  We have investigated Au atomic contacts in H$_{2}$ and D$_{2}$ environment by
conductance measurement and $dI/dV$ spectroscopy. A single H$_{2}$ or D$_{2}$
molecule was found to bridge Au electrodes. In the case of the Au/H$_{2}$/Au
junction, symmetric peaks were observed in $dI/dV$ spectra, while they were not
observed for the Au/D$_{2}$/Au junction. The shape of the peaks in $dI/dV$
spectra originated from the structural change of the single molecule junction
induced by the phonon excitation. The structural change could occur only for
the Au/H$_{2}$/Au junction. The difference in the two single molecule junctions
could be explained by larger zero point energy of Au-H$_{2}$ vibration mode
than that in the Au/H$_{2}$/Au junction.
