and most of them exhibit insulator to metal transitions (IMT) upon heating. Significantly, these transitions involve a structural change but are disconnected to magnetic ordering, with the exception of the most famous members of the series, V$_2$O$_3$ and VO$_2$. In the former the magnetic and structural transition occur at the same temperature, while in the latter there is a structural transition but no magnetic ordering at any temperature.

Vanadium dioxide is particularly appealing because its transition occurs close to room temperature, around 340K, so it may enable practical applications in novel electronic devices [@inoue2008_taming_mott_transition_novel_mott_transistor; @stoliar2017_leaky_integrate_and_fire_neuron]. In fact, the study of this material is receiving a great deal of attention. Therefore, a basic understanding of the nature of its electronic state and its insulator to metal transition (IMT) is of great importance.

VO$_2$ may be considered a realization of a Mott system, as it has only one electron per vanadium atom which should lead to a partially filled band. However, since it exhibits a non-magnetic insulating ground state, this classification has often been challenged. In fact, in an influential early paper, Goodenough [@goodenough1960_direct_cation_interactions_several_oxides] argued that the first order IMT occurs concomitant with a structural distortion of the vanadium chains in the 