Mercury Fluorides under high pressure: Hg as a pressure-induced transition metal

Hg has recently been found experimentally to be capable of forming a chemical compound, HgF$_4$, where it behaves as a transition metal, with an oxidation number of IV, but this molecule is very short lived. In this work we present theoretical evidence obtained through \textit{ab initio} calculations that higher oxidation states than II can be stabilized in crystalline form for Hg, under extreme pressure. We have performed a structural search and optimization by means of Particle Swarm Optimization and Density Functional Theory for the crystalline series of HgF$_n$ (n=3,4,5,6), and then used those data to draw the phase diagram of the equilibrium among those stoichiometries and HgF$_2$ and F$_2$. We have found that from $0$ to $38$ $GPa$ only the mixture of HgF$_2$ and F$_2$ phases is thermodynamically stable. HgF$_3$ and HgF$_4$ have been found to be thermodynamically stable in different pressure ranges (from $73$ $GPa$ to at least $500$ $GPa$ and from $38$ $GPa$ to $200$ $GPa$, respectively). We have also found that the HgF$_3$ crystal shows a very interesting band structure that suggests it could be a transparent conductor.