Knowledge Bank

Buckminsterfullerene ($C60$) is the roundest commercially available deformable spherical rotors $(DSR),a$. The Buckyballs'' are unique in that they have tri-axial rotation even in the fullerite solid-state above 140K; a box of frictionless ball bearings! Also, the $C_{60}$ cage is large enough to hold atoms and maybe even small molecules. In gas-phase this opens the possibility of a fully triaxial concentric DSR-DST rotor-rotor as well as many of the other more theoretically tractable cases like DSR-RDR or RST-RUP listed in the preceding talk. $(C_{60}$ solid-phase is a hetrocentric $(DSR)^{N}$ fcc crystal.) Finally, $C_{60}$ is practically unique in that it comes in distinct isotopic varieties, most notably a Bose-ball'' $\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}C60$, a mixed-ball'' $^{13}C_{59}$ and a Fermi-ball'' of ($\mathrm{<mrow\; data-mjx-texclass="ORD">13</mrow>}C60).bc$ Differences in symmetry between these casesis enormous. Bose-exclusion kills all but the Ag rovibrational species of $\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}C60$ and reduces spectral congestion by a factor of 60. In contrast, Pauli-Fermi-exclusion assigns 2$\mathrm{<mrow\; data-mjx-texclass="ORD">60</mrow>}$ 1.5E18 hyperfine levels to each rovibrational level of $\mathrm{<mrow\; data-mjx-texclass="ORD">13</mrow>}C60$. Mixed symmetry fullerenes $\mathrm{<mrow\; data-mjx-texclass="ORD">13</mrow>}Cm-12C60-m$[3] lie between the two extremes. The first ``mixed-ball'' $\mathrm{<mrow\; data-mjx-texclass="ORD">13</mrow>}C60-12C59$ corresponds to a strong-coupling limit of an hcDSR-RDR model. This observation helps to clarify the enormous symmetry-exclusion diversity. At the bottom of the rotor-rotor symmetry hierarchy are the hetrocentric hcRDR-RDR or hcRAT-RAT arrangements of elongated molecules connected more or less loosely end-to-end, that is, links of folding polymer chains. Such chains and links are nano-sized quantum mechanical analogs of ancient slings, whips, and trebuchets with a devilish dynamics to match! And, biological systems cannot live without them.