Reduced-gradient analysis of van der Waals complexes*

Different methods to describe dispersion interactions within DFT have been developed, which are essential to describing binding in van der Waals complexes. However, key properties such as binding energies, lattice constants, and binding distances also depend on the exchange description. Here, we present an analysis of the reduced-gradient values that determine the semi-local exchange for different classes of van der Waals complexes. We analyze molecular dimers, layered structures, surface adsorption, and molecular crystals. We find that reduced-gradient values of less than ~1 contribute attractively to the exchange binding, while higher values are repulsive. The attractive contributions can be attributed to low-density regions between the constituents with disk-like iso-surfaces. We identify a mechanism wherein the merging of iso-surfaces switches the gradient-correction to exchange from attractive to repulsive. This finding allows us to develop a generalized picture of the bond formation in weakly bonded materials in terms of the topology of their reduced-gradient iso-surfaces. This picture also uncovers desirable features of the exchange enhancement factor and can be used to understand why methods perform differently for different classes of van der Waals systems.