High throughput optimization of Fermi-orbital descriptors

The innovative Fermi-L\”{o}wdin-orbital self-interaction correction (FLO-SIC) to density functional theory (DFT) \footnote{ M. R. Pederson, A. Ruzsinszky, and J. P. Perdew, J. Chem. Phys. \textbf{140},121103 (2014).} uses N spatial points known as Fermi-orbital descriptors (FOD’s) to define a unitary transformation between the canonical Kohn-Sham orbitals and the local orbitals used to compute the DFT-SIC total energy. In this talk we describe a simple, unbiased method for optimizing these positions. It involves creating a large number of independent random starting arrangements and then performing a separate local optimization of the FOD positions for each, using derivatives of the total energy with respect to the FOD positions, i.e. FOD “forces”.\footnote{M. R. Pederson, J. Chem. Phys. \textbf{142}, 064112 (2015).} A good approximation of the optimal positions can be found by carrying out the local optimization on a frozen space of occupied orbitals. After the approximate positions are found, the occupied orbital space and FODs can be further optimized in tandem to minimize E$^{DFT-SIC}$. Results of using this approach for the Cr atom and Cr$_{2}$ will be discussed.