## Advanced Spectroscopy

### The recommended texts for this course:

- Group Theory for Chemists, Kieran C. Molloy, Harwood Publishing, Chichester
- Molecular Quantum Mechanics PW Atkins and RS Friedman, Oxford University Press, Oxford

### Suggested texts for extra information:

- Molecular Symmetry and Group Theory, Alan Vincent, John Wiley & Sons Ltd, Chichester
- Inorganic Spectroscopic Mehtods, Alan K. Brisdon, Oxford University Press, Oxford
- Molecular Spectroscopy, John M. Brown, Oxford University Press, Oxford
- Maths for Chemists, Martin Cockett and Graham Doggett, Royal Society of Chemistry
- Metal Ligand-Bonding by R. Janes and E. Moore, The Open University, Milton Keynes, published by the RSC.
- The Chemistry Maths Book by E. Steiner, The Oxford University Press, Oxford

### EXAMS!

- The format of the exam will be
**Answer any TWO of a), b) OR c)**each worth 12.5 marks, the questions will be spread over the whole course, and will be split roughly over**problem solving and equation derivations/understanding**. You can expect to see**vibrational, electronic and mathematics**based questions. - this course has changed over the last few years, parts have been removed and new material added, so you will see some questions that you will not recognise!
- if you want to look at previous exams use blackboard:
- 2018 same name with only minor changes to its current content
- 2017 the course did not run, no exam
- 2016 2nd year physical paper: Spectroscopy & Characterisation
- 2015 no exam
- 2014 and before inorganic IIIB: Symmetry & Spectroscopy

- don't forget there are questions some with answers in both "Group Theory for Chemists" and "Molecular Symmetry and Group Theory"
- I've provided many in-class problems and "homework/exam preparation" questions at the end of the lectures (with detailed model answers) I have also uploaded my hand-written examples from the class.
- Both workshops contain extensive fully worked problems
- any problems with the answers or questions, don't hesitate to e-mail me!

### Lecture 1 (2019)

- notes for the lecture:pdf
- flow chart and character tables:
- model answers
- reading: optional
- notes on Groups from the old 3rd year course: pdf
- symmetry labels pdf
- quick revision notes for matrices, including basic matrix mechanics operations pdf
- extra notes on how the matrices presented in the lecture were determined pdf
- Chapter 2: Groups and Representations, in "Group Theory for Chemists"
- multiplying and using matrices: Chapter 4: Matrices and Matrix Algebra of "Maths for Chemists"
- Section 5.5: Matrix Representations in Chapter 5 of "Molecular Quantum Mechanics"
- Programme 4: Matrices, in "Molecular Symmetry and Group Theory"
- for experts: material on transformation matrices in Chapter 5 of "Molecular Quantum Mechanics"

- resources related to this lecture optional
- Heisenberg developed matrix mechanics (Wiki on Heisenberg) and won the nobel prize in physics in 1932 for the creation of quantum mechanics
- Dirac noticed the connection between matrix mechanics and the Schrodinger's wave equation and put the two on an equal footing using matrices. Wiki on Dirac, Wiki on Schrodinger. Dirac and Schrodinger shared the nobel prize in physics in 1932 for the creation of quantum mechanics
- connection to rotation matrices: Wiki on flight dynamics
- on the importance of symmetry:

- Clusters can have very high symmetry
- in 1996 the chemistry nobel prize was awarded for the discovery of a new form of carbon, the fullerenes. These are carbon clusters that can form very high symmetry structures, the prototypical fullerene is Buckminsterfullerene C
_{60}which has the shape of a truncated-icosahedron. - the icosahedron has iscosahedral symmetry, and 120 symmetry operations. It is an example of a platonic solid, or three dimensional polygon. Each polygon is associated with a symmetry group (a polyhedral group) that leaves the polyhedron invariant. The polyhedral groups are the tetrahedral, octahedral and icosahedral.

- in 1996 the chemistry nobel prize was awarded for the discovery of a new form of carbon, the fullerenes. These are carbon clusters that can form very high symmetry structures, the prototypical fullerene is Buckminsterfullerene C

### Lecture 2 (2019)

- notes for the lecture:pdf
- model answers
- reading: optional
- notes on equivalence and classes in Groups from the old 3rd year course: pdf
- Chapter 3: Reducible Representations, in "Group Theory for Chemists"
- Programme 7: Applications to Molecular Vibration, in "Molecular Symmetry and Group Theory"
- Section 10.15: Group theory and molecular vibrations in Chapter 10 of "Molecular Quantum Mechanics"
- Chapter 4: Techniques of Vibrational Spectroscopy, in "Group Theory for Chemists"

- resources related to this lecture optional
- IR spectroscopy is utilised by astronomers to learn more about the universe. Water vapour exists in space and on far planets, and IR light can travel from these distant places to be analysed near earth. Water in the atmosphere blocks key parts of the spectrum, so the IR spectrometers need to be very high in the atmosphere (airborne observatories) or orbiting the earth (space telescopes).
- SOFIA (Stratospheric Observatory for Infrared Astronomy) is a Boeing 747SP airliner modified to carry a telescope for IR observations at ~12 km in the stratosphere
- Kuiper is a highly modified C-141A jet transport aircraft operated by NASA to support research in infrared astronomy.
- Most of the optical telescopes launched into space (such as the Hubble Space Telescope) can also perform infrared observations. NASA's Spitzer Space Telescope is dedicated entirely to IR observations
- Recently water vapor has been detected inside a forming star system. Nature
- IR techniques have recently found water on hot gas giants with temperatures of 1000K, see related article1 and article2 from NASA's web-site.

