On the vibrational assignment of fullerene CGO Vincenzo Schettino, Pier Remigio Salvi, Roberto Bini, and Gianni Cardini Laborutorio di Spettroscopia Molecolare, Dipartimento di Chimica, Universitd di Firenze, Via G. Capponi 9. 50121 Firenze, Italy (Received 23 September 1994; accepted 14 October 1994) A recent density functional perturbation theory calculation of the vibrational frequencies of Cc0 is compared with the infrared spectrum of the crystal. The vibrational assignment of C,, is completed with the help of the calculation plus the available infrared, Raman, and inelastic neutron scattering spectra. In a recent paper’ the infrared spectrum of thick samples of crystalline C,, has been discussed and compared with the spectra of two simple derivatives, C6e0 and C,‘H2, with symmetry much lower than icosahedral. From the analysis of the spectra a vibrational assignment of most of the silent modes of the isolated C6” cluster was proposed. The band assignment was facilitated by the help of some of the avail- able empirical calculationszW4 of the normal frequencies of fullerene. Since the mismatch between calculated and ob- served frequencies was quite appreciable in several cases the assignment was uncertain. Recently, a new calculation of the vibrational spectrum of C,, has been published5 based on density functional perturbation theory. The fit of this calcu- lation to the measured infrared and Raman active fullerene modes is excellent and much better than for all other avail- able empirical or semiempirical calculations.2-4*6-‘o It is re- markable that in this density functional calculation the fre- quencies of the silent modes are also in excellent overall agreement with the experimental infrared assignment as pro- posed in Ref. 1. This can be appreciated from Table I par- ticularly for the u-type silent modes that are expected to be more easily observed in the infrared spectrum. It is hard to believe that this kind of agreement is fortuitous. Assuming then that the density functional frequencies are reliable it is possible to slightly adjust the assignment proposed in Ref. 1 to further improve the fit between the calculation and experi- ment. In addition, by considering the inelastic neutron scat- tering (INS) spectra”,‘2 and the Raman spectra of the crystal”-‘6 it is possible to complete the assignment of the R-type species, whose fundamentals were only partly ob- served in the infrared spectrum of Ref. 1. One major point is the position of the A,, mode that in Ref. 1 was assigned to a band observed in the inelastic neu- tron scattering spectrum at 1327 cm-‘. Empirical calcula- tions are contradictory as to the position of this mode that in Ref. 5 is calculated at 943 cm-‘. This finding is supported by another recent ub initio molecular dynamics calculation’7 that is in good agreement with the density functional calcu- lation. According to this result the A, fundamental can be ascribed to the inelastic neutron scattering band at 971 cm-’ previously assigned as a T,, fundamental. A band at this frequency is also observed in the Raman spectrum.‘3-‘6 In turn, the INS band at 1324 cm-’ can be assigned as the second highest G, fundamental and the 1529 cm-’ infrared band previously taken as the highest G, mode could actually be a G, fundamental, as will be further discussed below. These adjustments are summarized in Table I. The second important point is that in Ref. 1 six silent modes were assigned above 1500 cm-’ while only three are calculated in Ref. 5. The vibrational assignment of Table I has been adjusted to take this into consideration as well. Finally it is worth discussing further the assignment of the G,, T1,, and T,, fundamentals that was rather incom- plete in Ref. 1. Taking as a basic guide the frequencies cal- culated by the density functional method we can extend our analysis to the Raman spectrum of C60. The Raman spectrum at low temperature has been reported by Mathus and Kuzmany13 and by van Loosdrecht et al. I4 for the single crystal and by Dong et a1.15 and by Love et a1.16 for poly- crystalline films. Mathus and Kuzmany’3 are mainly inter- ested in the discussion of the Raman active A, and H, fun- damentals. However it is apparent from Fig. 3 of Ref. 13 that beside the active fundamental bands several other weak bands are observed in the low temperature Raman spectrum. These are considered in Ref. 14 and tentatively assigned as Raman silent fundamentals. Dong ef a1.,15on the contrary, assign most of the weak features of the Raman spectrum as combinations or overtones. However, they report seven silent modes to be present in the spectrum below 700 cm-‘, where the number of possible binary combinations is obviously small, and only one more above 1000 cm-‘. According to the authors the same occurs in the infrared spectrum. However, it seems unreasonable that silent modes should become active preferentially at lower frequencies. As has been described in Ref. 1 most of the weak features of the infrared spectrum gain in relative intensity in lower symmetry fullerene deriva- tives. This has been reported to be the case also in the Raman spectrum’8 and can be taken as a significant evidence for their assignment as fundamentals. The sharpness of the Ra- man lines also points to this choice. In fact, several modes show a crystal splitting of the order of 10 cm-’ 13.19 and this should be reflected in the width of binary combinations par- ticularly in a case of low anharmonicity. The presence of several of the extra features observed in the infrared and Raman spectra in the inelastic neutron scattering experiments”*” is again in favor of their assignment as fun- damentals. This is further supported by the recent Raman data on the effect of sample imperfections and isotopic substitution.‘6 On the basis of these considerations and using the fre- quencies now available from the density functional calcula- tion it is possible to reconsider the assignment of these ad- J. Chem. Phys. 101 (12), 15 December 1994 0021-9606/94/l 01(12)/l 1079/3/$6.00 0 1994 American institute of Physics 11070