7
$\begingroup$

Imagine if you have a molecule with a large size, e.g. proteins. Anything that rotates experiences pseudoforces if my understanding is correct (e.g. coriolis, centrifugal etc).

Since every molecule rotates, does this have any effect on these molecules that we could measure? Or properties that arise because of these pseudoforces? My guess would be more smeared out electron clouds, or weaker covalent bonds or something. Or a clustering of more heavy atoms in the centre point since farther from the centre would mean weaker bonds.

My guess could also be that the effect is so small that it is negligble. Probably only really big molecules that spin very fast could have an effect (if any).

$\endgroup$
4
  • $\begingroup$ remember that molecules have to be described quantum mechanically. see link.springer.com/chapter/10.1007/978-3-642-32381-2_3 $\endgroup$
    – anna v
    Aug 12, 2023 at 8:54
  • 6
    $\begingroup$ Centrifugal forces have well-described effects on the vibrational spectra of the smallest (that is, diatomic) molecules, actually. en.wikipedia.org/wiki/… $\endgroup$
    – Buzz
    Aug 12, 2023 at 16:59
  • 1
    $\begingroup$ Even in atoms as small as hydrogen any state with $\ell>0$ has a term $\propto r^{-2}$ in the co-rotating frame's potential energy, which corresponds to centrifugal force. $\endgroup$
    – Ruslan
    Aug 12, 2023 at 17:05
  • 1
    $\begingroup$ Buzz you actually made me feel a little silly because you’re absolutely right; there is a very “simple case” example of this phenomenon. I basically gave the “shoot an ant with a bazooka” answer! But even in the diatomic case the centrifugal distortion terms are usually very small, which fits in my broader claims. Thanks for the easier working example! $\endgroup$ Aug 12, 2023 at 22:01

2 Answers 2

11
$\begingroup$

If you were to analyze the molecular vibrations and rotations rigorously correctly, you would end up with Coriolis coupling constants between the vibrations and rotations that arise due to the rotating reference frame of the molecule. This, unfortunately, vastly increases the complexity of such calculations, especially when quantum mechanical properties are taken into account. For a fully detailed treatment, see this paper, this paper, and this paper by Reza Islampour. The latter of these actually explicitly gives expressions of the Coriolis coupling constants. I warn you though, these papers are absolutely brutal to slog through. To an approximate degree, you can split off the terms involving just the vibrations and just the rotations from the electronic terms, but you would still need to properly account for the rotating reference frame if you wanted to correctly describe the rotations and rovibrational couplings. Of course, there are many simpler approximate theories, but you have hit the nail on the head that there are in fact very subtle effects that can arise due to the rotation of a molecule in a rotating reference frame.

Typically, however, these effects are so subtle as to be practically unmeasurable, particularly for systems as large and complicated as a protein. You would certainly not see such dramatic effects as you are suggesting, as the energetic favorability of bonding between atoms, especially multiple bonds such as occur all over the place in biological and organic molecules, are so profoundly stronger than the pseudoforces we are hypothesizing about that the latter simply don't matter at all. You are much more likely to see this affect something like conformational secondary structure than the actual skeleton of the molecules. Moreover, when these larger macromolecules are in vivo, they are never actually isolated. They are fully solvated in a massive bath of water, electrolytes, etc. This means that any rotation that they might do is frustrated, and you will typically see very weak rotational structure for these molecules. This is lucky for us, as it means that we can approximately justify ignoring the rotational contributions to the molecular Hamiltonian entirely for larger molecules in a solvent system!

$\endgroup$
5
$\begingroup$

In classical physics, there are not really any "properties that arise because of these pseudoforces". How can there be when we always have the option of working in an inertial frame? A system such as a molecule may very well have intrinsic properties that depend on angular velocity. But they arise because it is rotating so that is the better language.

In any case, one could get an expectation for how significant these effects are by solving the Schroedinger equation for the time-dependent potential \begin{align} V = \frac{e^2}{|\vec{r} - b\hat{x}\cos(\omega t) - b\hat{y}\sin(\omega t)|} + \frac{e^2}{|\vec{r} + b\hat{x}\cos(\omega t) + b\hat{y}\sin(\omega t)|} \end{align} for a diatomic molecule of radius $b$. This is not going to be solvable analytically but it should be within reach of simulations.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.