The Fermi-Lowdin Self-Interaction Method and Applications

Self-Interaction Corrections to Density Functional Theory have been suggested for decades as a means for improving the asymptotic form of the effective potential and as a means for more accurately accounting of chemical potentials between different atoms in materials. This can be especially important in applications to molecular systems where charge transfer needs to be quantitatively described between different systems or between states with differing angular momentum within a single atom. In this talk I will review the formalism, computational implementation, and application of a method now referred to as the Fermi-Lowdin Orbital Self-Interaction Correction (FLOSIC) which has taken place over the last decade. Highlighted items will include applications of the method to multiply charge anions in solution and to the need for these corrections in applications to molecular magnetics that are either isolated or adsorbed onto surfaces. I will review very recent progress on converting the methodology in a manner that allows one to take advantage of sparsity and discuss progress toward reduction of the method to a formulation that leads to a multiplicative Hamiltonian that exhibits the same simplicity those used in standard implementation of density functional theory. I will discuss the so-called downard quantum learning method that results from a rigorous existence theorem and allows one to rapidly find viable starting configurations for all atoms in the periodic table and highlight the application to the very heavy ions where on-atom self-coulomb repulsions complicate the selection of Fermi-Oribital Descriptors. Possible application for the Fermi-Lowdin-Orbital formalism to problems of interest to quantum transport and multi-reference systems will also be discussed.