Implicit density functionals for the exchange-correlation energy: Description of van der Waals bonds

The energy surface of the Helium dimer, as a prototype of a van der Waals bond molecule, is investigated within the framework of density functional theory. For the exchange-correlation energy an implicit density functional, depending on the Kohn-Sham orbitals, is applied in which exchange is treated exactly, while correlation is approximated by the lowest order contribution obtained by Kohn-Sham perturbation theory. The resulting energy surface is in fair quantitative agreement with highly accurate empirical data over the complete range of internuclear separations, demonstrating that the concept of orbital-dependent functionals can provide a seamless description of dispersion forces. As selfconsistent calculations with implicit functionals on the basis of the optimized potential method are rather time-consuming, the correlation part of the exchange-correlation functional is evaluated perturbatively in the Helium dimer calculations. However, we also present an approximate scheme for the evaluation of the corresponding correlation potential.