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The stationary functional of the all-electron density functional plusdynamical mean field theory (DFT+DMFT) formalism to perform free energycalculations and structural relaxations is implemented for the first time.Here, the first order error in the density leads to a much smaller, secondorder error in the free energy. The method is applied to several well knowncorrelated materials; metallic SrVO$_3$, Mott insulating FeO, and elementalCerium, to show that it predicts the lattice constants with very high accuracy.In Cerium, we show that our method predicts the iso-structural transitionbetween the $\alpha$ and $\gamma$ phases, and resolve the long standingcontroversy in the driving mechanism of this transition.

Free energy from stationary implementation of the DFT+DMFT functional