Instead of using electron density as the explicit variable, it is possible to use orbitals or the density matrix as the explicit variable in density functional approximation, with a better accuracy potentially. The Hatree-Fock (HF) approximation is such a functional. The hybrid functionals combining HF with GGA will be discussed, including its motivation and performance. For such orbital functionals, there are two ways to carry out self-consistency calculations, the optimized effective potential and the generalized Kohn-Sham. The theory and implementation of OEP will be presented.
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