Are there any theorems about packing of atoms in molecules subject to the Lennard-Jones potential?

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.


