Rotational Sublevels of an Ortho-Hydrogen Molecule Encapsulated in an Isotropic ${\mathbf{C}}_{60}$ Cage

From specific heat measurements in high quality ${\mathrm{H}}_2@{\mathrm{C}}_{60}$ samples performed over a broad temperature range, we obtain the smallest yet observed splitting of rotational energy sublevels of encapsulated single ${\mathrm{H}}_2$ molecules, 0.1–0.2 meV, in the nearly spherical potential well provided by highly isotropic ${\mathrm{C}}_{60}$ cages. Additionally, we find evidence of the quantized oscillation state of isolated ${\mathrm{H}}_2$ in the ${\mathrm{C}}_{60}$ cage. The minuscule splitting indicates that ${\mathrm{H}}_2@{\mathrm{C}}_{60}$ provides unprecedented opportunities to study free-molecule quantum dynamic properties.

Figure 1

X-ray diffraction pattern and electron density surface of ${\mathrm{H}}_2@{\mathrm{C}}_{60}$. The view (right side) shows that an endohedral ${\mathrm{H}}_2$ molecule locates in the center of the cage.

Figure 2

Specific heat of ${\mathrm{C}}_{60}$ and ${\mathrm{H}}_2@{\mathrm{C}}_{60}$. (a) Open circles are measured by a PPMS, and solid black circles are measured by a homemade calorimeter. The solid line was obtained by extrapolation.

Figure 3

Excess specific heat $\Delta C_p$. These data (black circles) were obtained by subtracting the $C_p$ data of ${\mathrm{C}}_{60}$ from that of ${\mathrm{H}}_2@{\mathrm{C}}_{60}$. For the calculation below 2 K, $C_p$ of ${\mathrm{C}}_{60}$ is estimated by extrapolation to 0 K from temperatures above 2 K [shown in Fig. 2b]. The magenta solid curve indicates the fitted specific heat $C_{\mathrm{fit}}$, which is the summation of $C_{\mathrm{trans}}$ (magenta dotted curve) and $C_{\mathrm{rot}}$ (magenta dashed curve), while the dashed cyan curve is the rotational $C_p$ of ${\mathrm{H}}_2$ with the equilibrium ortho-para ratio.

Figure 4

Excess specific heat $\Delta C_p$ and excess entropy $\Delta S$ below 4 K. (a) The black dashed, magenta, and cyan curves indicate the results of two-level, three-level, and dual two-level Schottky fits, respectively. (b) $\Delta S$ was calculated from $\Delta C_p$.