Math Chemistry: Can an Undergrad Research?

[pjmarshall]

I'm not a chemist, but I was wondering there are any promising fields in mathematical chemistry. Not necessarily chemical engineering/physics-wise, more so to do with molecular structure, topology, etc. Is there any chance an undergrad would be able to participate in this area of research? Or is it too dried up already/taken over by computational chemistry? Is this area more of a physicist's job? How far can an undergrad who hasn't even gone into graduate analysis go into the field?

 

[alxm]

There's a field known as 'mathematical chemistry', they even have a http://www.springerlink.com/content/101749/". But there are few groups or departments dedicated to the subject, and few who would label themselves a 'mathematical chemist' or similar.

What you have, is the mathematically-intensive areas of chemistry, which are: Physical chemistry, chemical physics, theoretical chemistry, computational chemistry in general and quantum chemistry in particular. (These aren't very distinct fields) In general, the more mathematical areas are also more physical, and so you have to learn physics, which doesn't necessarily mean you have to be a physicist. These fields have people from both backgrounds. So if you want to go into these areas, you should study math, physics, phys-chem etc.

As for research, grad school is more or less obligatory in any scientific field, there's no getting around that, really. Which doesn't mean you can't contribute at all; many universities have programs where undergrads get to assist in research. If yours doesn't, you could take the initiative and simply ask if they have some suitable small thing you could do as a project. Although the main problem isn't really finding a task - a good researcher should have more ideas than he has time. The main problem is whether they'd have to spend more time supervising/tutoring than it would've taken them to solve it themselves. (OTOH, that could possibly be delegated to a grad student)

 

[czelaya]

From my experience, mathematical chemistry is a very small area. Like axlm, has already stated chemistry and its sub-disciplines (physical chemistry, chemical physics, theoretical chemistry,... ) are an extension of physics dealing with chemical problems.

There are several books on major topics in mathematical chemistry which deals primarily with super algebras, group theory (lie groups, point group, SU(n)), topology, and applications of differential geometry. One of the most heavily researched areas in mathematical chemistry is graph theory.

topology:
https://www.amazon.com/dp/9056991744/?tag=pfamazon01-20

algebras:
(I would not recommend this book.) It states that an introduction to quantum mechanics is all that is needed, but gives no introduction on inner product spaces (Hilbert space), special functions beyond those in quantum mechanics, and requires a solid foundation in linear algebra beyond a single semester. It's just sitting on my shelf collecting dust:

https://www.amazon.com/dp/0849382920/?tag=pfamazon01-20

graph theory (there are many books on the subject):

https://www.amazon.com/dp/0849342562/?tag=pfamazon01-20


However, physical chemist, chemical physicist, theoretical chemistry, and so forth just utilize or extend what has already been researched in physics into chemical dynamics.

 

[alxm]

However, physical chemist, chemical physicist, theoretical chemistry, and so forth just utilize or extend what has already been researched in physics into chemical dynamics.

Well, I'm not sure I'd say that, though. If it was a matter of 'just utilizing' physics, then every applied physics field would end up in that category as well. I don't think the distinction between chemistry and physics is very meaningful here. Obviously a person who's say, developing DFT methods in Quantum Chemistry is not doing anything fundamentally different from a person developing DFT methods for Solid-State Physics, and have much more in common with each other than the solid-state guy does to an astrophysicist, or the quantum chemist to an organic chemist.

Pople got the Nobel in Chemistry (and Wikipedia calls him a 'theoretical chemist'), but regarded himself as a mathematician. He shared it with Kohn, who's labelled a 'theoretical physicist'. The banner of theoretical/quantum chemistry really spans the whole spectrum from actual theories-about-chemistry to theoretical physics to numerical analysis.

I myself do QC and work for a chemistry department now, but my PhD says 'chemical physics' and my advisor's degree said 'theoretical physics', even though we're doing the same stuff. IMO you really have to look closely at what a particular person's research is before deciding if it's more 'physics' or more 'chemistry' or even 'math'. It's not necessarily very meaningful, though. I know a number of cases where the departmental affiliation of a professor in the field ended up having more to do with university politics than with his research. Which I suppose is an upside to the field: Not getting along with the chemistry faculty? Go join physics. Or vice-versa.