  We used quantum chemical ab initio methods to determine the effective
parameters of Hubbard and $t-J$ models for the $\rm Na_{x}CoO_2$ compounds (x=0
and 0.5). As for the superconducting compound we found the $a_{1g}$ cobalt
orbitals above the $e_g^\prime$ ones by a few hundreds of meV due to the
$e_g^\prime$--$e_g$ hybridization of the cobalt $3d$ orbitals. The correlation
strength was found to increase with the sodium content $x$ while the in-plane
AFM coupling decreases. The less correlated system was found to be the pure
$CoO_2$, however it is still strongly correlated and very close to the Mott
transition. Indeed we found $U/t\sim 15$, which is the critical value for the
Mott transition in a triangular lattice. Finally, one finds the magnetic
exchanges in the $\rm CoO_2$ layers, strongly dependant of the weak local
structural distortions.
