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.

• Received 11 October 2017

DOI:https://doi.org/10.1103/PhysRevA.96.050501