  The electronic structure of the quasi-lowdimensional vanadium sulfide \bavs3
is investigated for the different phases above the magnetic ordering
temperature. By means of density functional theory and its combination with
dynamical-mean field theory, we follow the evolution of the relevant low-energy
electronic states on cooling. Hence we go in the metallic regime from the room
temperature hexagonal phase to the orthorhombic phase after the first
structural transition, and close with the monoclinic insulating phase below the
metal-insulator transition. Due to the low symmetry and expected intersite
correlations, the latter phase is treated within cellular dynamical mean-field
theory. It is generally discussed how the intriguing interplay between
band-structure and strong-correlation effects leads to the stabilization of the
various electronic phases with decreasing temperature.
