Range-Separation and the Multiple Radii Functional Approximation Inspired by the Strongly Interacting Limit of Density Functional Theory

The strongly-interacting limit of density functional theory has attracted considerable attention recently due to its ability to deal with the difficult strong correlation problem. Recent work [JPCL 8, 2799-2805 (2017)] introduced the "multiple radii functional" (MRF) approximation, inspired by this limit, which is designed to work well for strong correlations between dissociated fragments. Here, we analyse the MRF in exactly solvable one-dimensional molecules, to uncover how it matches, and deviates from, exact results; and use range-separation of the Coulomb potential in both exact and approximate theory to explore how this varies in space. Our work opens a path to new approximations incorporating the MRF, amongst other ingredients.