Group Theory: Fundamentals and Applications

CHEM20311 Group Theory: Fundamentals and Applications 10 Semester 1 Undergraduate Level 2 David Collison Unit coordinator Department of Chemistry 1 FHEQ level (Framework for Higher Education Qualifications) ' Middle part of Bachelors ' European Credit Transfer & Accumulation System Rating : 5.0 <div style="margin-left:18.0pt;"> <ul> <li>to identify symmetry elements (the identity, proper and improper rotation axes, mirror plane, inversion centre) in a given molecule and hence to assign the molecule to its point group, based on knowledge of its shape</li> <li>to understand the content of point group character tables and how to extract information from them</li> <li>to understand how to obtain the symmetries of the degrees of freedom in a molecule</li> <li>to understand how to use Group theory to perform a complete or partial vibrational analysis of a given molecule and to use that analysis together with experimental data to deduce molecular structure</li> <li>to use the concepts of high and low symmetry and the relationship between them to solve structural and spectroscopic problems</li> <li>to understand how to obtain the symmetries of groups of orbitals in a molecule</li> <li>how to set up a Walsh correlation diagram</li> <li>to use Group Theory to set up a molecular orbital bonding scheme for a d-transition metal complex</li> <li>to understand the ordering of ligands in the spectrochemical series</li> <li>to predict distortion based on symmetry considerations</li> <li>to introduce and to use the projection operator</li> <li>to understand and be able to use Walsh correlation diagrams and MO theory to explain key chemical trends in the p-block.</li></ul></div>  <ul><li>to identify symmetry elements (the identity, proper and improper rotation axes, mirror plane, inversion centre) in a given molecule and hence to assign the molecule to its point group, based on knowledge of its shape</li><li>to understand the content of point group character tables and how to extract information from them</li><li>to understand how to obtain the symmetries of the degrees of freedom in a molecule</li><li>to understand how to use Group theory to perform a complete or partial vibrational analysis of a given molecule and to use that analysis together with experimental data to deduce molecular structure</li><li>to use the concepts of high and low symmetry and the relationship between them to solve structural and spectroscopic problems</li><li>to understand how to obtain the symmetries of groups of orbitals in a molecule</li><li>how to set up a Walsh correlation diagram</li><li>to use Group Theory to set up a molecular orbital bonding scheme for a d-transition metal complex</li><li>to understand the ordering of ligands in the spectrochemical series</li><li>to predict distortion based on symmetry considerations</li><li>to introduce and to use the projection operator</li><li>to understand and be able to use Walsh correlation diagrams and MO theory to explain key chemical trends in the p-block. </li></ul> <div>The unit aims to enable students at the end of this module to:<ul> <li>describe and explain the fundamental principles of group theory as used in Chemistry</li> <li>apply group theory methods to interpret, predict and rationalise spectroscopic data</li> <li>apply group theory to develop models to rationalise chemical bonding</li> <li>apply group theory to describe the electronic structure of d-transition metal complexes</li></ul></div>  On successful completion of the course students should be able to:  ILO1 - describe and explain the fundamental principles of group theory as used in Chemistry  ILO2 - apply group theory methods to interpret, predict and rationalise spectroscopic dataILO3 - apply group theory to develop models to rationalise chemical bondingILO4 - apply group theory to describe the electronic structure of d-transition metal complexes   <ul> <li> Use concepts of molecular symmetry to identify physical properties</li> <li> Construct molecular orbitals and understand their role in determining molecular properties and reactivity</li></ul> <ul> <li> Reflective skills on prior learning</li> <li> Chemical problem-solving</li> <li> Spectroscopic data analysis</li> <li> Structure analysis and prediction</li> <li> Understand the principles and application of spectroscopic techniques to the determination of molecular structure</li></ul> <div>Problem-solving, analytical skills and time management.