  Puzzling properties of sodium cobaltates Na${}_x$CoO${}_2$ become an issue of
numerous recent theoretical and experimental investigations because of very
high thermopower and intricate phase diagram of this material. Experiments
indicated Na${}_{2/3}$CoO${}_2$ to have a kagome-like cobalt sublattice, which
implies additional complexity of this strongly correlated system. In the
present work we have employed the ab-initio GGA+U modeling method to
investigate spin states of Na${}_{2/3}$CoO${}_2$, using an exact crystal cell
established in the experiment. Stability of sodium imprint for concentration
$x=2/3$ proposed in the publications has been obtained. An AFM-A type magnetic
ordering has been recognized as a ground state. Moreover, a competition between
low spin state (LS) and intermediate spin state (IS) has been established to
depend on on-site Hubbard $U$ correction parameter. LS state has been
identified as a ground state of Na${}_{2/3}$CoO${}_2$.
