Theoretical studies stemming from first-principles calculations have played a crucial role in understanding the plethora of interesting properties exhibited by condensed matter systems. Density functional theory (DFT) based calculations have been widely used to study the electronic structure in various classes of materials. Strongly correlated materials possess unusual properties that challenge the assumptions of band-structure theory. Examples of such materials include Mott insulators, unconventional superconductors, heavy fermion materials, etc. Simplified models such as the Hubbard model have been developed to account for the correlated behavior of electrons. The DFT+U method as well as the many-body based Dynamical mean field theory (DMFT) methods provide a better description of strongly correlated materials.

In this work, we study the aspects of the Mott transition in a transition metal compound, \ce{Sr_2Mn_2O_3As_2}. The study was experimentally motivated by measurements showing an interplay between the magnetic ordering and transport properties. We first obtain the electronic structure using DFT+U, showing signs of a Mott transtion. We identify the orbitals involved in magnetic ordering and the Mott transition. In order to model the system, we construct an effective tight-binding Hamiltonian involving two orbitals with the help of Wannier functions. We then solve the model using the approaches of DMFT as well as Variational cluster approximation (VCA). The results show the opening of the Mott gap in an orbital-selective fashion, i.e. the orbitals develop a gap at different critical values of the Hubbard interaction.

In this dissertation, I first introduce the theoretical aspects of DFT, Wannier functions methodology, and DMFT. In the next chapter, I discuss the study on the material, \ce{Sr_2Mn_2O_3As_2}. I summarise the results obtained from DFT and DMFT to describe an orbital-selective Mott transition. In the last chapter, I include a few applications of DFT calculations to complement recent experimental findings in Yb-based heavy fermion compounds, and magnetic materials with competing interactions.