The Source of SomeEmpirical Density Functionals vander 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.