  The results of first principles electronic structure calculations for the
metallic rutile and the insulating monoclinic M1 phase of vanadium dioxide are
presented. In addition, the insulating M2 phase is investigated for the first
time. The density functional calculations allow for a consistent understanding
of all three phases. In the rutile phase metallic conductivity is carried by
metal t_2g orbitals, which fall into the one-dimensional d_parallel band, and
the isotropically dispersing e_g^pi bands. Hybridization of both types of bands
is weak. In the M1 phase splitting of the d_parallel band due to metal-metal
dimerization and upshift of the e_g^pi bands due to increased p-d overlap lead
to an effective separation of both types of bands. Despite incomplete opening
of the optical band gap due to the shortcomings of the local density
approximation, the metal-insulator transition can be understood as a
Peierls-like instability of the d_parallel band in an embedding background of
e_g^pi electrons. In the M2 phase, the metal-insulator transition arises as a
combined embedded Peierls-like and antiferromagnetic instability. The results
for VO2 fit into the general scenario of an instability of the rutile-type
transition-metal dioxides at the beginning of the d-series towards dimerization
or antiferromagnetic ordering within the characteristic metal chains. This
scenario was successfully applied before to MoO2 and NbO2. In the d^1
compounds, the d_parallel and e_g^pi bands can be completely separated, which
leads to the observed metal-insulator transitions.
