  The 3d electronic structure and phase transition in pure and Cr doped V2O3
are theoretically investigated in relation to the 3d spin-orbit interaction and
lattice distortion. A model consisting of the nearest-neighbor V ion pair with
full degeneracy of the 3d orbitals is studied within the many-body point of
view. It is shown that each V ion with S=1 spin state has a large orbital
magnetic moment $\sim 0.7 \mu_{\rm B}$ and no orbital ordering occurs in the
antiferromagnetic insulating (AFI) phase. The anomalous resonant Bragg
reflection found in the AFI phase is attributed to the magnetic ordering. In
the AFI and paramagnetic insulating (PI) phases, Jahn-Teller like lattice
instability leads to tilting of the V ion pairs from the corundum c-axis and
this causes large difference in the orbital occupation between the paramagnetic
metal and the insulating phases, which is consistent with linear dichroic V 2p
XAS measurements.
  To understand the AFI to PI transition, a model spin Hamiltonian is also
proposed. The transition is found to be simultaneous order-disorder transition
of the magnetic moments and tilting directions of the V ion pairs. Softening of
elastic constant C44 and abrupt change in short range spin correlations
observed at the transition are also explained.
