On the perturbation methods for some nonlinear quantum chemistry models

The purpose of this article is to (a) give a sound mathematical foundation to perturbation methods for some nonlinear quantum chemistry models. This contributes to the understanding of computations on molecular systems in situ, such as solvated molecules or molecules subjected to a uniform external electric field and (b) prove in the latter setting a result of non-existence of solutions to the Thomas-Fermi-Von Weizsäcker and to the Hartree-Fock equations, which is the nonlinear counterpart of a result by Avron and Herbst.².