On the vibrational assignment of fullerene C60

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Laborutorio di Spettroscopia Molecolare, Dipartimento di Chimica, Universitd di .... of C,, (frequencies are in cm-'). Calc. Obs. (Ref. 1). Obs. (this note). (Ref. 5). IR.
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 available empirical calculationszW4 of the normal frequencies of fullerene. Since the mismatch between calculated and observed 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 calculation to the measured infrared and Raman active fullerene modes is excellent and much better than for all other available empirical or semiempirical calculations.2-4*6-‘o It is remarkable that in this density functional calculation the frequencies of the silent modes are also in excellent overall agreement with the experimental infrared assignment as proposed in Ref. 1. This can be appreciated from Table I particularly 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 experiment. In addition, by considering the inelastic neutron scattering (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 observed 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 neutron scattering spectrum at 1327 cm-‘. Empirical calculations 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 calculation. 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. J. Chem. Phys. 101 (12), 15 December 1994

0021-9606/94/l

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 incomplete in Ref. 1. Taking as a basic guide the frequencies calculated 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 polycrystalline films. Mathus and Kuzmany’3 are mainly interested in the discussion of the Raman active A, and H, fundamentals. 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.,15 on 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 derivatives. 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 Raman lines also points to this choice. In fact, several modes show a crystal splitting of the order of 10 cm-’ 13.19and this should be reflected in the width of binary combinations particularly 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 fundamentals. 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 frequencies now available from the density functional calculation it is possible to reconsider the assignment of these ad-

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0 1994 American institute of Physics

11070

Letters to the Editor

11080 TABLE

I. Vibrational

assignment

of C,, (frequencies

Obs. (Ref. 1) Calc. (Ref. 5)

IR

INS”

Obs. (this note) INSa

Ramailb

488 1448

494 1468

264 432 715 765 1089 1258 1448 1563

266 431 709 772 1095 1248 1421 1574

563 840

567 860 1289

535 765 813 1327

535 764 796 1345

480

488 563

1142 1307 1508

1122 1327

485 577 738 1142 1310 1521

IR

4

495 1504

H*

259 425 711 783 1120 1281 1450 1578

270 430 707 766 1100 1255 1443 1572

264 432 715 765 1089 1258 1448 1563

r Ig

564 823 1296

535 1025 ...

563 1020 ...

1290

548 767 794 1363

640 826 ...

...

535

1508

813 971 .. .

1330

480 566 762 1118 1322 1511

432 611 796 1166 1470 ...

1581

-4,

943

...

1327

T lu

527 586 1218 1462

525 578 1180 1430

357 716 993 1228 1535

354 756 1037 1190 1566

399 530 662 741 1231 1363 1569 349 748 752 925 1334 1452

T2*

G*

T2u

HI4

GU

404 621 ... ... 1..

are in cm-‘).

270 425 707 766 1100 1255 1443 1572

971

976

525 578 1180 1430

526 576 1185 1448

529 581 1187

355 742 1044 1185 1563

354 712 1037 1190 1566

355 715 1044 1185 1563

356 714 1038

403 485 667 738 1215 1503 1540

404 488 673 765 1202

404 488 673 742 1202

403

1520

403 485 667 738 1215 1342 1540

345 712 776 963 1418 1529

344 715 765 971 1420 1520

345 757 776 963 1315 1410

344 765 765 971 1327 1420

668 1215

1520 345 757

Qelastic neutron scattering data are from Refs. 11 and 12. bRaman data are from Refs. 13, 14, and 16.

ditional features of the Raman spectrum of the crystal. The lowest G, mode is calculated at 480 cm-’ and was assigned’ to the infrared band at 432 cm-‘. This band, however, was assigned twice. An alternative and more likely choice would be the weak Raman band at 482 cm-‘, almost coincident with a H, fundamental. Three modes are calculated in the 500-600 cm-’ range, one for each of the T,,, T,,, and G,

species. One of these was assigned to an infrared band at 535 cm-‘. This mode is observed also in the Raman spectrum where two other very weak bands are also observed at -570 and 580 cm-‘. Therefore, this triplet of bands are nicely assigned as reported in Table I. In a similar way we note that there are four fundamentals calculated at ~800 cm-’ and two of these were associated with the weak infrared bands at 826 and 800 cm-‘. These are also weakly observed in the Raman spectrum. In addition in the Raman spectrum well defined bands are observed at 738 and 862 cm-‘. This suggests the assignment proposed in Table I. The G, mode calculated at 1118 cm-’ was previously assigned to the infrared band at 1166 cm-‘. This should more likely be assigned to the infrared band at 1142 cm-’ that has a well-defined counterpart in the Raman spectrum at the same frequency. The infrared bands observed at 1295, 1310-1315, and 1345 cm-’ were left unassigned. Very weak feature are present in the Raman spectrum in this region. These bands are good candidates for the fundamentals calculated in this region. Finally, the 1508 cm-’ infrared band previously assigned as a T,, fundamental has a well-defined counterpart in the Raman spectrum and is the best candidate as the highest frequency G, fundamental. As a result of these additional considerations a full vibrational assignment is now obtained that is in extremely good agreement with calculations (cf. Table I). It can be noted that in some cases infrared and Raman bands very close in frequency have been assigned as separate fundamentals. For instance, this is the case for the infrared and Raman band at ~950 cm-‘. This band has a multiplet structure in both spectra and a well-defined doublet is observed in the surface enhanced Raman spectrum.” A full assignment of the silent modes has been suggested also by Dong et al. I5 from their analysis of the binary combinations in the Raman spectrum: this assignment is in agreement with calculations in several cases but differs considerably in some others. In conclusion, it is worth noting the richness of the infrared and Raman spectra of fullerene where most of the free molecule silent modes are actually observed. Most of the g fundamentals are also observed in the infrared spectrum and some of the u modes are seen in the Raman spectrum. This results should be ascribed to the concurrence of crystal field effects (and symmetry reduction at the sites occupied in the crystal by the C60 clusters) and of the isotopic natural composition that makes the fullerene crystal actually a mixture of ‘2C, and ‘3C’2C,, in the approximate ratio 10:6. The frequencies of the isotopically monosubstituted fullerene have been calculated to be lower by less than 1 cm-’ and fall in the so-called amalgamation limit.” The effect of crystal imperfections and disorder (Love ef al.16) should be considered. We thank Professor M. L. Klein (University of Pennsylvania) for reading the manuscript. ‘G. Cardini, R. Bini, P. R. Salvi, V. Schettino, M. L. Klein, R. M. Strongin, L. Brard, and A. B. Smith, J. Phys. Chem. 98, 9966 (1994). *F. Negri, G. Orlandi, and F. Zerbetto, Chem. Phys. Lett. 144, 3 1 (1988). ‘F’. Procacci, G. Cardini, P. R. Salvi, and G. Marconi, Mol. Cryst. Liq. Ctyst. 229. 75 (1993). 4G. Onida and G. Benedek, in World ScienriJic Advances Series in Fullerenes, Vol. 1 (World Scientific, London, 1992), p, 181.

J. Chem. Phys., Vol. 101, No. 12, 15 December 1994

Letters

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J. Chem.

Phys.,

11081

to the Editor

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6i4 (1992).

Vol. 101, No. 12, 15 December

1994