  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.
