  An alternative separation of short-range exchange and correlation energies is
used in the framework of second-order range-separated density-functional
perturbation theory. This alternative separation was initially proposed by
Toulouse et al. [Theor. Chem. Acc. 114, 305 (2005)] and relies on a long-range
interacting wavefunction instead of the non-interacting Kohn-Sham one. When
second-order corrections to the density are neglected, the energy expression
reduces to a range-separated double-hybrid (RSDH) type of functional, RSDHf,
where "f" stands for "full-range integrals" as the regular full-range
interaction appears explicitly in the energy expression when expanded in
perturbation theory. In contrast to usual RSDH functionals, RSDHf describes the
coupling between long- and short-range correlations as an orbital-dependent
contribution. Calculations on the first four noble-gas dimers show that this
coupling has a significant effect on the potential energy curves in the
equilibrium region, improving the accuracy of binding energies and equilibrium
bond distances when second-order perturbation theory is appropriate.
