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Theoretical chemistry is nowadays almost synonymous with computational (and usually quantum) chemistry.

Are there any examples of recent (let's say post 2000) research in chemistry that is theoretical (i.e. non-experimental) but does not use extensive computations (i.e. HPC), does not aim to produce better computational methods, or does not investigate mathematical foundations of computational chemistry methods?

Something I imagine can exist are models or model Hamiltonians in quantum chemistry that are analytically solvable (or with minimal help from computers), or abstract mathematics like topology applied to chemistry.

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  • $\begingroup$ Since practically no Hamiltonian can be solved analytically (ok, H aside), all you left is computers. Topology is a nice branch of mathematics, but I haven’t seen any relevant applications. Graph theory is your only shot, it may have new applications, mostly in chemoinformatics or such. $\endgroup$ – Greg Aug 20 at 10:01
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    $\begingroup$ maybe something like aip.scitation.org/doi/10.1063/1.5002894? $\endgroup$ – orthocresol Aug 20 at 10:34
  • $\begingroup$ @Greg my question was actually motivated by a graph theory question at the Matter Modelling SE mattermodeling.stackexchange.com/questions/1360/… So I was curious about other examples. By exactly solvable Hamiltonians I mean 2-state models, BCS Hamiltonian... that reveal the essential physics even though they do not give qualitative answers and are popular with physicsts. I heard a joke that says "Chemists seek approximate solutions to the exact Hamiltonian while physicists seek exact solutions to approximate Hamiltonians." $\endgroup$ – LukasK Aug 20 at 11:24
  • $\begingroup$ @LukasK The theoretical physicists I know are spending considerable amount of time in front of HPCs and doing tons of numerical work. So that joke maybe were true 30 years ago, I am not sure it is true any more. Also, if a Chemist solves a toy Hamiltonian eg for spectroscopy, generally everyone (especially the Physisists) say it was Physics, just accidentally were applied by a Chemist. $\endgroup$ – Greg Aug 20 at 11:46
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    $\begingroup$ I really don't mean to toot my own horn, but I'm curious whether something like this counts. $\endgroup$ – Nicolau Saker Neto Aug 20 at 12:37
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I think I can answer this in the affirmative. There are articles which find connections between abstract mathematics and chemistry, sometimes even bypassing physics altogether. Of course, these kinds of articles are considerably rarer, but they're sprinkled out there.

I can think of two articles which I'd love to discuss, but I literally do not have the necessary background, it just goes way over my head. The first one is Quantum Interference, Graphs, Walks, and Polynomials, Chem. Rev. 2018, 118, 10, 4887–4911. This is some rather pure graph theory which is not related to cheminformatics. In particular, I find it interesting that the connectivity in azulene is comparatively unusual, and this probably is deeply connected to its unusual photophysical properties. And then there's The Rouse Dynamic Properties of Dendritic Chains: A Graph Theoretical Method, Macromolecules 2017, 50, 10, 4007–4021, more graph theory with a little bit of physics, and whose content eludes me entirely.

Surely some amount of computer assistance was employed in deriving the results for these papers, because there's no reason to give up that tool. However, I don't think this counts as "extensive computations" in the sense you may have had in mind.

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The answer is yes.

There is work in non-equilibrium thermodynamics that is purely theoretical, e.g.:

Jarzynski, Christopher. "Rare events and the convergence of exponentially averaged work values." Physical Review E 73.4 (2006): 046105. https://journals.aps.org/pre/abstract/10.1103/PhysRevE.73.046105

Jarzynski, Christopher. "Fluctuation relations and strong inequalities for thermally isolated systems." Physica A: Statistical Mechanics and its Applications 552 (2020): 122077. https://arxiv.org/pdf/1907.09604.pdf

You may recognize Jarzynski as the creator of the famous Jarzynski equality: https://en.wikipedia.org/wiki/Jarzynski_equality

And some of the work on phase transitions and criticality certainly meets your criteria. Here you'll see papers whose principal purpose is to develop better theoretical models to explain these phenomena and, to the extent computation is used, it's to test those models. But the heart of these papers is the development of the theoretical models themselves. Here's one example:

Goodrich, Carl P., Andrea J. Liu, and James P. Sethna. "Scaling ansatz for the jamming transition." Proceedings of the National Academy of Sciences 113.35 (2016): 9745-9750. https://www.pnas.org/content/113/35/9745.short

Finally, if you'll accept work on biological macromolecules as falling within the realm of chemistry, there is also work in theoretical chemistry/theoretical biophysics that meets your criteria, in which theoretical models are developed to predict and explain the properties of macromolecules, and the models are then tested either computationally or experimentally:

Yoffe, Aron M., et al. "The ends of a large RNA molecule are necessarily close." Nucleic acids research 39.1 (2011): 292-299. https://academic.oup.com/nar/article/39/1/292/2409062

Chakrabarti, Shaon, Christopher Jarzynski, and D. Thirumalai. "Processivity, Velocity, and Universal Characteristics of Nucleic Acid Unwinding by Helicases." Biophysical journal 117.5 (2019): 867-879. https://www.biorxiv.org/content/biorxiv/early/2018/07/10/366914.full.pdf

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