We discuss energy densities in the strong-interaction limit of density functional theory, deriving an exact expression within the definition (gauge) of the electrostatic potential of the exchange-correlation hole. Exact results for small atoms and small model quantum dots (Hooke's atoms) are compared with available approximations defined in the same gauge. The idea of a local interpolation along the adiabatic connection is discussed, comparing the energy densities of the Kohn-Sham, the physical, and the strong-interacting systems. We also use our results to analyze the local version of the Lieb-Oxford bound, widely used in the construction of approximate exchange-correlation functionals. © 2012 American Chemical Society.
Mirtschink, A., Seidl, M., & Gori Giorgi, P. (2012). Energy Densities in the Strong-Interaction Limit of Density Functional Theory. Journal of Chemical Theory and Computation, 8, 3097-3107. https://doi.org/10.1021/ct3003892