Given a radius $R$ and points $N$, I want to distribute points in a sphere volumetrically so that they are as far apart as possible.
I know that for $N = 1$, I can place it anywhere. For $N = 2$, diametrically opposite. But what about $N > 2$ ?
I have seen a lot of questions which look like this but all of them deal with distribution of points on the surface of the sphere.
I will just state my use case, if that would be useful. If there are $N$ electrons contained in a sphere, what will be there positions ?
Also what exactly subfield do these kinds of problem lie in ? How do I go about approaching problems like these ?
Update: As per @Zang MingJie 's query, I want to minimize the sum total distance between point pairs. Because that would be the minimum energy configuration in my electron case (explained above)