Quantum Theory, Spectroscopy and Bonding

Overview

1. QUANTUM THEORY AND ATOMIC STRUCTURE (12 Lectures/workshops) Lecturer: Dr Lane (Room 0G.123) E-mail: i.lane@qub.ac.uk
Basic quantum theory: Planck and quantization: Einstein and the explanation of the photoelectric effect
Old quantum physics: the Zeeman effect and Stern-Gerlach experiments: the discovery of electron spin: Aufbau Principle: the failure to describe the helium atom and Anomalous Zeeman effect

Quantum mechanics: Solving the Schrödinger equation for the hydrogen atom and understanding the radial and angular wavefunctions
The coupling of spin and orbital angular momenta, fine structure and the complete explanation of the Stern-Gerlach and Zeeman experiments.
Atomic spectroscopy and selection rules for electric dipole transitions.

The problem of electron correlation and solving the energy levels of helium (perturbation theory): symmetric and antisymmetric wavefunctions. The Pauli Principle and its application in quantum statistics: experimental proof of Exclusion Principle. Explaining why helium triplet states must be antisymmetric orbital wavefunctions.



2. QUANTUM MECHANICS AND CHEMICAL BONDING (6 Lectures/workshops)
Lecturer: Dr Lane (Room 0G.123) E-mail: i.lane@qub.ac.uk

The quantum mechanical explanation of chemical bonding: exchange integrals. Some basic principles of chemical bonding: Linear Combination of Atomic Orbitals, (LCAO) method applied to homonuclear and heteronuclear diatomics and ‘orbital mixing’.
Drawing molecular orbital energy diagrams for 1st and 2nd row diatomics: application to hydrides.

Parity and wavefunctions: molecular Term Symbols and the Wigner-Witmer rules for diatomic molecules.
Basic rules of molecular electronic spectroscopy: Franck Condon principle, zero-point energy and vibrational wavefunctions.
A brief introduction to bonding in symmetric triatomic molecules: Walsh diagrams and the explanation of molecular geometry.


3. ROTATIONAL SPECTRA (4 Lectures/workshops)
Lecturer: Prof. Bell (Room LG.432A) E-mail: s.bell@qub.ac.uk

Rotational spectroscopy. Quantized rotational energy levels of molecules. Experimental methods.


Treatment of rigid diatomic molecules: energy levels, selection rules, reduced mass, moments of inertia, isotope effects.

Determination of bond lengths in diatomic molecules using rotational spectroscopy. Non-rigid rotors. Rotations of polyatomic molecules.

Analytical applications of molecular rotational resonance spectroscopy.
Appearance of rotational fine structure in vibrational spectra, PQR and PR profiles.


4. PHOTOCHEMICAL KINETICS (6 Lectures)
Lecturer: Prof. A Mills (Room 01.401) E-mail: andrew.mills@qub.ac.uk
Photochemical kinetics and techniques
The Stern-Volmer equation and deviations from it.
Photochemical techniques: (i) single photon counting, (ii) phase modulation and (iii) flash photolysis.

.
5. INTRODUCTION TO QUANTUM CHEMISTRY (5 Lectures/1 seminar) Lecturer: Prof. Bell (Room LG.432A) E-mail: s.bell@qub.ac.uk
Introduction to valence bond (VB) theory. VB description of bonding in diatomic molecules. VB treatment of polyatomic molecules and the concept of hybridisation.

Molecular orbital (MO) theory. Molecular orbitals as linear combinations of atomic orbitals, normalisation of wavefunctions. Overlap integrals. Bonding in homonuclear and heteronuclear diatomic molecules. Coulomb and resonance integrals, the variation principle.

Learning Objectives

Learning Outcomes

By the end of this module students should:

• be able to explain the basic concepts and terminology of quantum mechanics, as applied to systems of chemical interest and have a general awareness of experimental evidence for quantization;
• have an awareness of the need for approximate methods in quantum mechanics e.g. the variational principle, self-consistent field theory, perturbation theory;
• understand chemical bonding in simple quantum mechanical terms, applied to diatomic and triatomic molecules including their symmetry properties;
• describe the basic features of rotational spectra of diatomic molecules and vibration-rotation spectra of di- and simple poly-atomic molecules;
• be able to use quantum chemistry methods to model the structures of molecular compounds, calculate their energy levels and predict their spectroscopic properties.
• be able to discuss the basics of photo absorption and the decay of excited molecules;
• understand the role of the Pauli principle in the nature of atomic and molecular wavefunctions, the derivation of Slater determinants and the basis for the Hartree – Fock method.
QAA benchmark statements covered by the module

• The principles of quantum mechanics and their application to the description of the structure and properties of atoms and molecules;
• The principal techniques of structural investigations, including spectroscopy.

Skills

At the skills level, the module focuses on abilities relating to numerical problem solving in which practice is given in areas of spectroscopy and simple quantum mechanics.

In the compulsory practical element, skills relating to the conduct of laboratory work in spectroscopy are practised.

Assessment

Assessment
• 60% Final examination (excludes Quantum theory and atomic structure)
exam time: 120 minutes

• 20% Open book test (Quantum theory and atomic structure lectures only)
• 15% Practical (four experiments)
• 5% Tutorial (four classes)

Course Requirements:
Compulsory elements consist of practicals and tutorials, with a
75% attendance at practicals required. 40% veto exam and coursework