  A systematic LSDA+U study of doping effects on the electronic and structural
properties of single layer CoO2 is presented. Undoped CoO2 is a charge transfer
insulator within LSDA+U and a metal with a high density of states (DOS) at the
Fermi level within LSDA. (CoO2)$^{1.0-}$, on the other hand, is a band
insulator with a gap of 2.2 eV. Systems with fractional doping are metals if no
charge orderings are present. Due to the strong interaction between the doped
electron and other correlated Co d electrons, the calculated electronic
structure of (CoO2)$^{x-}$ depends sensitively on the doping level x. Zone
center optical phonon energies are calculated under the frozen phonon
approximation and are in good agreement with measured values. Softening of the
$E_g$ phonon at doping x ~0.25 seems to indicate a strong electron-phonon
coupling in this system. Possible intemediate spin states of Co ions, Na
ordering, as well as magnetic and charge orderings in this system are also
discussed.
