The Source of Some Empirical Density Functionals van der Waals Forces

Density functional approximations became indispensable
tools in
many fields of chemistry due to their excellent cost-to-accuracy ratio.
Still, consideration is required to select an appropriate approximation
for each task. Highly parameterized Minnesota functionals are known
for their excellent accuracy in reproducing thermochemical properties
and, in particular, weak medium-range interactions. Here, we show
that the latter ability of many Minnesota functionals comes from exploiting
the basis set incompleteness. This finding shows how empirical functionals
can trick their makers by learning to operate in a physics-defying
way and likely explains the previously observed tendency of Minnesota
functionals to distort electron densities. Thus, satisfaction of the
Hellmann–Feynman theorem should be considered an important
test and parameterization goal for the future generations of highly
parameterized density functionals, including those based on neural
networks.