In this talk I will review and put into perspective several results on the large-coupling strength expansion of two adiabatic connections (AC) widely used in electronic structure theory. The first one is the density fixed AC of DFT that connects the Kohn-Sham determinant with the physical state. Its large-coupling strength limit defines a multimarginal optimal transport problem, also known in physics as the strictly-correlated-electrons (SCE) functional. The second one is the AC that connects the Hartree-Fock Slater determinant with the physical state and has as small-coupling expansion the Møller-Plesset perturbation theory. I will discuss differences and similarities between the two large-coupling strength expansions and their use in designing and improving approximations in quantum chemistry.
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