  We present cluster-DMFT (CTQMC) calculations based on a downfolded
tight-binding model in order to study the electronic structure of vanadium
dioxide (VO_2) both in the low-temperature (M_1) and high-temperature (rutile)
phases. Motivated by the recent efforts directed towards tuning the physical
properties of VO_2 by depositing films on different supporting surfaces of
different orientations we performed calculations for different geometries for
both phases. In order to investigate the effects of the different growing
geometries we applied both contraction and expansion for the lattice parameter
along the rutile c-axis in the 3-dimensional translationally invariant systems
miming the real situation. Our main focus is to identify the mechanisms
governing the formation of the gap characterizing the M_1 phase and its
dependence on strain. We found that the increase of the band-width with
compression along the axis corresponding to the rutile c-axis is more important
than the Peierls bonding-antibonding splitting.
