Volume 190, number 3,4 CHEMICAL PHYSICS LETTERS 6 March 1992 The vibrational frequencies of C6o Fabrizia Negri, Giorgio Orlandi and Francesco Zerbetto Dipartimento di Chimica "G. Ciarnician'" Universitd di Bologna, via F. Selmi 2, 40126 Bologna, Italy Received 15 November 1991; in final form 13 December 1991 The C6o inelastic neutron scattering and high-resolution electron-energy-loss spectra are assigned through semi-empirical quan- tum-chemical calculations. Since the discovery [ 1 ] and the subsequent iso- lation [2] of C6o, a large body of experimental and theoretical data has been gathered on this molecule. In particular, great progress has been achieved in the study of its vibrational normal modes. Because of the Ih point-group symmetry of this cluster, the 174 vi- brational modes span only 46 distinct vibrational frequencies of which 4 are infrared (IR) active (tlu symmetry) and 10 are Raman active (8 hg + 2 ag). All the IR and Raman active modes have been ob- served and assigned [ 3 ]. Recently, by use of the ine- lastic neutron-scattering technique (INS), the dis- tribution of all the vibrational modes was measured [4,5 ]. In this experiment, no selection rule based on symmetry consideration applies. However, in the C6o cluster, all the atoms are equivalent by symmetry, so that the norm of the atomic normal-mode displace- ments (which are responsible for the spectral inten- sities) are the same for every atom in every normal mode and the fundamental transition of each mode contributes the same intensity to the INS spectrum [6]. From the INS spectrum, information about the vi- brations that are inactive in IR and Raman was thus obtained for the first time. The very fact that all the vibrational frequencies are present in the INS spec- trum makes its analysis on a purely empirical basis virtually impossible. Thus, Prassides et al. [4] dis- cussed their results in the light of the experimentally available infrared and Raman frequencies, while Cappelletti et al. [ 5 ] analyzed their INS spectrum by using the results of three quantum-chemical calcu- lations [ 7-9 ] of vibrational frequencies. The agree- ment achieved between the theoretical frequencies [ 7-9 ] and the INS spectrum [5] was only qualita- tive. As CappeUetti et al. [ 5 ] noted, each set of cal- culated frequencies presents some discrepancies with the INS spectrum and also with the IR and Raman spectra. A meaningful assignment of the vibrational frequencies of C6o should also include the high-res- olution electron-energy-loss (HREELS) spectrum very recently obtained by Gensterblum et al. [ 10 ] in the vibrational domain. Their data are especially valuable in the 1100-1600 cm- 1range where the INS spectrum shows poor resolution. In 1988, before any experimental data were avail- able, we calculated all the vibrational frequencies of C60 [ 11 ]. The IR and Raman active frequencies sub- sequently measured [3 ] were found to be in excel- lent agreement with our calculated frequencies: the average deviation between the two sets was less than 30 cm- 1 with the largest errors observed in the high- frequency region with differences up to 68 cm -~. In this Letter, we show that also the vibrational- frequency distribution obtained in the INS spectrum and the bands appearing in the HREELS spectrum are suprisingly well represented by the calculated fre- quencies given in ref. [ 11 ]. In fig. 1, we show the well-resolved INS spectrum in the range 200-650 cm- 1 taken from fig. 2 of ref. [ 5 ] together with the HREELS bands [ 10]. Below it, we display our cal- culated vibrational frequencies which are repre- sented by lines whose length is proportional to the degeneracy of the level. The right and left arrows in- 174 0009-2614/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.