The isotope effect in the

infrared spectrum of C₆₀

The experiment and theory of the isotope effect in C60 was published in M. C. Martin, J. Fabian, et al. Phys. Rev. B 51, 2844 (1995).

The molecule C60 has 4 infrared-active vibrational modes. This is dictated by the molecule's icosahedral symmetry. The observed infrared (IR) spectrum (usually taken when the molecules form a solid), however, displays a broad range of infrared activities, ranging up to about 4000/cm. (The four pristine IR-active modes have frequencies smaller than 1500/cm.) About 2000 small (also called silent) peaks were identified in the observed IR spectrum, all coming apparently from some kind of symmetry breaking. The question is what breaks the symmetry. The most obvious symmetry-breaking mechanism is the isotope effect. Most carbon atoms in nature are 12C, but there is naturally about 1.08% of the isotope 13C present. The presence of 13C atoms in a C60 molecule lowers the icosahedral symmetry, giving rise to new IR-active vibrational modes (although not all 2000 as observed). I describe below how we combined experiment and theory to reject the isotope hypothesis. We showed experimentally that by doping C60 with 13C beyond the natural abundance the IR spectrum does not change appreciably. If the isotope effect were the main reason behind the symmetry breaking, with increasing isotope mixture the silent peaks would become more pronounced, as was confirmed by our numerical calculation. In addition, our calculation revealed that isotope symmetry breaking would be too small to be observed (silent peaks would be about three orders of magnitude smaller than the four pristine peaks, while experimentally the silent peaks were only 10-100 times smaller).

Other possible symmetry-lowering mechanisms are extrinsic impurities and anharmonicity. Impurities would lead to different spectra for different samples, which is not observed. Anharmonicity turned out to be THE relevant mechanism and is dealt with in Anharmonicity in the Infrared Spectrum of C60. 

Above: Measured IR spectrum of C60 for two different ¹³C-isotope concentrations. The top figure is for C60 with the natural 1.08% abundance of the isotope. The middle graph is C60 with artificially enhanced isotope concentration (8%). The lowest graph is a result of a simulation which only broadens the top curve by considering 8% isotope concentration and assuming that increasing the concentration will only cause broadening of the peaks. This indeed happens, since the last two curves are almost identical. The curves are rescaled so that the silent peaks are visible.

Above: Computer Monte-Carlo simulation of the isotope effect in the C60 IR spectrum. The four (three are visible, the first splits into two a bit above the graph) pristine peaks are visible, with small hidden peaks activated because of the isotope contamination. As the isotope concentration increases from the natural value to 8% (this is the experimental value in the above figure), the intensity of the small peaks greatly increases. This is not seen in the experiment above. Also, the small peaks are really small to be seen experimentally. They are one to ten thousand times smaller than the four main peaks. The conclusion: the isotope effect is not the main reason for symmetry breaking seen in the IR spectrum.