We study the stability of molecules in reduced density-matrix theories (RDMT), mainly Mueller theory. It is well-known that, going back to the work of Lieb and Thirring (1986, Phys. Rev. A 34), neutral atoms and molecules are stable in the nonrelativistic Schroedinger theory.
On the other hand, density-functional theory may not have the same feature, since it deals only with single particle densities. Indeed, Thomas-Fermi (TF) theory cannot describe the binding stability of molecules by Teller's no-binding theorem.
For Hartree and TF type theories Catto and Lions found some binding condition in a series of works (1992, Commun Part Diff Equ). We will extend the method of Catto and Lions to treat RDMT of molecules.