  The metal-insulator transition (MIT) of the Magneli phase V_4O_7 is studied
by means of electronic structure calculations using the augmented spherical
wave method. The calculations are based on density functional theory and the
local density approximation. Changes of the electronic structure at the MIT are
discussed in relation to the structural transformations occuring
simultaneously. The analysis is based on a unified point of view of the crystal
structures of all Magneli phase compounds V_nO_2n-1 (3 =< n =< 9) as well as of
VO_2 and V_2O_3. This allows to group the electronic bands into states behaving
similar to the dioxide or the sesquioxide. In addition, the relationship
between the structural and electronic properties near the MIT of these oxides
can be studied on an equal footing. For V_4O_7, a strong influence of
metal-metal bonding across octahedral faces is found for states both parallel
and perpendicular to the hexagonal c_hex axis of V_2O_3. Furthermore, the
structural changes at the MIT cause localization of those states, which mediate
in-plane metal-metal bonding via octahedral edges. This band narrowing opens
the way to an increased influence of electronic correlations, which are
regarded as playing a key role for the MIT of V_2O_3.
