Some mathematical problems in molecular quantum chemistry.

Summary This thesis gathers a set of works devoted to the mathematical study of different molecular models used in quantum chemistry in numerical simulations. We are first interested in the thomas-fermi models, in particular the thomas-fermi-dirac-von weizsacker model and the thomas-fermi model with fermi-amaldi correction, then in the hartree-fock models, such as the multideterminant models. For each model, the results we prove concern the compactness of the minimizing sequences, the existence of a minimum, and its qualities (uniqueness, decay to infinity, non-degeneracy of the Lagrange multiplier,. . . ). A numerical application of these theoretical models is also presented. In the appendix, a result of group theory is presented.