Salient signature of van der Waals interactions

Abstract

van der Waals interactions govern the physics of a plethora of molecular structures. It is well known that the leading term in the distance-based London expansion of the van der Waals energy for atomic and molecular dimers decays as $1/{R}^{6}$, where $R$ is the dimer distance. Using perturbation theory, we find the leading term in the distance-based expansion of the intracule pair density at the interatomic distance. Our results unveil a universal $1/{R}^{3}$ decay, which is less prone to numerical errors than the $1/{R}^{6}$ dependency, and it is confirmed numerically in ${\mathrm{H}}_{2}$ and ${\mathrm{He}}_{2}$ molecules. This signature of van der Waals interactions can be directly used in the construction of approximate pair density and energy functionals including vdW corrections.