  Bandstructure calculations with different spin arrangement for the spin-chain
compound MgVO_3 have been performed, and paramagnetic as well as magnetic
solutions with ferro- and antiferromagnetically ordered chains are found, the
magnetic solutions being by 0.22 eV per formula unit lower than the
paramagnetic one. The orbital analysis of the narrow band crossing the Fermi
level in the paramagnetic solution reveals that the band has almost pure
vanadium 3d character, the lobes of the relevant d-orbitals at the neighboring
in-chain sites being directed towards each other, which suggests direct
exchange. The tight-binding analysis of the band confirms the strong exchange
transfer between neighboring in-chain V-ions. Besides, some additional
superexchange transfer terms are found, which give rise both to in-plane
coupling between the chains and to frustration, the dominant frustration
occuring due to the interchain interaction.
