Density Functionals from the Multiple-Radii Approach: Analysis and Recovery of the Kinetic Correlation Energy

Inspired by the exact form of the strongly interacting limit of density functional theory, Vuckovic and Gori-Giorgi have recently proposed [ J. Phys. Chem. Lett. 2017 , 8 , 2799 ] the multiple radii functional (MRF), a new framework for the construction of exchange-correlation (xc) energy approximations able to describe strong correlation electronic effects. To facilitate the construction of improved approximations based on the MRF functional, in the present work we use reverse engineering strategies to reveal the forms of the MRF functional which reproduce the exact xc functional for small atoms. Using the adiabatic connection representation of the xc functional, we also develop an interpolation form which uses xc energy densities from the physical, weakly and strongly interacting regimes as input ingredients. We discuss how this interpolation form can be used for recovering the presently missing kinetic component of the correlation energy in the MRF framework and we asses its accuracy using highly accurate ingredients for small atoms. Applying the same interpolation form to LiH along the dissociation curve, we highlight its advantages over previous adiabatic connection-based models for the treatment of strong correlation.