Fullerene Quantum Gyroscope

We report the observation of quantized rotational states of a diatomic ${\mathrm{C}}_2$ unit in solid endohedral fullerene ${\mathrm{C}}_2{\mathrm{S}\mathrm{c}}_2{@\mathrm{C}}_{84}$. The rotational transitions induce a periodic line pattern in the low energy Raman spectrum. The rotational constant $B$ and the C-C distance were found to be $1.73{\mathrm{c}\mathrm{m}}^{-1}$ and 0.127 nm, respectively. Density functional calculations revealed an intrinsic rotational barrier of the order of only a few meV for the ${\mathrm{C}}_2$ unit. The Schrödinger equation involving the potential barrier was solved and the Raman tensor matrix elements were calculated, yielding good quantitative agreement with the experiment. To our best knowledge this is the first intrinsic rotational spectrum of a diatomic plane molecular rotor.

Figure 1

Structure of ${\mathrm{C}}_2{@\mathrm{S}\mathrm{c}}_2{\mathrm{C}}_{84}$. The two spheres represent the Sc ions on the ${\mathrm{C}}_2(z)$ symmetry axis; the $y$ axis lies in plane of the sheet. The central part of the figure represents a superposition of carbon states as evaluated from DFTB MD calculations at 300 K.

Figure 2

Low energy Raman spectra for ${\mathrm{C}}_2{@\mathrm{S}\mathrm{c}}_2{\mathrm{C}}_{84}$ at 80 K. The dotted line is an exponential background and the full line is the fit using Voigtian lines. PL identifies a plasma line. The arrows indicate positions for equidistant Raman lines. The inset shows the high-energy part of the spectra for ${\mathrm{S}\mathrm{c}}_2{\mathrm{C}}_{84}$, ${\mathrm{C}}_2{@\mathrm{S}\mathrm{c}}_2{\mathrm{C}}_{84}$, ${\mathrm{C}}_{84}$ (from top to bottom). The arrow points to the C-C vibration at $1745{\mathrm{c}\mathrm{m}}^{-1}$ which is missing in ${\mathrm{C}}_{84}$ and ${\mathrm{C}}_2{@\mathrm{C}}_{84}$.

Figure 3

Low energy Raman response of ${\mathrm{C}}_2{@\mathrm{S}\mathrm{c}}_2{\mathrm{C}}_{84}$ as recorded with the red laser for selected temperatures indicated and after background subtraction.

Figure 4

Eigenenergies of the perturbed plane rotor as a function of the dimensionless parameter, $q=-V_0/4B$. Only those energies are displayed which belong to the unperturbed rotational states with even $m$. Numbers denote the values of the quantum state $m$ in the absence of the potential; $\pm$ signs refer to the parity of the wave function upon inversion, $\gamma \to -\gamma$. The inset shows the rotational potential obtained from ab initio calculations (circles) and the fit with the function $V(\gamma )=V_0(1-\cos 4\gamma )/2$ (solid line).

Figure 5

Experimental (circles) and as calculated (solid lines) rotational spectra of the ${\mathrm{C}}_2$ molecule for different temperatures. Linewidths of the as calculated lines were taken from the experiment. The intensity was normalized to the maximum intensity of the experimental spectrum.