  Systems of adatoms on semiconductor surfaces display competing ground states
and exotic spectral properties typical of two-dimensional correlated electron
materials which are dominated by a complex interplay of spin and charge degrees
of freedom. We report a fully ab initio derivation of low energy Hamiltonians
for the adatom systems Si(111):X, with X=Sn, Si, C, Pb, that we solve within
self-consistent combined GW and dynamical mean field theory ("GW+DMFT").
Calculated photoemission spectra are in agreement with available experimental
data. We rationalize experimentally observed tendencies from Mott physics
towards charge-ordering along the series as resulting from substantial
long-range interactions.
