Charge order in magnetite. An LDA+U study

The electronic structure of the monoclinic structure of $\chem{Fe_3O_4}$ 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.