We establish the formula representing
cubic nanocrystals
(NCs)
as hard cubes taking into account the role of the ligands and describe
how these results generalize to any other NC shapes. We derive the
conditions under which the hard cube representation breaks down and
provide explicit expressions for the effective size. We verify the
results from the detailed potential of mean force calculations for
two nanocubes in different orientations as well as with spherical
nanocrystals. Our results explicitly demonstrate the relevance of
certain ligand conformations, i.e., “vortices”, and
show that edges and corners provide natural sites for their emergence.
We also provide both simulations and experimental results with single
component cubic perovskite nanocrystals assembled into simple cubic
superlattices, which further
corroborate theoretical predictions. In this way, we extend the Orbifold
Topological Model (OTM) accounting for the role of ligands beyond
spherical nanocrystals and discuss its extension to arbitrary nanocrystal
shapes. Our results provide detailed predictions for recent superlattices
of perovskite nanocubes and spherical nanocrystals. Problems with
existing united atom force fields are discussed.