Efficient localized Hartree-Fock methods as effective exact-exchange Kohn-Sham methods for molecules

The form of the Kohn-Sham (KS) exchange potential, which arises from the ap proximation that the Hartree-Fock (HF) and the exchange-only KS determinant are equal, is derived. Two related procedures to determine the KS exchange potential follow from this approximation: a self-consistent localized HF p rocedure and a transformation localized HF procedure yielding the local KS exchange potential from HF orbitals. Both procedures can be considered as a lmost exact exchange KS methods which require only occupied orbitals and ar e invariant with respect to unitary transformations of the orbitals, i.e., depend only on the first order density matrix. The resulting local KS excha nge potentials are free of Coulomb self-interactions and exhibit the correc t long-range 1/r-behavior. The Krieger, Li, and Iafrate (KLI) procedure to determine the KS exchange potential can be considered as an approximation t o the introduced localized HF procedures. Highly efficient methods to carry out the presented localized HF as well as KLI procedures are introduced. A n efficient basis set approach to calculate the Slater potential is present ed. The methods can easily be implemented in present standard quantum chemi stry codes. Applications to small and medium size molecules and clusters ar e presented. The Hartree-Fock and the exchange-only KS determinant are foun d to be surprisingly close. Qualitatively correct, Coulomb self-interaction free KS orbitals and eigenvalue spectra are obtained. (C) 2001 American In stitute of Physics.