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Fermi Orbital Derivatives in Self-Interaction Corrected Density Functional Theory: Applications to Closed Shell Atoms

A recent modification of the Perdew-Zunger self-interaction-correction (SIC) to the density-functional formalism (Pederson, Ruzsinszky, Perdew) has provided a framework for explicitly restoring unitary invariance to the expression for the total energy. The formalism depends upon construction of Lowdin orthonormalized Fermi-orbitals (Luken et al) which parametrically depend on variational quasi-classical electronic positions. Derivatives of these quasi-classical electronic positions, required for efficient minimization of the self-interaction corrected energy, are derived and tested here on atoms. Total energies and ionization energies in closed-shell atoms, where correlation is less important, using the PW92 LDA functional are in very good to excellent agreement with experiment and non-relativistic Quantum-Monte-Carlo (QMC) results.