  We study one dimensional models of diatomic molecules where both the
electrons and nuclei are treated as quantum particles, going beyond the usual
Born-Oppenheimer approximation. The continuous system is approximated by a grid
which computationally resembles a ladder, with the electrons living on one leg
and the nuclei on the other. To simulate DMRG efficiently with this system, a
three-site algorithm has been implemented. We also use a compression method to
treat the long-range interactions between charged particles. We find that 1D
diatomic molecules with spin-1/2 nuclei in the spin-triplet state will unbind
when the mass of the nuclei reduces to only a few times larger than the
electron mass, while the molecule with nuclei in the singlet state always
binds, given the two electrons in their singlet state in both cases.
