is there a way to simulate a cluster of quantum dots?

[Ulrik G. Vej-Hansen]

As Anders says, predicting nanoparticle shapes with certainty is quite complicated. See for example: http://www.sciencedirect.com/science/article/pii/S0021951711002673

If you want to investigate the HOMO-LUMO gap for a certain geometry and vary the number of atoms, I would make a Wulff construction and then remove the highest-coordinated atoms. This is no guarantee that your shapes will have a large weight in the actual distribution of shapes, but it should at least provide you with fairly low-energy shapes.

[Anders Blom]

Probably it's more relevant to look at various properties as function of size (radius) rather than the exact number of atoms.