van der Waals dispersion interactions play a key role in a wide range of phenomena at the molecular scale, having a pronounced influence on the macroscopic properties of matter. Dispersion forces influence the structure of biomolecules and are relevant in the context of substrate-enzyme recognition. Being dominant in the interaction between non-polar species; much less is known about the role of vdW dispersion interactions in condensed phases made from polar or ionic species.In particular, it is important to understand the cohesive properties and the corresponding role of dispersion interactions in solids subject to (high) temperature and pressure. Specifically, CsI and AlOOH are two distinct ionic compounds with solid-solid phase transitions and they were recently studied in absence of the dispersion interactions. Cesium iodide shows a strong reduction in the band gap along the compression and two structural phase transitions occur between 0 and 60 GPa. Aluminum hydroxides are components of the earth mantle and two phases with formula AlOOH have been found in nature, while a third one has been only observed in high pressure experiments. In both cases, the predicted phase transitions strongly depend on the selected density functional approximation, but the PBE exchange and correlation energy functional provided the best estimations. On the other hand, the PBE functional is not the most accurate approach at zero pressure. Dispersion corrections or modified GGA improve the results at zero pressure but the effect of the dispersion interactions at high pressures is still unknown.At this moment, there are several quantum-based approximations to estimate the dispersion forces at the molecular level. In this project, we will apply these models to estimate their effects in the stability of the different phases of ionic materials under high pressures.