Binding of atoms and stability of molecules in hartree and thomas-fermi type theories.

This paper is the third of a series devoted to the study of the binding of atoms, molecules and ions and of the stability of general molecular systems including molecular ions, in the context of Hartree and Thomas-Fermi type theories. For Thomas-Fermi-von WeizsÖcker or Thomas-Fermi-Dirac-von Weizsäcker models, we prove here that neutral systems can be bound and in view of the results shown in the preceding parts this yields the stability of arbitrary molecules (general neutral molecular systems). For the Hartree and Hartree-Fock models, we prove that neutral planar systems can be bound and this yields the stability of arbitrary tetraatomic molecules for instance. Various variants and extensions are also considered.