  In the framework of Density Functional Theory with Strongly Correlated
Electrons we consider the so called bond dissociating limit for the energy of
an aggregate of atoms. We show that the multi-marginals optimal transport cost
with Coulombian electron-electron repulsion may correctly describe the
dissociation effect. The variational limit is completely calculated in the case
of N=2 electrons. The theme of fractional number of electrons appears naturally
and brings into play the question of optimal partial transport cost. A plan is
outlined to complete the analysis which involves the study of the relaxation of
optimal transport cost with respect to the weak* convergence of measures.
