  We report {\it ab initio} calculations of the charge ordering in
$\alpha^\prime NaV_2O_5$ using large configurations interaction methods on
embedded fragments. Our major result is that the $2p_y$ electrons of the
bridging oxygen of the rungs present a very strong magnetic character and
should thus be explicitly considered in any relevant effective model. The most
striking consequence of this result is that the spin and charge ordering differ
substantially, as differ the experimental results depending on whether they are
sensitive to the spin or charge density.
