The accurate description of correlated electronic states in magnetic strongly correlated systems, e.g. many transition metal oxides (TMOs), presents a significant challenge in density functional theory (DFT), especially when dealing with noncollinear magnetism. Identifying noncollinear ground states is inherently complex and computationally demanding due to the high-dimensional landscape of spin configurations and the critical role of spin-orbit coupling. This dissertation addresses these challenges through a sequential and integrated computational approach, encompassing the development of workflows, implementation of new exchange-correlation (XC) functionals, and the introduction of a novel optimization algorithm for identifying noncollinear magnetic ground states.

First, we present a high-throughput computational study using the DFT+U method to correct self-interaction errors (SIE) in the description of correlated electronic states. This study focuses on the accurate determination of Hubbard U and Hund J parameters using the linear response (LR) methodology. We compute the U and J values for transition metal d-electron states in over 1000 TMOs, providing a valuable reference for researchers. An automated workflow developed within the atomate framework enables these calculations on massively parallel supercomputing architectures. The applicability of this workflow is demonstrated through the calculation of spin-canting magnetic structures and unit cell parameters of the multiferroic olivine LiNiPO4, showing strong effects of Ni-d U and J corrections and significant improvements in computed lattice parameters when including an O-p U value.

Building on this foundation, we expand the source-free (SF) exchange-correlation (XC) functional developed by Sangeeta Sharma and co-workers to plane-wave DFT based on the projector augmented wave (PAW) method. This implementation, integrated within the VASP source code, leverages parallel three-dimensional fast Fourier transforms (FFTs) for improved computational efficiency. We explore the enhanced convergence behavior and the impact on non-collinear magnetic ground states when applying the SF constraint to the GGA-PBE+U+J functional. Our findings show significantly improved agreement with experimentally measured magnetic structures. Additionally, we analyze the importance of probability current densities and XC torque in spin-polarized systems, highlighting connections to spin-current density functional theory (SCDFT) and paving the way for future extensions of the SF corrected XC functional.

Finally, we propose and implement a novel hybrid meta-heuristic optimization algorithm, SpinPSO, designed to identify noncollinear global ground states in magnetic systems. This algorithm combines particle swarm optimization (PSO) with atomistic spin dynamics, allowing for the accurate determination of magnetic ground states using inputs directly from non-collinear DFT calculations. The workflow, implemented in atomate, is optimized for high-performance computing environments. SpinPSO successfully converges to experimentally resolved magnetic ground states for diverse test materials exhibiting exotic spin textures.

This dissertation demonstrates a comprehensive and integrative approach to tackling the complexities of correlated electronic states and magnetic ordering in TMOs, contributing useful computational tools and methodologies to the field of condensed matter physics.