  The electronic structure of the monoclinic structure of Fe$_3$O$_4$ is
studied using both the local density approximation (LDA) and the LDA+$U$. The
LDA gives only a small charge disproportionation, thus excluding that the
structural distortion should be sufficient to give a charge order. The LDA+$U$
results in a charge disproportion along the c-axis in good agreement with the
experiment. We also show how the effective $U$ can be calculated within the
augmented plane wave methods.
