  The accuracy of applying density functional theory to noncovalent
interactions is hindered by errors arising from low-density regions of
interaction-induced change in the density gradient, error compensation between
correlation and exchange functionals, and dispersion double counting. A new
exchange-correlation functional designed for noncovalent interactions is
proposed to address these problems. The functional consists of the
range-separated PBEsol exchange considered in two variants, pure and hybrid,
and the semilocal correlation functional of Modrzejewski et al. [J. Chem. Phys.
137, 204121 (2012)] designed with the constraint satisfaction technique to
smoothly connect with a dispersion term. Two variants of dispersion correction
are appended to the correlation functional: the atom-atom pairwise additive
DFT-D3 model and the density-dependent many-body dispersion with
self-consistent screening (MBD-rsSCS). From these building blocks a set of four
functionals is created to systematically examine the role of pure versus hybrid
exchange and the underlying models for dispersion. The new functional is
extensively tested on benchmark sets with diverse nature and size. The truly
outstanding performance is demonstrated for water clusters of varying size,
ionic hydrogen bonds, and thermochemistry of isodesmic n-alkane fragmentation
reactions. The merits of each component of the new functional are discussed.
