  We present first-principles calculations of the dI/dV characteristics of an
H2 molecule sandwiched between Au and Pt electrodes in the presence of
electron-phonon interactions. The conductance is found to decrease by a few
percentage at threshold voltages corresponding to the excitation energy of
longitudinal vibrations of the H2 molecule. In the case of Pt electrodes, the
transverse vibrations can mediate transport through otherwise non-transmitting
Pt $d$-channels leading to an increase in the differential conductance even
though the hydrogen junction is characterized predominately by a single almost
fully open transport channel. In the case of Au, the transverse modes do not
affect the dI/dV because the Au d-states are too far below the Fermi level. A
simple explanation of the first-principles results is given using scattering
theory. Finally, we compare and discuss our results in relation to experimental
data.
