## 4 Conclusions  
An energy stability analysis was conducted for the perovskite-type system CaTi\({}_{1-x}\)Cr\({}_{x}\)O\({}_{3}\) (x = 0.0, 0.25, 0.5, 0.75, 1.0), establishing the most favorable crystallographic configurations in the Pbnm space group (#62) for various substitution ratios of Cr\({}^{4+}\) at the Ti\({}^{4+}\) sites. The density of electronic states and band structure results revealed that the unsubstituted CaTiO\({}_{3}\) material exhibits direct bandgap semiconductor-like behavior, with orbitals defining symmetric bands for the two spin polarizations both below and above the Fermi level. The introduction of Cr in the unit cell led to the emergence of states that decrease the bandgap value, with a more pronounced reduction for the spin-up orientation, resulting in a bandgap that is 28% of the value for the pure system. For the other spin polarization, the bandgap value is 83%. Furthermore, the presence of Cr introduced asymmetry between the states for the spin orientations, transforming the material into an indirect bandgap semiconductor type. This behavior is indicative of magnetic semiconductor characteristics, suggesting significant potential for technological applications in generating spin-polarized currents. However, this study is not without its limitations. The primary limitation is the absence of an experimental validation of the theoretical findings, which would be crucial for confirming the practical applicability of the results. Additionally, the study focuses on specific Cr doping levels, leaving other potentially relevant concentrations unexplored. Future research could address these limitations by conducting experimental validations and investigating a broader range of doping levels. Such studies would further elucidate the tunability of perovskite materials and their potential for advanced spintronic applications. To transition from theory to real-world applications, several practical steps need to be considered. First, the experimental validation of the theoretical findings is essential to confirm the predicted properties. This includes synthesizing the Cr-doped CaTiO\({}_{3}\) materials and characterizing their electronic and magnetic properties using techniques such as X-ray diffraction, scanning electron microscopy, and magnetometry. Second, the scalability of the material synthesis process must be evaluated to ensure that these materials can be produced on an industrial scale. Challenges such as maintaining material uniformity and controlling defect concentrations will need to be addressed. Finally, integrating these materials into actual spintronic devices will require collaboration with industry partners to test their performance in real-world conditions. These steps are critical for realizing the full potential of the theoretical insights gained from this study. The originality and relevance of this study lie in its detailed theoretical analysis using density functional theory to elucidate the specific effects of Cr doping on the electronic and magnetic properties of CaTiO\({}_{3}\). The findings provide novel insights into the tunability of perovskite materials for advanced spintronic applications, highlighting the ability to engineer materials with tailored electronic and magnetic properties for next-generation electronic devices. Conceptualization, C.E.D.-T., D.A.L.-T. and J.R.-R.; methodology, C.E.D.-T., D.A.L.-T. and J.R.-R.; software, C.E.D.-T., D.A.L.-T. and J.R.-R.; validation, C.E.D.-T., E.A.A.-E., D.A.L.-T. and J.R.-R.; formal analysis, C.E.D.-T., E.A.A.-E., D.A.L.-T., D.V. and J.R.-R.; investigation, C.E.D.-T., E.A.A.-E., D.A.L.-T. and J.R.-R.; resources, C.E.D.-T., E.A.A.-E., D.A.L.-T., D.V. and J.R.-R.; data curation, C.E.D.-T., E.A.A.-E., D.V. and J.R.-R.; writing--original draft preparation, C.E.D.-T., E.A.A.-E. and J.R.-R.; writing--review and editing, C.E.D.-T., E.A.A.-E., D.V. and J.R.-R.; visualization, C.E.D.-T., E.A.A.-E., D.A.L.-T., D.V.