Direct observations of the Earth's interior properties are very restricted. Most of the information comes from indirect studies related to geophysics, which need to be related to materials studies in the laboratory to be correctly interpreted. Laboratory experiments, however, need to be performed under extreme pressure and temperature conditions, which is a very difficult task to achieve. In this context, theoretical studies are fundamental in supporting the elaboration of models on the structure and internal composition of the Earth. The purpose of our work is to use first principles methods to help elucidate the behavior of magnesium and calcium silicates (MgSiO 3 and CaSiO 3) and carbonates (MgCO 3 and CaCO 3) under the extreme thermodynamic conditions of the lower mantle. The study of the energy stability of these carbonates and silicates, as well as of other mantle minerals, provides new evidence on how calcium can best be incorporated into the mantle and to determine which carbonate is the main carbon host in the Earth's deep mantle. The properties of the systems were obtained within the density functional theory, using several approximations for the exchange and correlation energy, and the PAW (Projector Augmented Wave) method. The thermodynamic properties were investigated using the quasi-harmonic approximation and the density functional perturbation theory. The computational simulations were performed using the Quantum ESPRESSO code. We observe that the decomposition of the silicates in their respective alkali earth oxides, MgO and CaO, plus SiO 2 is not favorable. In addition, the coexistence of silicates MgSiO 3 and CaSiO 3 is more stable than the formation of alloys like Mg 1−x Ca x SiO 3. Thus, we conclude that the calcium in the lower mantle exists in an independent phase, being part of a silicate (CaSiO 3). Our results also indicate that the decomposition of the carbonates into their respective alkali earth oxides, MgO and CaO plus CO 2 is unfavorable, showing that there should be a low concentration of free CO 2 in the mantle, and that the magnesium carbonate is more stable than calcium carbonate. Therefore, our investigation proposes that MgCO 3 is the main oxidized carbon host in the lower mantle. Finally, we note that the structural and thermodynamic properties are best described when the van der Walls interactions are taken into account in the exchange and correlation energy, indicating that these more accurate calculations constitute an important step to improve the construction of theoretical models on the properties and composition of the mantle.