423 Molecular Orbital Theory

Course information:

All the information you need for this course will be accessible from this site.

use the sidebar to access a specific lectures and other materials.

Tutorials and homework form part of this course and are examinable.

Extra reading and on-line material is associated with each lecture, this is entirely optional!

If you want to find out still more please contact me, I can recommend a wider variety of texts, including those which cover material in more detail.

Need some help!

Check the recommended text for this course:

Group Theory for Chemists, Kieran C. Molloy, Harwood Publishing, Chichester, 2004.

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Lecture 1

(updated for 2026)

1. notes for the lecture: pdf
2. slides from the lecture pdf (14 MB file)
3. flow chart pdf
4. character tables for the lecture: pdf
5. model answers to the in-class problems/self-study problems/test preparation: pdf
6. added after feedback practice problems for point group flow chart: pdf
7. resources related to this lecture optional
   • Reading: Part 1: Ch1 Symmetry from Group Theory for Chemists
   • Chemtube3d is a good website for viewing symmetry elements on 3d rotateable molecules: Chemtube3d
   • Otterbein Gallery has some good examples, and the molecules can be rotated/moved: Otterbein Gallery
   • wiki on symmetry in general
   • chem207 workshop1: symmetry

Lecture 2

(updated for 2026)

1. notes for the lecture: pdf
2. slides from the lecture pdf (8 MB file)
3. model answers to the in-class problems/self-study problems/test preparation: pdf
4. resources related to this lecture optional
   • Reading: Part 1: Ch2 Groups and Representation from Group Theory for Chemists
   • Greek letters
   • "The Orbitron"
   • Improper rotations for the O_h point group pdf
   • Where the symbols for the irreducible representations come from pdf

Lecture 3

(updated for 2026)

1. notes for the lecture: pdf
2. slides from the lecture pdf (8 MB file)
3. model answers to the in-class problems/self-study problems/test preparation: pdf
4. resources related to this lecture optional
   • Reading: Part 3: Ch6 Fundamentals of MO Theory from Group Theory for Chemists
   • Reading: Chapter 1.13: Homonuclear diatomic MO theory from Inorganic Chemistry Catherine Housecroft and Alan Sharpe, 2nd Edition, Pearson, Prentice Hall, Harlow, 2005
   • Reading: Chapter 2: MO theory from Shriver and Atkins Inorganic Chemistry Atkins, Overson, Rourke, Weller, Armstrong , 4th Edition, Oxford University Press, Oxford, 2006
   • recent Chemistry World (magazine of the Royal Chemical Society) article Bond order through a molecular orbital lens
   • recent Chemistry and Engineering News (magazine of the American Chemical Society) article Boron makes quadruple bond with rhodium
   • famous theoreticians:
     • in 2009 Prof. Eisenstein a theoretical chemist recieved the American Chemical Society award for organometallic chemisty Interview with Prof Eisenstein
     • Emily Carter Professor in Energy and the Environment Princeton University and elected as a Fellow of the American Chemical Society in 2012
     • Sharon Hammes-Schiffer elected as a Member of the National Academy of Sciences, 2013
     • the nobel prize in chemisty 1981 went to Fukui and Hoffmann Fukui elucidated the importance of orbital symmetry within the framework of frontier molecular orbital (FMO) theory. Hoffmann developed a similar ideas for organic chemistry, in particular in the context of pericyclic reactions: The Woodward-Hoffmann rules.
     • the nobel prize in chemisty 1998 went to Kohn and Pople
     • the nobel prize in physics 2008 went to Yoichiro Nambu, Makoto Kobayashi, Toshihide Maskawa
     • the nobel prize in chemisty 2013 went to Martin Karplus, Michael Levitt, Arieh Warshell
     • Who was Christopher Longuet-Higgins?

