Reduced-gradient analysis of van der Waals complexes

Different methods to describe dispersion interactions within density functional theory have been developed, which is essential to describe binding in van der Waals complexes. However, several key aspects of such complexes-including binding energies, lattice constants, and binding distances-also depend on the exchange description that is paired with the description of dispersion interactions. This is particularly true for the vdW-DF family of van der Waals density functionals, which has a clear division between truly non-local correlations and semi-local generalized-gradient exchange. Here, we present a systematic analysis of the reduced-gradient values that determine the semi-local exchange for different classes of van der Waals complexes. In particular, we analyze molecular dimers, layered structures, surface adsorption, and molecular crystals. We find that reduced-gradient values of less than similar to 1 to similar to 1.5-depending on the system-contribute attractively to the exchange binding, while reduced gradients above those values are repulsive. We find that the attractive contributions can be attributed to low-density regions between the constituents with disk-like iso-surfaces. We further identify a mechanism wherein the surface area of these disks decreases through merging with other iso-surfaces and switches the gradient-correction to exchange from attractive to repulsive. This analysis allows us to explain some of the differences in performance of vdW-DF variants and initiates a discussion of desirable features of the exchange enhancement factor. While our analysis is focused on vdW-DF, it also casts light on van der Waals binding in a broader context and can be used to understand why methods perform differently for different classes of van der Waals systems.