Computational advancements towards scalable density functional calculations with and without self-interaction correction

Advances in high performance computing (HPC) have provided a way to treat large, computationally demanding tasks using thousands of processors. With the development of more powerful HPC architectures, the need to create efficient and scalable code has grown more important. Electronic structure calculations are valuable in understanding experimental observations and are routinely used for new materials predictions. For the electronic structure calculations, the memory and computation time are proportional to the number of atoms. Memory requirements for these calculations scale as N2, where N is the number of atoms. While the recent advances in HPC offer platforms with large numbers of cores, the limited amount of memory available on a given node and poor scalability of the electronic structure code hinder their efficient usage of these platforms. This Thesis will present new scaling and parallelization paradigms using MPI-3 shared-memory functionality which extends the range of applicability of the UTEP-NRLMOL code to large systems over 10,000 atoms, or using up to 67,000 basis functions, and making use of HPC architectures using over 6,000 processors. This Thesis also presents developments in self-interaction correction (SIC) methods using the Fermi-Löwdin SIC method (FLOSIC) which include application using state-of-the-art meta-GGA functionals like the SCAN functional. We also develop a new local-scaling SIC method (LSIC) that outperforms the Perdew-Zunger SIC method. We also develop a method to generate multiplicative effective potentials in the UTEP-NRLMOL code from SIC Kohn-Sham orbitals and densities. Previous implementations of the FLOSIC method have been limited to Gaussian-based codes. We develop the first implementation of the FLOSIC method into the real-space methodology as implemented in the SPARC code. Doing so requires the implementation of an alternative method to self-consistency in FLOSIC. We further explore self-consistency in FLOSIC using the Krieger-Li-Iafrate approximation to the optimized effective potential and compare with previous implementations