Gradient search method for orbital-dependent density-functional calculations

We describe a gradient search method appropriate for electronic structure problems where the energy functionals are explicitly orbital dependent. The ground state is found by minimizing the total energy with respect to the scalar and vector potentials that enter the Kohn-Sham equations. The method is exact in principle and provides an alternative to the conventional procedure that requires the numerical solution of an integral equation. We demonstrate the method for atoms with spherical effective potentials using (i) a local-spin-density functional that does not depend explicitly on the orbitals and (ii) an exact exchange functional that does depend explicitly on the orbitals.