Does the Exchange-Correlation Kernel ƒxc Have a Very Long-Ranged Dependence on the Groundstate Electron Density?

We consider the dispersion energy between two well-separated molecules. Provided that exchange overlap effects can be neglected, the Generalized Casimir Polder (GCP) formula gives the dispersion energy exactly to second order in the inter-system Coulomb pair potential, in terms of the density response functions of the isolated molecules. One can alternatively calculate the dispersion interaction from the density response in a supramolecular (dimer) energy TDDFT/ACFD calculation. This uses the density response from Time Dependent Density Functional Theory (TDDFT) and the Adiabatic Connection (ACFD) groundtstate electronic energy formula, and treats the two systems together. Some of us recently [JCTC 13, 5829 (2017)] showed that the supramolecular TDDFT/ACFD approach can fail to reproduce the exact GCP result, when the exchange-correlation kernel ƒxc in the TDDFT calculation is assumed to be local. Here we examine ways in which a nonlocal density dependence of ƒxc might be able to remove this discrepancy.