  Correlated oxides, such as BiMnO$_3$ and LaMnO$_3$, show complex interplay of
electronic correlations and crystal structure exhibiting multiple first order
phase transitions, some without a clear order parameter. The quantitative
theoretical description of this temperature dependent electronic-structural
interplay in the vicinity of a Mott transition is still a challenge. Here we
address this issue by simultaneously considering both structural and electronic
degrees of freedom, within a self-consistent density functional theory with
embedded dynamical mean field theory. Our results show the existence of novel
electronic states characterized by coexistence of insulating, semi-metallic and
metallic orbitals. This state is in agreement with resonant X-ray scattering.
We also show that electronic entropy plays a decisive role in both electronic
and structural phase transitions. By self-consistent determination of both, the
electronic state and the corresponding crystal structure, we show that the
temperature evolution of these phases can be quantitatively explained from
first principles, thus demonstrating the predictive power of the theoretical
method for both the structural and the electronic properties.
