The (band) edge states, fundamental gaps, optical gaps,
exciton binding energies and UV-Vis spectra for a series of cuboidal
nanoparticles of the prototypical oxide magnesium oxide (MgO), the largest of
with has 216 atoms and edges of 1 nm, were predicted using many-body
perturbation theory (ev<i>GW</i>-BSE). The evolution of the properties with particle
size was explicitly studied. It was found that while the edge states and
fundamental gap change with particle size, the optical gap remains essentially
fixed for all but the smallest nanoparticles, in line with what was previously
observed experimentally. The explanation for these observations is demonstrated
to be that while the optical gap is associated with an exciton that is highly
localised around the particle’s corner atoms, the edge states, while primarily
localised on the magnesium corner atoms (electron) and oxygen corner atoms (hole),
show significant delocalisation along the edges. The strong localisation of the
exciton associated with the optical gap on the corner atoms is argued to also explain
why the nanoparticles have a much smaller optical gaps and red-shifted spectra
than bulk MgO. Finally, it is discussed how this non-quantum confinement
behaviour, where the properties of the nanoparticles arise from surface defects
rather than differences in localisation of edge or exciton states, appears typical
of alkaline earth oxide nanoparticles, and that the true optical gap of bulk
crystals of such materials is also probably the result of surface defects, even
if unobservable experimentally. <br>