_{Anharmonicity in the infrared spectrum of C60}

Investigation of the effect of anharmonicity on the IR activity of C60 can be found in J. Fabian, “Theoretical investigation of the C60 IR spectrum”, Phys. Rev. B 53, 13 864 (1996).

In the harmonic approximation the vibrations in C60 can be decomposed into 174 normal modes, of which only several are infrared (IR) active. The IR active modes have 4 distinct frequencies and so there are only 4 main peaks in the IR spectrum of C60. The observed spectrum, however, contains about 2000 identified smaller peaks which come mostly from anharmonicity. There are two types of anharmonicity which can give rise to these features in the IR spectrum. The first is the so called mechanical anharmonicity, which reflects anharmonic dynamics of the vibrational normal modes (and comes from the anharmonicity of the interatomic forces). Two normal modes, for example, can combine together and the result is a quasi mode (with the frequency equal to the sum of the frequencies of the original modes) which can be IR active; the so called ``combinational'' peak arises. Similarly, two modes can create a ``differential'' peak, if the resultant quasi mode has the frequency equal to the difference of the original frequencies. The second type of anharmonicity--electrical--has its origin in the nonlinear expansion of the dipole moment in the normal modes coordinates (light couples to two or more normal modes directly). We showed that only electrical anharmonicity can explain the observed IR spectrum of C60. Mechanical anharmonicity would give visible peaks only around the four main peaks (through the phenomenon known as the Fermi resonance), but otherwise, and especially at large frequencies (beyond 2000/cm), contributes negligibly. Electrical anharmonicity, on the other hand, results in appreciable IR activity throughout the whole spectrum; this is observed experimentally. The pictures below show the results of our simulations of both types of anharmonicity, using some models that we developed for that purpose. 

Above: Measured IR spectrum of C60. The four main (harmonic) peaks are at frequencies 530, 580, 1180, and 1430 1/cm. All the other peaks come from some kind of symmetry breaking or anharmonicity. The upper curve was measured at 300 K, the lower at 77 K. (1000/cm is about 100 meV.)

Calculated IR spectrum with mechanical anharmonicity. The top figure has the scale set by the four main peaks. The three figures below are scaled so that the small peaks coming from the anharmonicity are visible. At 2000-4000/cm, where the experiment sees visible peaks, we had to rescale the vertical axis by 10000 to see the peaks. Clearly, mechanical anharmonicity does not solve the problem. Note that mechanical anharmonicity becomes most active around the four main peaks (Fermi resonance). 

Calculated IR spectrum with electical anharmonicity. The spectrum nicely resembles the experimental one. In contrast to the case of mechanical anharmonicity (above), even on the scale of the four harmonic peaks the small anharmonic IR activity is visible. Most intense anharmonic effects are at high frequencies, between 1000 and 3000 1/cm. We have concluded that electrical anharmonicity is responsible for most of the observed IR spectrum of C60.