Lecture 4

(updated for 2026)

1. notes for the lecture: pdf
2. slides from the lecture pdf
3. model answers to the in-class problems/self-study problems/test preparation: pdf
4. resources related to this lecture optional
   • Reading: Chapter 1.13: Homonuclear diatomic MO theory from Inorganic Chemistry, Catherine Housecroft and Alan Sharpe, 2nd Edition, Pearson, Prentice Hall, Harlow, 2005
   • On-line interactive tutorial on [CN]- try it!
   • Bonding in simple diatomic molecules is still of interest today!
     Evaluating chemical bonding in dioxides for the development of metal–oxygen batteries: vibrational spectroscopic trends of dioxygenyls, dioxygen, superoxides and peroxides" P. Radjenovic and L. Hardwick, Phys. Chem. Chem. Phys., 2019,21, 1552-156, https://doi.org/10.1039/C8CP04652B
   • Bond Order and Chemical Properties of BF, CO, and N₂ , Ryan J. Martinie, Jarred J. Bultema, Mark N. Vander Wal, Brandon J. Burkhart, Douglas A. Vander Griend, and Roger L. DeKock, J. Chem. Educ., 2011, 88 (8), pp 1094-1097
   • Bonding in simple diatomic molecules is not straight forward!
     Connections between Concepts Revealed by the Electronic Structure of Carbon Monoxide Ying Liu, Bihui Liu, Yue Liu, and Michael G. B. Drew, J. Chem. Educ., 2012, 89 (3), pp 355-359
   • for experts! A paper on the complexity of mixing in diatomic molecules
     Role of s-p Orbital Mixing in the Bonding and Properties of Second-Period Diatomic Molecules" F. Matthias Bickelhaupt, Jeffrey K. Nagle and William L. Klemm, J. Phys. Chem. A 2008, 112, 2437-2446

Lecture 5

(updated for 2026)

1. notes for the lecture: pdf
2. slides from the lecture when available pdf
3. model answers to the in-class problems/test preparation: pdf
4. resources related to this lecture optional
   • chem207 workshop2: MO diagrams, see the slides for how to draw the MO diagram of water

Lecture 6

(updated for 2026)

1. notes for the lecture: pdf
2. slides from the lecture when available pdf
3. model answers to the in-class problems/test preparation: pdf
4. resources related to this lecture optional
   • Reading from Group Theory for Chemists: Ch7 H₂O Linear or Angular? and Ch8 NH₃ Planar or Pyramidal?
   • Paper for the PES of ammonia: T. Buttersack, P. Mason, R. McMullen, T. Martinek, K. Brezina, D. Hein, H. Ali, C. Kolbeck, C. Schewe, S. Malerz, B. Winter, R. Seidel, O. Marsalek, P. Jungwirth, S. Bradforth, "Valence and Core-Level X-ray Photoelectron Spectroscopy of a Liquid Ammonia Microjet", JACS, 2019, 141 (5), p1838-1841, DOI: 10.1021/jacs.8b10942
5. resources related to forming complex MO diagrams optional for experts
   • "Qualitative molecular orbital study of ethane and diborane" by B.M. Gimarc, J. Am. Chem. Soc, 1973, 95(5), p1417-1421 DOI: 10.1021/ja00786a010.
   • "Strengths of A-A Single Bonds in Symmetric A2B2n Molecules and Ions" by B. Gimarc, S. Khan and M.Kohn, J. Am. Chem. Soc, 1978, 100(7), p1996-2003 DOI: 10.1021/ja00475a004.

Assignment!

(updated for 2026)

1. assignment questions sheet: pdf
2. assignment model answers: pdf
3. example model question: pdf
4. example model answers: pdf

Lecture 7

(updated for 2026)

1. notes for the lecture: pdf
2. slides from the lecture pdf
3. model answers to the in-class problems/test preparation: pdf
4. resources related to this lecture optional
   • the B₂H₆ MO diagram pdf

Lecture 8, a Tutorial

(updated for 2026)

1. the MO diagram of PL5 pdf
2. symmetry adapted FOs example pdf