CH3204: Symmetry, Spectroscopy and Quantum Mechanics
|School||Cardiff School of Chemistry|
|External Subject Code||F170|
|Number of Credits||20|
|Language of Delivery||English|
|Module Leader||Dr David Willock|
Outline Description of Module
This module develops understanding of the fundamental nature of matter at the quantum level, along with experimental and theoretical methods used to probe this. The range of spectroscopic methods by which atoms and molecules are studied will be examined in detail, focussing on the physical information contained within spectra. Quantum mechanical description of model systems will set the foundations for deeper understanding of the structure and spectra of atoms and simple molecules, and of the bonding in more complex molecules. Consideration of symmetry and group theory is crucial in all aspects of this module; this will be introduced at the start of the module and applied throughout.
On completion of the module a student should be able to
Knowledge and Understanding
a) Recognise symmetry elements and operations in molecules, and use these to assign point groups;
b) Appreciate the use of character tables to describe the results of symmetry operations on molecules;
c) Use group theoretical arguments to predict features of rotational, infra-red and Raman spectra;
d) Know the parts of the electromagnetic spectrum used in common forms of spectroscopy, and describe the physical processes these are used to probe;
e) Understand the origins and appearance of typical rotational and vibrational absorption/emission and Raman spectra, predict their appearance for simple molecules, and extract chemical information from spectra;
f) Appreciate how electronic energy levels in atoms and molecules arise, predict spectra, and extract chemical information;
g) Describe theoretical treatment of wave properties of matter within the quantum mechanical approach;
h) Appreciate how solutions of the Schrödinger equation are found for model systems, and recognise the physical and chemical significance of these solutions;
i) Use quantum mechanical and group theoretical concepts to describe the bonding in diatomic and polyatomic molecules;
j) Apply concepts of molecular orbital and valence bond theories to describe simple molecules and coordination complexes.
a) Appreciate fundamental aspects of matter at the quantum level, and the experimental evidence for theoretical descriptions;
b) Extract physical and chemical data from spectra, and relate this to theoretical concepts of molecular and electronic structure;
c) Utilise appropriate combinations of spectroscopic data to identify molecular structures.
d) Relate the three dimensional structure of molecules to their physical properties and use group theory to relate the two.
e) Infer molecular structure from spectroscopic data based on symmetry arguments.
f) Construct molecular orbital diagrams from a combination of symmetry and bonding theory.
How the module will be delivered
The module will consist of 33 x 1 hour lectures; 18 (6 x 3) hours problem-based workshops: 1 x 3 hr symmetry, 1 x 3 hr spectroscopy, 2 x 3 hr quantum mechanics, 2 x 3 hr LCAO/MO theory; 26 (6 x 3 + 2 x 4) hours of practical; 4 x 1 hour tutorial.
Skills that will be practised and developed
Chemistry-specific skills are based upon developing an understanding and appreciation of the fundamental properties of matter, theoretical description of atomic and molecular structure, and the physical evidence for this. This knowledge will be applied to the use of spectroscopic and related experimental data to infer molecular structure through the application of group theory. More generally, strong skill elements of the module are transferable: problem solving and mathematical analysis underpin the majority of the module content and the student-led activities.
How the module will be assessed
A written exam (3 h) will test the student’s knowledge and understanding as elaborated under the learning outcomes. The coursework (workshops and tutorials) will allow the student to demonstrate his/her ability to judge and critically review relevant information. Practical skills will be assessed via a series of laboratory-based exercises.
|Examination - Spring Semester||60||Symmetry Spectroscopy And Quantum Mechanics||3|
|Written Assessment||8||Autumn Semester Workshops||N/A|
|Practical-Based Assessment||10||Autumn Semester Practical||N/A|
|Written Assessment||2||Autumn Semester Tutorials||N/A|
|Practical-Based Assessment||10||Spring Semester Practical||N/A|
|Written Assessment||8||Spring Semester Workshops||N/A|
|Written Assessment||2||Spring Semester Tutorials||N/A|
Elements and operations, classification of axes and planes, assignment of point groups.
Group Theory: Introduction of a basis, operations as matrices, characters to describe the results of operations, background to the construction of character tables.
Applications of Group theory: Use of characters to describe the result of operations on a basis, construction of reducible representations and application of the reduction formula, mathematical basis of selection rules, example applications in Rotational, IR, Raman spectroscopy and in chemical bonding.
Molecular Spectroscopy (9L):
Rotational and vibrational spectra: Microwave spectra, moments of inertia, selection rules in rotational transitions, the rotation of molecules, energy levels and effects of angular momentum in rotational spectra, diatomic and polyatomic molecules, rigid rotator and non-rigid rotator.
The vibrating diatomic molecule (Hooke’s law and the simple harmonic oscillator), molecular vibrations (selection rules), vibration-rotation spectra, P, Q, R branches, vibrations in polyatomic molecules, normal modes of vibration, IR spectroscopy.
Raman spectra, molecular polarizability, pure rotational Raman spectra for linear and spherical top molecules,
Electronic spectra (molecules): electronic spectra of diatomic molecules, Born-Oppenheimer approximation, term symbols for linear molecules, angular momentum and selection rules. Electronic states, and Franck-Condon factors, dissociation energies, fine structure, Fortrat diagram.
Quantum mechanics and Atomic Spectra (8L):
Wave properties of matters, kinetic and potential energy, wave-particle duality, postulates of QM, Schrödinger equation, uncertainty principle.
Applications of Schrödinger equation: Boundary conditions, Particle in a box, barrier tunnelling, harmonic oscillator, rotations and angular momentum, the hydrogen atom, hydrogen like orbitals.
Extensions of basic theory: Many electron atoms (He), the Pauli principle, the chemical bond, the periodic table.
Electronic spectra (atoms): electronic wave functions, Coulombic interaction and term symbols, exchange interactions (multiplicity of states) and spin-orbit interactions, Russell-Saunders coupling and j-j coupling, the effect of an external magnetic field and the Zeeman effect.:
Chemical Bonding (8L):
Linear Combination of Atomic Orbitals: LCAO applied to the construction of molecular orbital diagrams for heteronuclear diatomics (HF, CO), and polyatomics (BeH2, BH3, CH4, SF6) by use of group orbitals. Delocalised molecular orbitals. Normalisation constants.
Comparison of molecular orbital and valence bond approaches to chemical bonding.
Walsh diagrams for H2O and BeH2 – MO approach to molecular geometry.
Extension of LCAO/MO approach to co-ordination complexes of Oh, Td and D4h symmetry. Symmetry descriptors of relevant orbitals, relationship to/differences from CFT.
Essential Reading and Resource List
An indicative reading list will be included in the Course Handbook.
Background Reading and Resource List
An indicative reading list will be included in the Course Handbook.