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Related to the problem of minimization of the Lennard-Jones potential in a molecule with $n$ atoms, where $n$ is, say, between $5$ and $10$, questions arise such as (but not limited to) the following:

  1. Is it possible to determine a lower bound on the radius of the molecule?
  2. Is it possible to determine an upper bound on the radius of the molecule?
  3. Is it possible to improve the upper and lower bounds using symmetry considerations?

I consider molecules to consist of point-like atoms, so the radius in question is the smallest radius of a sphere containing all points.

If there are theorems regarding similar questions, that would facilitate determining a reasonable search domain for the optimal configuration.

Jake
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  • IMHO, "cluster" is the correct word for it, rather than "molecule". – Ivan Neretin Feb 03 '20 at 05:30
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    It's not possible to answer this without knowing the structure of the molecule, since both the connectivty and the rigidity will affect the radius of gyration. – theorist Feb 03 '20 at 06:34
  • All I can offer is that if such things exist, a good place to look would be the work of David Wales at Cambridge. He has also done extensive global optimizations (i.e. searches for all minima) of LJ clusters of various sizes. If such a thing existed though, it would be very useful to clarify if the proposed global minima for the bounds you describe. – jheindel Feb 04 '20 at 03:58

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