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.
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