We report ab initio calculations of the charge ordering in α′ NaV 2 O 5 using large configurations interaction methods on embedded fragments. Our major result is that the 2 p 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.