The standard adiabatic connection of density functional theory (DFT) is obtained by rescaling the electron-electron repulsion with a linear parameter, while keeping the density fixed, equal to the one of the physical, interacting, system. At zero coupling strength we recover the non-interacting Kohn Sham (KS) system. In this lecture I will focus on the opposite limit, in which the coupling strength approaches infinity, which has been first studied by Seidl and coworkers. I will show that this limit has a mathematical structure much simpler than the one at physical coupling strength, with a functional derivative that has a clear physical meaning. I will also briefly discuss the connection with the field of mass transportation theory (Monge-Kantorovich).
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