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This site is an excellent, well-organized collection of the chemically relevant character tables. I find it particularly helpful because it includes the cubic functions, allowing you to determine the symmetry labels of the f orbitals in a given point group; these are not included in most of the collections of character tables in general inorganic chemistry textbooks. Additionally, it has a tool that automatically reduces (correctly derived) reducible representations into their component irreducible representations.
A student should be able to use this tool as a quick way to reduce reducible representations, though they should be adept at doing so by hand before using this resource. Additionally, the student should be able to use these tables to find the symmetry labels of f orbitals in lanthanide and actinide complexes.
I generally don't inform my students about this site until I've given them plenty of practice reducing reducible representations -- it can be a cop-out to use the reduction tool.
Secondly, there is sometimes a small glitch when using the automated reduction tool to reduce selected vibrational motions; a error message will appear, saying "Representation has the wrong dimension to be a molecular vibrational representation (
vib).
Nevertheless the symmetry of the force field can be determined." I am not sure why this message appears (I'm not a real group theorist), but it doesn't seem to affect the actual outcome of the reduction algorithm.
I use this site all of the time, it is quite useful.
Austin, do you have any good examples of problems involving the symmetries of the f-orbitals that you could post on VIPEr? I always feel like I skimp on my coverage of the f-block in my courses, because I don't have enough experience to draw from. I would particularly value questions connecting symmetry and group theory tools to the chemistry of actual lanthanide and actinide complexes, and it sounds like you may already be doing this in your teaching. Please share!
Maggie, I do have several problems on f-block complexes, though they're a couple years old and need to be updated. When I have them in a presentable format, I'll be sure to post them!
I just tried using the site to attain the reducible representations and it said 0 for all point groups???