  In quantum dots or molecules with vibrational degrees of freedom the
electron-vibron coupling renormalizes the electronic charging energy. For
sufficiently strong coupling, the renormalized charging energy can become
negative. Here, we discuss an instability towards adding or removing an
arbitrary number of electrons when the magnitude of the renormalized charging
energy exceeds the single-particle level spacing. We show that the instability
is regularized by the anharmonic contribution to the vibron energy. The
resulting effective charging energy as a function of the electron number has a
double-well structure causing a variety of novel features in the Coulomb
blockade properties.
