Self-consistent field algorithms for Kohn--Sham models with fractional occupation numbers

The calculations of electronic ground state energies, following either the Hartree–Fock or the Kohn–Sham schemes, are major issues in quantum chemistry. In a recent publication, we have proposed a new numerical method, namely the relaxed constrained algorithms (RCA), to solve the Hartree–Fock problem. The purpose of the present paper is to discuss the extension of this method to the case of the Kohn–Sham problem. It is shown that RCA seems to be more robust than other self-consistent field algorithms currently used and that they provide in addition a natural way to solve the extended Kohn–Sham problem, obtained by allowing fractional occupancy of the single-particle orbitals. © 2001 American Institute of Physics.