Rotational and Vibrational Excitations of a Hydrogen Molecule Trapped within a Nanocavity of Tunable Dimension

The rotational and vibrational transitions of a hydrogen molecule weakly adsorbed on the Au(110) surface at 10 K were detected by inelastic electron tunneling spectroscopy with a scanning tunneling microscope. The energies of the $j=0$ to $j=2$ rotational transition for para-${\mathrm{H}}_2$ and HD indicate that the molecule behaves as a three-dimensional rigid rotor trapped within the tunnel junction. An increase in the bond length of ${\mathrm{H}}_2$ was precisely measured from the downshift in the rotational energy as the tip-substrate distance decreases.

Figure 1

(a) Schematic diagram of the diffusion and trapping of a hydrogen molecule in the tunnel junction. The average lifetime of each trapped molecule in the junction is estimated to be far shorter than the response time of STM electronics. The spectroscopic signals arise from the average of many such diffusion and trapping processes. (b) STM topographic image of a bare Au(110) $2\times 1$ reconstructed surface obtained at constant current mode prior to dosing with hydrogen. Imaging conditions: tunneling gap set with sample bias $V_B=13.5\mathrm{mV}$ and tunneling current $I_T=2\mathrm{nA}$. (c) STM topographic image obtained under the same conditions as (b) but after dosing with ${\mathrm{H}}_2$ molecules. (d) $dI/dV$ image at 0 mV bias and (e) $d^{2}I/d{V}^2$ image at 10 mV bias for surface adsorbed with ${\mathrm{H}}_2$. Tunneling gap setting conditions: $V_B=50\mathrm{mV}$ and $I_T=2\mathrm{nA}$ for (d), $V_B=100\mathrm{mV}$ and $I_T=10\mathrm{nA}$ for (e).

Figure 2

Tunneling spectra taken before and after dosing molecular hydrogen or its isotopes. The tunneling gap is set with $V_B=50\mathrm{mV}$ and $I_T=2\mathrm{nA}$ for all the spectra. The bias for the $x$ axis in the spectra has been shifted up by 1 mV to compensate for instrumental offset. (a) From the top to the bottom: $dI/dV$ spectra of ${\mathrm{H}}_2$, HD, ${\mathrm{D}}_2$, and a clean gold surface (background). (b) From the top to bottom: $d^{2}I/d{V}^2$ spectra of ${\mathrm{H}}_2$, HD, ${\mathrm{D}}_2$, and a clean gold surface (background). The magnified line shapes for the rotational excitation are also presented. The excitation energies are marked by arrows. The signal at $\pm 42.0\mathrm{mV}$ in ${\mathrm{H}}_2$ spectra and the signal at $\pm 31.5\mathrm{mV}$ in HD spectra are assigned to the $j=0\to 2$ rotational excitation. The small structure around $\pm 42\mathrm{mV}$ in the HD and ${\mathrm{D}}_2$ spectra is attributed to contamination from co-adsorption of the background ${\mathrm{H}}_2$ in the vacuum chamber. The strong signals at $\pm 11.4$, $\pm 8.9$, and $\pm 8.2\mathrm{mV}$ in the spectra for ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$ are assigned to the $v=0\to 1$ vibrational excitation within the physisorption potential well.

Figure 3

(a),(b) $d^{2}I/d{V}^2$ spectra taken at different tip-substrate separation for ${\mathrm{H}}_2$ (a) and HD (b). The sample bias $V_B$ is changed from 5 (bottom) to 120 mV (top) in (a) and from 5 (bottom) to 70 mV in (b). $I_T$ is kept at 2 nA for all these spectra. A $z\mathrm{\text{−}}V$ curve is measured to convert the change in $V_B$ to the corresponding change in the tip-substrate separation ($\Delta z$). The tunneling gap distance at $V_B=5\mathrm{mV}$ and $I_T=2\mathrm{nA}$ is used as the reference point ($\Delta z=0$). The uncertainty in $\Delta z$ is around 0.095 Å. The shiftings of the rotational and vibrational excitation energies are indicated by the dashed lines. The magnified line shapes of the rotational excitation are also presented. (c) The $j=0\to 2$ excitation energy of hydrogen increases from 41 to 43 mV as $\Delta z$ increases by 1 Å. The horizontal dashed line indicates for reference the excitation energy of a free molecule. (d) The $v=0\to 1$ excitation energy decreases from 18 to 7.5 mV as $\Delta z$ increases by 1 Å for ${\mathrm{H}}_2$, and from 15 to 8 mV as $\Delta z$ increases by 0.8 Å for HD.

Figure 4

(a) DFT calculations of the interaction energy between the trapped molecule and the tunneling junction, and H-H bond length at different tip-substrate separation. The blue shaded area indicates the approximate range probed by STM. (b) The H-H bond length, derived from the measured $j=0\to 2$ excitation energies, decreases from 0.766 to 0.746 Å as $\Delta z$ increases by 1 Å. The dashed line indicates for reference the H-H bond length of a free molecule.