here the work by Eyert, whose calculations based on hybrid functionals [@eyert2011_vo2_novel_view] may also open a gap in the monoclinic phase.

While the technical improvements of the computational methods of realistic correlated materials made significant steps forward in our understanding of the electronic states, it is also true that their technical complexity represents a challenge. For instance, despite multiple studies dedicated to this material [@biermann2005_dynamical_singlets_correlation_assisted_peierls_transition_invo2; @belozerov2012_monoclinic_m_phase_vo; @weber2012_vanadium_dioxide; @brito2016_metal_insulator_transition_in_vo] some basic issues remain unaccounted for, such as the existence of a first order thermally driven insulator-metal transition just above room temperature. Finite temperature studies are in principle beyond the applicability of DFT methods although we should point out the recent work of Plašienka et al. [@plasienka2017_ab_initio_molecular_dynamics_study]. We investigated the issue of a first order IMT in VO$_2$ in a recent paper [@najera2017_resolving_vo2_controversy] employing a model Hamiltonian approach within CDMFT. Although the model is rather schematic, namely, a lattice of correlated dimers, it was intended to qualitatively capture the dimerization-delocalization competition in the monoclinic phase of VO$_2$. We showed that adopting model parameters relevant for VO$_2$ there is a thermally driven first order Mott transition that occurs at a temperature range compatible with the experimental observation. Moreover, we have also provided an 