Signature of van der Waals interactions in the cumulant density matrix

Here we propose and implement a universal signature of the van der Waals interactions based on the cumulant part of the two-electron reduced density matrix (2-RDM). Due to the connected property of the cumulant, we can use it to detect the van der Waals interactions between two molecular moieties. In particular, we use the squared Frobenius norm of the cumulant of the 2-RDM, which has been previously shown to provide a size-extensive measure of the electron correlation. As two moieties are separated to infinity, the cumulant Frobenius norm exhibits an r(-6) decay to its asymptotic limit, providing a density-based measure of the van der Waals interaction. We study this signature of van der Waals forces in a collection of small molecules of varying geometries. These computations agree with experimental trends of known literature values.