  We evaluate the optical gap and Stokes shift of several candidate 1 nm
silicon nanocrystal structures using density functional and quantum Monte Carlo
(QMC) methods. We find that the combination of absorption gap calculations and
Stokes shift calculations may be used to determine structures. We find that
although absorption gaps calculated within B3LYP and QMC agree for spherical,
completely hydrogenated silicon nanocrystals, they disagree in clusters with
different surface bonding networks. The nature of the Stokes shift of the
ultrabright luminescence is examined by comparing possible relaxation
mechanisms. We find that the exciton which reproduces the experimental value of
the Stokes shift is most likely a state formed by a collective structural
relaxation distributed over the entire cluster.
