New Algorithms for the Fermi-Löwdin Orbital Self-Interaction Correction Calculations.*

Self--interaction error (SIE) is in most approximate exchange-correlation functionals, and removing SIE is important for improving the performance of the Kohn-Sham density-functional theory (KS-DFT) when applied to systems of chemical and physical interest. The Fermi-Löwdin Orbital Self-Interaction Correction (FLO-SIC) methodology was recently introduced as a unitarily invariant reformulation of the Perdew-Zunger SIC scheme to remove unphysical SIE from DFT.
We propose new algorithms that aim to speed up and extend the applicability of this methodology. The "two-step" algorithm was designed to reduce the number of times that orbital-dependent potentials need to be calculated in the self-consistency cycle, addressing one computational bottleneck of SIC calculations. We also introduced unified Hamiltonian formalism in FLOSIC as a way to solve the system of Schrödinger-like equations. An advantage of the unified Hamiltonian approach is that it can replace a cumbersome "Jacobi sweep" method with a well-optimized diagonalization routine. It also is a convenient formalism for allowing unoccupied states to "see" an SIC potential. We present atomic and molecular applications that show the performance of FLOSIC with these new algorithms.