- Why is Water Blue?
- Water absorbs in the red part of the visible spectrum and thus light which pass through and which is reflected from several meters of water appears blue. The red absorptions are due to high overtone and combination states of the vibrational spectrum of water which is shifted by the presence of H-bonding and just penetrates the red end of the visible spectrum. Deuterated water is colourless because the isotope effect is sufficient to shift this vibrational band out of the visible spectrum.
- sourced from here and published in: J. Chem. Edu., 1993, 70(8), 612

- IR spectroscopy is utilised by astronomers to learn more about the universe. Water vapour exists in space and on far planets, and IR light can travel from these distant places to be analysed near earth. Water in the atmosphere blocks key parts of the spectrum, so the IR spectrometers need to be very high in the atmosphere (airborne observatories) or orbiting the earth (space telescopes).

### Lecture 3 (2019)

- notes from the lecture:pdf
- model answers
- reading: optional
- where do the reduction formula and projection operator come from?
- Notes from the old 3rd year course:pdf
- Chapter 5: Group Theory, section 5.10-5.11, in "Molecular Quantum Mechanics"

- From "Group Theory for Chemists", by Kieran Molloy
- Chapter 4: Techniques of Vibrational Spectroscopy
- Appendix 1: Projection Operators

- Programme 7: Applications to Molecular Vibration in "Molecular Symmetry and Group Theory"
- related to the lecture from "Molecular Quantum Mechanics", by Peter Atkins and Ronald Friedman.
- revision Appendix 8 and 9: The radial and angular wavefunctions
- revision Appendix 7: The harmonic oscillator: the standard solution
- Section 10.8: The Vibrations of diatomic molecules
- Section 10.13: Normal modes
- Appendix 19: Normal modes: an example in "Molecular Quantum Mechanics"

- where do the reduction formula and projection operator come from?
- resources related to this lecture optional
- below are animations of the A
_{1}out-of-plane bending (umbrella) mode and totally symmetric stretching mode of NH_{3}

- below are animations of the A
- resources related to more advanced group theory and material removed from the course optional
- more on the similarity transformation, Albelian groups
- Chapter 5: Group Theory in "Molecular Quantum Mechanics"
- Chapter 2: The Group Concept, in "Elements of Molecular Symmetry" by Yngve Ohrn. The later chapters are extremely technical, so only look at these if you are particularly keen!
- Wiki Neils Abel

- more on the use of symmetry in crystallography
- extra material on the relationship between crystal and point group symmetries pdf
- crystal symmetry

- more on the similarity transformation, Albelian groups

### Lecture 4 (2019)

- notes from the lecture:pdf
- reading optional
- Extra on the Einstein coefficients:pdf
- Extra on the CoM transition dipole moment:pdf
- From "Molecular Quantum Mechanics", by Peter Atkins and Ronald Friedman.
- Chapter 6: Sections 6.2, 6.3 and 6.4 for Perturbation theory
- those who wish to look at degenerate states or time-dependent perturbation theory can complete Chapter 6 : Techniques of Approximation advanced!
- the Oxford University Press website has student resources from the text, they plot out the solutions to some of the perturbation equations, I'll leave you to play around with the worksheets
- Section 6.17: The Einstein transition probabilities
- Appendix 16: Electric dipole transitions

- Molecular Spectroscopy, John M. Brown, Oxford University Press, Oxford. This is one of the Oxford University primers, so it is a small compact and excellently writen booklet. highly recommended

### Workshop 1 (2019)

- I don't advise looking at these notes until after the workshop as they contain the model answers for the material that will be covered. You will get more out of the experience if you can first work on the problem independently.
- typed notes from the workshop:pdf
- my handwritten notes from the day!
**when ready** - Text book -Chapter 5: The Vibrational Spectrum of Xe(O)F
_{4}, in "Group Theory for Chemists" - Relevant paper: Raman, X-ray and computational study: doi:10.1016/j.jfluchem.2011.05.010 "A Raman spectroscopic study of the XeOF4/XeF2 system and the X-ray crystal structure of alpha-XeOF4 center dot XeF2", M.J. Hughes, D.S. Brock, H.P Mercier and G.J. Schrobilgen,
*J. Fluorine Chem.*,**2011**, 132(10), p660 - A much older paper: doi:10.1063/1.1696273 "Vibrational Spectra and Valence Force Constants of the Square Pyramidal Molecules XeOF
_{4}, IF_{5}, BrF_{5}, and ClF_{5}" G.M. Begun, W.H. Fletcher and D.F. Smith,*J. Chem. Phys.*,**1965**, 42 (6), p2236