Electron paramagnetic resonance (EPR) spectroscopy is a powerful technique for probing the electronic structure of paramagnetic systems and for identifying defects in semiconductors and insulators through parameters such as the g-tensor and hyperfine interactions. While the prediction of these quantities is well established for molecular systems, their calculation in solids remains particularly challenging because the electronic states associated with defects are both localized and embedded in a periodic environment. Within an ab initio framework based on density functional theory and plane waves, a realistic description of dilute defects requires large supercells in order to reduce artificial interactions between periodic images, making the computational cost of magnetic-property calculations very high.

The first objective of this thesis was to modernize the former implementation of the converse approach for the calculation of the g-tensor in Quantum ESPRESSO. The historical routines, originally developed for a now obsolete version of the code, were extensively refactored and reorganized into an autonomous module, QE-CONVERSE, compatible with modern versions of Quantum ESPRESSO. This modernization makes it possible to exploit recent improvements in the software infrastructure, particularly in terms of parallelization, scalability, and the use of optimized numerical libraries.

The second major contribution of this thesis is the implementation of a single-point formulation of the converse approach. Motivated by the computational cost of the large supercells required to study defects in solids, this development avoids the repeated Hamiltonian diagonalizations involved in previous formulations, thereby significantly reducing the numerical cost while improving the stability of the calculations.

The single-point approach was validated through a systematic study demonstrating both its excellent accuracy and its favorable scalability with supercell size. Finally, the method was applied to systems of experimental interest. In the case of the charged divacancy in silicon, g-tensor calculations help clarify the fundamental electronic structure of the defect. The approach was also used to investigate several nickel-related defects in diamond, where the g-tensor provides a useful quantitative signature for assessing different microscopic models proposed in the literature.

Overall, this thesis establishes a robust and efficient framework for the ab initio calculation of the EPR g-tensor in periodic systems, combining software modernization, methodological development, numerical validation, and applications to real defects in solids.