Direct minimization to generate electronic states with proper occupation numbers

We carry out the direct minimization of the energy functional proposed by Mauri, Galli, and Car [Phys. Rev. B $47,$ 9973 (1993)] to derive the correct self-consistent ground-state solution of the Kohn-Sham equation. Since this method completely avoids the instability caused by the level crossing, one can determine the electronic structure of metallic systems to a high degree of accuracy without the aid of level broadening of the Fermi-distribution function. The efficiency of the method is illustrated by calculating the ground-state energy of C₂ and Si₂ molecules and the $W(110)$ surface to which a tungsten adatom is adsorbed.