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We present a general methodology that enables the disentanglement of theelectronic and lattice contributions to the metal-insulator transition bybuilding an energy landscape from numerical solutions of the equation of state.The methodology works with any electronic structure method that provideselectronic expectation values at given atomic positions. Applying the theory torare-earth perovskite nickelates ($R$NiO$_3$) and Ruddlesden-Popper calciumruthenates (Ca$_2$RuO$_4$) in bulk, heterostructure and epitaxially strainedthin film forms using equation of state results from density functional plusdynamical mean field calculations we show that the electron-lattice coupling isan essential driver of the transition from the metallic to the insulating statein these materials.

Energy Landscape analysis of metal-insulator transitions: theory and application to Ca$_2$RuO$_4$, $R$NiO$_3$ and their heterostructures