</div>  <div>Isotropy and anisotropy  Symmetry elements and symmetry operations, the identity, rotations, reflections, inversions, roto-reflections, symbols for these  Identifying molecular point symmetryAssigning a molecule to a point group  Infinite axes, high symmetry groups, cubic, linear, dihedral, axial and non-axial point groupsSymmetry, chirality and permanent dipole moment The idea of a groupTranslational and rotational vectors, linear and quadratic functions, spherical symmetryThe structure of point group character tablesClasses of symmetry operations, order of a groupMulliken symbols, A/B, E and T labels, g and u labels, 1 and 2 subscripts, prime (′) and double prime (″) superscripts  The totally symmetric representation of a point group (Γ1) Analysis of molecular motion as 3 × N degrees of freedom in an N atom moleculeSeparation of translations and rotationsThe concepts of “unshifted atom” and “contribution to character”, leading to a full vibrational analysisThe reduction formula, a reducible representation and its decomposition into irreducible components The triple product description of a spectroscopic transitionPolarisation of transitionsMultiplication of charactersThe totally symmetric representation of an integral and a vibrational ground stateThe symmetry basis of a selection ruleDipole moment and polarisability changesThe Raman experimentThe mutual exclusion ruleBond stretch analysisTotal vibrational analysisCharacteristic group frequencies and isotope effectsIllustrations from across the Periodic Table, e.g. carbonyl complexes, [BF4]− Distortion of a tetrahedron to produce lower symmetry species and to decrease degeneracyConsequences of lowering symmetry in vibrational spectroscopyHierarchy of point groups and their subgroupsTables of descent or correlationThe T states from population of eg and t2g orbitalsSelection rules in electronic absorption spectroscopy and coupling with vibrational modes Symmetry-adapted linear combination (SALC) of atomic orbitals.Derivation of the MO diagram for simple AXn structures.Illustrations selected from: H2O, NH3, CH4, SF6   σ- and π-bonding in MLn complexes  spectrochemical series based on π-bonding To introduce and to use the projection operator to generate the wavefunction and pictorial representation of SALCs and hence molecular orbitals and visual representations of IR/ Raman active stretching vibrations Walsh Diagrams, fundamentals and use in predicting structureUse of Group theory/MO theory to explain the variation in properties in the p-block. </div>  0 Other 20% 1 Written exam 80% Online tests  - 20% <div>Workshops (1 hour weekly)Tutorials (3 × 1 hour during course)E-learning (on-line formative quizzes, self-help tutorial web-sites)Office hours (weekly during course)Rolling feedback (answers to FAQs on <blackboard>)Pre-examination revision sessions (practice test for on-line assessment, revision class during examination period)Post-examination feedback (able to view marked examination scripts)</div> CHEM10101 Introductory Chemistry Pre-Requisite Compulsory CHEM10212 Energy and Change Pre-Requisite Compulsory CHEM10312 Coordination Chemistry Pre-Requisite Compulsory CHEM10412 Structure and Reactivity Pre-Requisite Compulsory CHEM10520 Pre-Requisite Compulsory CHEM20510 Chemistry Research Skills II Co-Requisite Compulsory CHEM20611 Spectroscopy Co-Requisite Compulsory CHEM20411 Organic Synthesis Co-Requisite Compulsory N Recommended textbooks:Introductory texts (a)    Group theory for chemists: fundamental theory and applications, K. C. Molloy, 541.5/M91 https://www.sciencedirect.com/book/9780857092403/group-theory-for-chemists  (b)    Molecular symmetry and group theory: a programmed introduction to chemical applications, A. Vincent, 541.5/V17 (c)    Introduction to molecular symmetry, J. S. Ogden, Oxford Chemistry Primer, no. 97, 541.5/O31 https://bibliu.com/app/#/view/books/9780198559108/epub/html/toc.html  (d)    Group theory for chemists, G. Davidson, 541.5/D6 (e)    Beginning group theory for chemists, P. H. Walton, 541.5/W29Advanced texts (a)    Chemical applications of group theory, F. A. Cotton, 541.5/C (b)    Symmetry and structure (readable group theory for chemists), S. F. A. Kettle, 541.5/K26 (c)    Molecular symmetry, D. J. Willock, 541.5/W33  https://onlinelibrary-wiley-com.manchester.idm.oclc.org/doi/book/10.1002/9780470747414  (d)    Orbital Interactions in Chemistry, T. A. Albright, J. K. Burdett, M.-H. Whangbo     online e-book: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118558409Compilation of data Point group character tables and related data, J. A. Salthouse and M. J. Ware, 541.5/SInteractive websites for symmetry https://www.ch.ic.ac.uk/local/symmetry/  https://symotter.org/   https://www.chemtube3d.com/category/structure-and-bonding/symmetry/  https://www.staff.ncl.ac.uk/j.p.goss/symmetry/Molecules_pov.html  Assessment written exam 2 eAssessment 1 Lectures 11 Practical classes & workshops 11 Tutorials 3 0 72 There is a strict work and attendance requirement on this course.  In particular, attendance at workshops will be closely monitored and if attendance falls below 66% you will be excluded from taking the resit exam.You must inform your lecturer or the School of Natrual Sciences Hub immediately if you miss a workshop for a legitimate reason e.g. medical..