  To shed new light on the mechanism of superconductivity in sodium cobalt
oxide bilayer-hydrate (BLH), we perform a density functional calculation with
full structure optimization for BLH and its related nonsuperconducting phase,
monolayer hydrate (MLH). We find that these hydrates have similar band
structures, but a notable difference can be seen in the $a_{1g}$ band around
the Fermi level. While its dispersion in the $z$ direction is negligibly small
for BLH, it is of the order of 0.1 eV for MLH. This result implies that the
three dimensional feature of the $a_{1g}$ band may be the origin for the
absence of superconductivity in MLH.
