Lattice Energetics, Geometrical Constraints and Correlation-Driven Metal-Insulator Transitions: the case of Ca$_2$RuO$_4$*

Many materials exhibit metal-insulator transitions that are driven by electron correlation effects but are closely associated with changes in local lattice structure. This paper uses density functional and dynamical mean field theory methods to construct a free energy that elucidates the interplay of electronic and lattice energies in one such material, Ca$_2$RuO$_4$. We find that the change in lattice energies across the metal-insulator transition is comparable to the change in electronic energies. An important consequence is that the imposition of geometrical constraints (for example a lattice parameter fixed by epitaxial growth on a substrate) can change the lattice energetics enough to eliminate the metal-insulator transition entirely. A comparison to recent data is presented, and the generalization of the theory to other transition metal oxides is discussed.