  We present the idea and illustrate potential benefits of having a tool chain
of closely related regular, unscreened and screened hybrid exchange-correlation
(XC) functionals, all within the consistent formulation of the van der Waals
density functional (vdW-DF) method [JPCM 32, 393001 (2020)]. Use of this chain
of nonempirical XC functionals allows us to map when the inclusion of truly
nonlocal exchange and of truly nonlocal correlation is important. Here we begin
the mapping by addressing hard and soft material challenges: magnetic elements,
perovskites, and biomolecular problems. We also predict the structure and
polarization for a ferroelectric polymer. To facilitate this work and future
broader explorations, we furthermore present a stress formulation for spin
vdW-DF and illustrate use of a simple stability-modeling scheme to assert when
the prediction of a soft mode (an imaginary-frequency vibrational mode,
ubiquitous in perovskites and soft matter) implies a prediction of an actual
low-temperature transformation.
