  We analyze the electronic structure of the Os(0001) surface by means of
first-principle calculations based on Fully Relativistic (FR) Density
Functional Theory (DFT) and a Projector Augmented-Wave (PAW) approach. We
investigate surface states and resonances analyzing their spin-orbit induced
energy splitting and their spin polarization. The results are compared with
previously studied surfaces Ir(111), Pt(111), and Au(111). We do not find any
surface state in the gap similar to the L-gap of the (111) fcc surfaces, but
find Rashba split resonances that cross the Fermi level and, as in the recently
studied Ir(111) surface, have a characteristic downward dispersion. Moreover,
for some selected surface states we study the spin polarization with respect to
${\bf k}_{\parallel}$, the wave-vector parallel to the surface. In some cases,
such as the Rashba split resonances, the spin polarization shows a smooth
behavior with slow rotations, in others the rotation is faster, due to mixing
and anti-crossing of the states.
