Kohn—Sham density-functional theory within a finite basis set

The Kohn—Sham self-consistent equations, using a finite orbital basis expansion, are formulated for exchange-correlation functionals which depend on local densities and their gradients. It is shown that these can be solved iteratively without evaluation of density Hessians. A general expansion is given for the energy gradient (with respect to nuclear motion) after self-consistency has been achieved.