

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