  The study of the strength of correlations in Na$_x$CoO$_2$ is extended to the
x=0 end of the phase diagram where Mott insulating behavior has been widely
anticipated. Inclusion of correlation as modeled by the LDA+U approach leads to
a Mott transition in the $a_g$ subband if U is no less than U$_c$=2.5 eV. Thus
U smaller than U$_c$ is required to model the metallic, nonmagnetic CoO$_2$
compound reported by Tarascon and coworkers. The orbital-selective Mott
transition of the $a_g$ state, which is essentially degenerate with the
$e'_{g}$ states, occurs because of the slightly wider bandwidth of the $a_g$
bands. The metal-insulator transition is found to be strongly coupled to the
Co-O bond length, due to associated changes in the $t_{2g}$ bandwidth, but the
largest effects occur only at a reduced oxygen height that lies below the
equilibrium position.
