I recently found that there is actually a small field of research called mathematical chemistry. It seems that a lot of the research done in this field focuses on graph-theory as applied to chemistry, and topology as applied to defining the structure of molecules.

It's a bit disappointing to me that mathematical chemistry is not a larger field, but it also makes sense because for some reason chemistry does not seem to be as easily asbtracted into a mathematical framework as physics or biology. Note that I don't mean applying mathematical models to chemistry as we do this all the time. For instance, in mathematical physics, which is a very diverse field populated by people trained as both mathematicians and physicists, physical problems are reframed in a natural mathematical framework and solved accordingly. I think a lot of work on the Navier-Stokes equation would qualify as the type of work I mean.

So, is anybody aware of any notable results which have come from the field of mathematical chemistry? Furthermore, do any of these results indicate anything physical which we did not already know to be true? Also, an answer which addressed potential applications of some results of mathematical chemistry would be interesting.

I suppose I will say that I am looking for references as well as summaries so as to narrow the scope of the question.

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    $\begingroup$ While not exactly a discovery, the application of graph theory and related to (sub)structure search in tools like Scifinder is of great importance. Group theory of point groups, space groups as applied to spectroscopy and x-ray diffraction is also a very important tool. $\endgroup$ – TAR86 Mar 8 '17 at 5:44
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    $\begingroup$ Do you want to exclude quantum say for MO theory, and molecular dynamics? There has been quite a lot in the past so what about 'pencil and paper' theory ( I mean non computer based to get results) such as Marcus electron transfer, Forster energy transfer, radiationless transitions in molecules (Lin, Jortner, Siebrand) and ligand field /crystal field theory. $\endgroup$ – porphyrin Mar 8 '17 at 9:49
  • $\begingroup$ Those sound like reasonable answers to me. I had in mind more of the modern work which uses graph theory and some higher level applications of group theory. I suppose what I'm thinking of when saying mathematical chemistry is that the work is done similar to pure mathematics where a paper basically consists of presenting a proof along with some commentary. $\endgroup$ – jheindel Mar 9 '17 at 0:14

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