First-principles modeling techniques offer the ability to simulate a wide range of systems under different physical conditions, such as temperature, pressure, and composition, without relying on empirical knowledge. Density functional theory (DFT), a quantum mechanical method, has become an exceptionally successful framework for materials science modeling. Employing DFT makes it possible to gain valuable insights into the fundamental state of a system, enabling the reliable determination of equilibrium crystal structures. Over time, DFT has become an essential tool that can be incorporated into various schemes for predicting the properties of a material related to its structure, insulating/metallic behavior, magnetism, and optics. DFT is regularly applied in numerous fields, spanning from fundamental subjects in condensed matter physics to the study of large-scale phenomena in geosciences. In the latter, the effectiveness of DFT stems from its ability to simulate the properties found on the Earth, other planets, and meteorites, which may pose challenges for their direct study or laboratory investigation. In this thesis, a comprehensive examination of a family of monosulfides and a perovskite heterostructure was conducted. These materials are relevant for their potential applications in technology, energy harvesting, and in the case of monosulfides, their speculated abundance on the planet Mercury. Firstly, a DFT approach was used to analyze two non-magnetic monosulfides, CaS and MgS. We determined their structural properties and then focused on the modeling of their reflectivity in the infrared region. The calculation of the reflectivity considered both harmonic and anharmonic contributions. In the harmonic limit, the non-analytic correction was employed to accurately determine the LO/TO splitting, which is necessary to delimit the retstrahlend band, that is, the maximum of the reflectivity. The anharmonic effects given by up to three-phonon and isotopic scatterings, which were included using perturbation theory, primarily smeared the reflectivity spectra edges in the high-wave region. Secondly, four polymorphs of MnS were studied using a combination of first-principles methods to simulate their antiferromagnetic (AFM) and paramagnetic (PM) states. The integration of DFT+$U$ with special quasirandom structures (SQS) supercells, and occupation matrix control techniques was crucial for achieving convergence, structural optimization accuracy, and obtaining finite energy band gaps and local magnetic moments in the PM phases. The addition of the Hubbard $U$ correction was necessary to treat the highly-correlated Mn $d$-electrons. The success of our approach was clear based on our electronic structure predictions for the PM rock-salt B1-MnS polymorph. Experimentally this phase has been observed to be an insulator, but multiple \emph{ab initio} works resulted previously in metallic behavior. Our computations, on the other hand, predicted insulating and magnetic properties that compare well with available measurements. Additionally, the pressure-field stability of the four MnS polymorphs was studied. In the case of the PM phases, B1-MnS was identified to be the most stable up to about 21 GPa, then transforming into the B31-MnS polymorph. This finding was in close agreement with high-pressure experiments reporting a similar phase transformation. The optical properties of B1-, B4-, and B31-MnS were also simulated. The SQS technique was used to obtain soft-mode-free phonon band structures within the harmonic approximation. Then, the anharmonic effects were included, and the reflectivity was calculated for B1-MnS and B4-MnS. In both cases, a good agreement for the LO/TO splitting was achieved in comparison to experimental results. Lastly, the oxygen-deficient heterostructure of LaAlO$_{3-\delta}$ /SrTiO$_{3-\delta}$ was investigated also employing DFT+$U$, with a particular emphasis on the potential impact of vacancy clustering at the interface. Six distinct configurations of pairs of vacancies were studied and their energies were compared to find the most stable one. The orbital reconstruction of Ti orbitals was also examined based on their location with respect to the vacancies and the local magnetic moments were calculated. The final results showed that linearly arranged vacancies located opposite to Ti ions give the most energetically stable configuration.
