Avoiding asymptotic divergence of the potential from orbital- and energy-dependent exchange-correlation functionals

We investigate the asymptotic behavior of the exchange-correlation potentials deriving from orbital- and energy-dependent (OED) functionals potentially able to describe van der Waals interactions. We take some simple functionals based on the adiabatic connection fluctuation-dissipation (ACFD) theorem as examples. Although the potentials deriving from arbitrary OED functionals can be expected to diverge asymptotically, we find that these ACFD potentials are in fact well behaved. They indeed depend on Kohn-Sham orbitals and energies only through the Kohn-Sham Green function, allowing for complete analytical treatment. However, the dependence on the empty Kohn-Sham orbitals and energies must be treated with care. We discuss some precautions to be taken for practical calculation of these potentials. Last, we introduce approximate potentials, which are much simpler to compute than the exact ones, but are still quite accurate. (C) 2004 Wiley Periodicals, Inc