  Elucidating the polymorphism of transition metal dichalcogenide layers and
the interplay between structure and properties is a key challenge for the
application of these materials. We identify a novel low energy metastable phase
of monolayer VSe$_2$ and elucidate its magnetic and electronic properties. This
structure is distinct from the previously identified charge density wave (CDW)
phase. However, while having rather distinct properties it is very close in
energy to the CDW phase and is likely to be realized in experiments.
Importantly, local bonding instabilities, as characterized by reconstruction of
the electronic structure over a wide energy range, are important for this
distortion, which includes both V off-centering in the octahedral coordination
cages and a partial disproportionation into two distinct types of V. The phase
does not have a ferromagnetic ground state. The results show that the physics
of 1$T$ VSe$_2$ are richer than previously known with an interplay of Fermi
surface instabilities and local bonding effects.
