Abstract
We present first-principles calculations of the $dI/dV$ characteristics of an ${\text{H}}_{2}$ molecule sandwiched between Au and Pt electrodes in the presence of electron-phonon interactions. The conductance is found to decrease by a few percentages at threshold voltages corresponding to the excitation energy of longitudinal vibrations of the ${\text{H}}_{2}$ molecule. In the case of Pt electrodes, the transverse vibrations can mediate transport through otherwise nontransmitting $\text{Pt}\text{ }d$ 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 $\text{Au}\text{ }d$ 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.
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