  We have carried out collinear and non-collinear electronic structure
calculations to investigate the structural, electronic and magnetic properties
of isolated Cr atoms, dimers and compact trimers. We find that the Cr monomer
prefers to adsrob on the fcc hollow site with a binding energy of 3.13 eV and a
magnetic moment of of 3.93 $\mu_B$. The calculated Kondo temperature of 0.7 K
for the monomer is consistent with the lack of a Kondo peak in scanning
tunneling microscopy (STM) experiments at 7 K. The compact Cr dimer orders
antiferromagnetically and its bond length contracts to 1.72 $\AA$ close to the
value for the free-standing Cr dimer. The very low magnetic moment of 0.005
$\mu_B$ for the Cr atoms in the dimer is due to the strong $d-d$ hybridization
between the Cr adatoms. Thus, these calculations reveal that the absence of the
Kondo effect observed in STM experiments is due to the small local moments
rather than the Kondo quenching of the local moments suggested experimentally.
The Cr compact trimer exhibits non-collinear co-planar magnetism with vanishing
net magnetic moment in agreement with experiment.
