Electronic Exchange and Correlation in van der Waals Systems: Balancing Semilocal and Nonlocal Energy Contributions

Short-range
correlations in motion of electrons in matter are captured
well by semilocal exchange–correlation (XC) functionals in
density functional theory (DFT), but long-range correlations are neglected
in such models and must be treated by van der Waals (vdW) dispersion
methods. Whereas the effective range of distances at which fluctuations
are correlated is usually explicit in the vdW models, the complementary
range of semilocal functionals can be observed only implicitly, requiring
an introduction of empirical damping functions to couple the semilocal
and nonlocal contributions to the XC energy. We present a comprehensive
study of the interplay between these short-range and long-range energy
contributions in eight semilocal functionals (LDA, PBE, TPSS, SCAN,
PBE0, B3LYP, SCAN0, M06-L) and three vdW models (MBD, D3, VV10) on
noncovalently bonded organic dimers (S66×8), molecular crystals
(X23), and supramolecular complexes (S12L), as well as on a series
of graphene-flake dimers, covering a range of intermolecular distances
and binding energies (0.5–130 kcal/mol). The binding-energy
profiles of many of the DFT+vdW combinations differ both quantitatively
and qualitatively, and some of the qualitative differences are independent
of the choice of the vdW model, establishing them as intrinsic properties
of the respective semilocal functionals. We find that while the SCAN+vdW
method yields a narrow range of binding-energy errors, the effective
range of SCAN depends on system size, and we link this behavior to
the specific dependence of SCAN on the electron localization function
α around α = 1. Our study provides a systematic procedure
to evaluate the consistency of semilocal XC functionals when paired
with nonlocal vdW models and leads us to conclude that nonempirical
generalized-gradient and hybrid functionals are currently among the
most balanced semilocal choices for vdW systems.