I am advising a student on her senior math thesis. She would like to involve chemistry somehow (her other major). I know no chemistry. I have read in several places that representation theory features prominently in some areas of chemistry. When I try to read anything online I am not sure how much chemistry one needs to assume. So, if my student is in her senior year of a chemistry major, are there any places where she can start to look for a project in group theory and chemistry?
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1$\begingroup$ Dover has a good book in this area, but I am not enough of an expert to compare it to other references amazon.com/David-M.-Bishop/e/B001IQW5FI/… $\endgroup$– jonscaCommented Sep 17, 2013 at 0:56
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$\begingroup$ I think in every Physical Chemistry book there is a chapter about group theory I've study it from Atkins $\endgroup$– G MCommented Sep 17, 2013 at 18:14
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$\begingroup$ And every Inorganic Chemistry text should have multiple chapters applying group theory and symmetry to the structure and spectroscopy of organometallic compounds. $\endgroup$– Ben NorrisCommented Sep 19, 2013 at 11:12
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2 Answers
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Several answers and comments have suggested general texts that have good foundation information; however if a student is writing a thesis, these sources will be insufficient since they are geared towards the teaching of group theory rather than the application of group theory to generate new knowledge. Even at an undergraduate level, there should be an attempt to generate new knowledge in a thesis. To do this, the student would need to get her nose in the chemical literature, and I assume any student in an ACS accredited undergraduate program has experience with literature searches. My very brief survey of group theory reviews came up with the following potentially interesting areas:
- understanding the structure of natural and synthetic perovskites, which have a number of technological applications. Journal of Physics: Condensed Matter (2013), 25(17), 175902
- Stereochemistry of medicinal compounds: Helvetica Chimica Acta (2013), 96(1), 4-30.
- the role of group theory in furthering our understanding of superconductivity: Comptes Rendus Physique (2011), 12(5-6), 532-541.
- Group theory and biomolecular conformations: Journal of Physics: Condensed Matter (2010), 22(32), 323103/1-323103/21.
- A somewhat esoteric area of nuclear point groups: Acta Physica Polonica B (2013), 44(3), 305-318.
Almost certainly, a senior has encountered the importance of symmetry in Inorganic Chemistry and IR spectroscopy, and these areas may be more accessible to the student. In the end, however, good questions and topics for a senior thesis are going to require getting ones nose in the literature.
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The first 4 chapters of Chemical Applications of Group Theory by F A Cotton* should be enough for your student. However there are numerous books available.
Again LibreText Chemistry (formerly known as UC Davis ChemWiki, link via the Internet Archive) has a good documentation on group theory.
* The Internet Archive holds both the first edition by 1962, as well as the third by 1989. Both are available as .epub and .pdf for a 14 day loan.
