The aim of the project is to investigate the existence and decay rates of weakly bounded states for molecules and the Fröhlich Multipolaron. Motivated by our recent results on the existence and decay behavior of weakly coupled bound states at the edge of the continuum for atoms and the Fröhlich Bipolaron we want to consider two related but much more involved physically relevant settings. We aim to generalize our newly developed method for deriving decay rates of finite norm eigenfunctions of Hamiltonians to the considerable more complex quantum systems of molecules and multipolarons. More precisely we plan to investigate properties of ground state configurations of molecular systems in the neighborhood of the threshold of the essential spectrum. Moreover we want to look into the existence of a ground state for the Fröhlich Multipolaron in the zero total momentum channel at critical coupling and if it exists, study its asymptotic decay properties