  Examining phase stabilities and phase equilibria in strongly correlated
materials asks for a next level in the many-body extensions to the
local-density approximation (LDA) beyond mainly spectroscopic assessments. Here
we put the charge-self-consistent LDA+dynamical mean-field theory (DMFT)
methodology based on projected local orbitals for the LDA+DMFT interface and a
tailored pseudopotential framework into action in order to address such
thermodynamics of realistic strongly correlated systems. Namely a case study
for the electronic phase diagram of the well-known prototype Mott-phenomena
system V$_2$O$_3$ at higher temperatures is presented. We are able to describe
the first-order metal-to-insulator transitions with negative pressure and
temperature from the self-consistent computation of the correlated total energy
in line with experimental findings.
