  XYG3-type doubly hybrid approximations (xDH) have gained a widespread
recognition for their accuracy in describing a diverse range of chemical and
physical interactions. However, a recent study (J. Phys. Chem. 2021, 12,
800-807) has highlighted the limitation of xDH methods in calculating the
dissociation of the NaCl molecule. This issue has been related to the density
and orbitals used for evaluating the energy in xDH methods, which are obtained
from lower-rung hybrid density functional approximations (DFAs) and display
substantial density errors in the dissociation limit. In this work, we
systematically investigate the influence of density on several challenging
datasets and find that the xDH methods are less sensitive to the density errors
compared to semi-local and hybrid DFAs. Furthermore, we demonstrate that the
self-interaction corrected SCAN density offers superior accuracy compared to
the self-consistent SCAN density and Hartree-Fock (HF) density, as evidenced by
the charge analysis on the dissociation of heterodimers, such as NaCl and LiF.
Building on these insights, we propose a 5-parameter xDH method using the SCAN
density and orbitals corrected by the PZ-SIC scheme. This new xDH@SCAN(SIC)
method provides a balanced and accurate description across a wide range of
challenging systems.
