Free Energy from Stationary Implementation of the DFT plus DMFT Functional

The stationary functional of the density functional plus embedded dynamical mean field theory formalism to perform free energy calculations and structural relaxations is implemented for the first time. Here, the first order error in the density leads to a much smaller, second order error in the free energy. The method is applied to several well-known correlated materials: metallic SrVO3, Mott insulating FeO, and elemental cerium, to show that it predicts the lattice constants with good accuracy. In cerium, we show that our method predicts the isostructural transition between the a and. phases, and resolve the long-standing controversy in the driving mechanism of this transition.