I shall present the mathematical analysis of a limit problem in Density Functional Theory as a small parameter in front of the kinetic energy (the Planck constant) tends to zero, and explain how this relates to a bond dissociating model. This recent work shows that the multi-marginals optimal transport cost with Coulombian electron-electron repulsion may correctly describe the dissociation effect, and how the theme of fractional number of electrons appears naturally in this context, along with many open questions.