  We present ab-initio electronic structure results on the surface of sqr3
adsorbates. In particular, we address the issue of metal-insulator
instabilities, charge-density-waves (CDWs) or spin-density-waves (SDWs), driven
by partly filled surface states and their 2D Fermi surface, and/or by the onset
of magnetic instabilities. The focus is both on the newly discovered
commensurate CDW transitions in the Pb/Ge(111) and Sn/Ge(111) structures, and
on the puzzling semiconducting behavior of the Pb/Ge(111), K/Si(111):B and
SiC(0001) surfaces. In all cases, the main factor driving the instability
appears to be an extremely narrow surface state band. We have carried out so
far preliminary calculations for the Si/Si(111) surface, chosen as our model
system, within the gradient corrected local density (LDA+GC) and local spin
density (LSD+GC) approximations, with the aim of understanding the possible
interplay between 2D Fermi surface and electron correlations in the surface +
adsorbate system. Our spin- unrestricted results show that the sqr3
paramagnetic surface is unstable towards a commensurate SDW with periodicity
3x3 and magnetization 1/3.
