Orbital-dependent functionals: Hartree-Fock,
Kohn-Sham exact-exchange and beyond
Prof Evert Jan Baerends, Vrije Universiteit, Amsterdam, Pays-Bas
Jeudi 23 juin 2005, 11h00, salle 2/3,
Bâtiment St.Raphael, 3 rue Galilée, 94200 Ivry-sur-Seine
After the local-density approximation and the very successful generalized
gradient approximations, it is often stated that using an exact exchange (EXX)
functional is the next step up our ladder of DFT approximations. It would
notably solve the self-interaction problem that plagues DFT. It only leaves
the much smaller correlation energy to be treated with some approximate
functional.
We will argue that the EXX approach cannot be considered a step forward
compared to the GGAs. It reintroduces a very important flaw present in the
Hartree-Fock approximation. Arguably the great success of DFT is a consequence
of avoiding the typical Hartree-Fock error, obviating the distinction between
exchange and correlation that is so ingrained in quantum chemistry after
decades of the reigning paradigm: first Hartree-Fock, and then beyond.
We will argue that, once one is prepared to accept the computational
complications and the price of dealing with
orbital dependent functionals, it is still not necessary, and maybe even
against the origin of the success of DFT, to go back to the exact-exchange
starting point. It is possible to go back to the statistical definition of
correlation in terms of two-electron probability distributions, or exchange
and correlation holes,1 treating exchange and correlation jointly
rather than separately, and devise orbital dependent functionals that
incorporate exchange and correlation on equal footing.2,3 This is
closely connected to density-matrix functional theory. We will demonstrate
that such full exchange-correlation functionals can be formulated successfully,
and present applications in the context of density-matrix functional
theory.4 If such full exchange-correlation functionals will also be
successful in Kohn-Sham DFT they may ultimately justify the increased
computational expense of dealing with orbital-dependent functionals.
1. M. A. Buijse and E. J. Baerends, Mol. Phys. 100 (2002) 401.
2. E. J. Baerends, Phys. Rev. Lett. 87 (2001) 133004.
3. M. Grüning, O. V. Gritsenko and E. J. Baerends, J. Chem. Phys. 118
(2003) 7183.
4. O. Gritsenko, K. Pernal, E. J. Baerends, J. Chem. Phys., to be published.