Damped gradient iteration and multigrid relaxation: tools for electronic structure calculations using orbital density-functionals

A method for efficient solution of the Kohn–Sham equations, the central equations of density-functional electronic structure calculations, is presented. It combines the simplicity of the damped gradient iteration with the efficiency of multigrid techniques. The long-standing problem of calculating the optimized effective potential of Kohn–Sham theory for orbital density functionals has been solved with this algorithm.