  The electronic structure of the low-temperature (LT) monoclinic magnetite,
Fe3O4, is investigated using the local spin density approximation (LSDA) and
the LSDA+U method. The self-consistent charge ordered LSDA+U solution has a
pronounced [001] charge density wave character. In addition, a minor [00{1/2}]
modulation in the phase of the charge order (CO) also occurs. While the
existence of CO is evidenced by the large difference between the occupancies of
the minority spin t_{2g} states of ``2+'' and ``3+'' Fe_B cations, the total 3d
charge disproportion is small, in accord with the valence-bond-sum analysis of
structural data. Weak Fe orbital moments of ~0.07 mB are obtained from
relativistic calculations for the CO phase which is in good agreement with
recent x-ray magnetic circular dichroism measurements. Optical, magneto-optical
Kerr effect, and O K-edge x-ray absorption spectra calculated for the charge
ordered LSDA+U solution are compared to corresponding LSDA spectra and to
available experimental data. Reasonably good agreement between the theoretical
and experimental spectra supports the relevance of the CO solution obtained for
the monoclinic LT phase. The results of calculations of effective exchange
coupling constants between Fe spin magnetic moments are also presented.
