The vibrational spectroscopy of C60H36: An experimental and theoretical study

Chemical Physics 232 Ž1998. 75–94

The vibrational spectroscopy of C 60 H 36 : An experimental and theoretical study R. Bini a , J. Ebenhoch b, M. Fanti c , P.W. Fowler d , S. Leach e,) , G. Orlandi c , b Ch. Ruchardt , J.P.B. Sandall d , F. Zerbetto c ¨ a

European Laboratory for Nonlinear Spectroscopy (LENS), Largo E. Fermi 2, 50124 Florence, Italy Institut fur ¨ Organische Chemie und Biochemie, UniÕersitat ¨ Freiburg, D-79014 Freiburg, Germany Dipartimento di Chimica ‘G. Ciamician’, UniÕersita` degli Studi di Bologna, Via F. Selmi 2, 40126 Bologna, Italy d Department of Chemistry, UniÕersity of Exeter, Exeter EX4 4QD, UK e DAMAP, CNRS-URA 812, ObserÕatoire de Paris-Meudon, 92195-Meudon, France b

c

Received 7 October 1997

Abstract Several samples of C 60 H 36 have been prepared by the transfer hydrogenation method and studied by infrared and Raman spectroscopy. The results are compared with published infrared spectra of C 60 H 36 samples synthesized by other techniques such as high pressure hydrogenation and zinc reduction of C 60 . Raman spectra of C 60 H 36 have not previously been reported. Based on previous data in the literature, five isomers of low-energy were selected for semiempirical quantum chemical calculations. They are one each of S 6 , T and T h symmetry and two isomers of D 3d symmetry. The calculations predict that very few IR lines will be coincident with Raman bands, even in the case of the T isomer for which t symmetry vibrations can be both infrared and Raman active, and for which the few coincident lines should be extremely weak. The interplay between theory and experiment places some strong constraints on the possible symmetries and structures of the various samples of the C 60 H 36 molecule. The results indicate that each of two samples prepared by transfer hydrogenation contains a mixture of two principal isomers, of D 3d and S 6 symmetries, the former being the major component in one, and the latter in the other, sample. The analysis also confirms a D 3d isomer as being the major component of a sample of C 60 H 36 prepared by high pressure hydrogenation and proposes the S 6 isomer as the major component of a sample prepared by zinc reduction of C 60 in aromatic solvents. q 1998 Elsevier Science B.V. All rights reserved.

1. Introduction The discovery w1x and subsequent preparation of macroscopic quantities of fullerenes w2x have led to the investigation of the properties of C 60 and other fullerenes and to attempts to prepare bulk quantities of fullerene derivatives. In these species, the

)

Corresponding author. Tel.: q33-1-45077561; fax: q33-145077100; e-mail: [email protected].

carbon–carbon bonding differs from that of both conjugated and saturated organic molecules. Addition of a functional group to a fullerene framework saturates the valencies of a framework atom which is then no longer fully available for the p electron conjugation. Because of the pyramidalisation at the fullerene surface, the local atomic orbitals of tri- and tetra-valent atoms may still have considerable overlap, more so than would be expected in a planar conjugated system with an sp 3 substituent. One can expect unusual properties to arise from

0301-0104r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 0 3 5 - 4

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R. Bini et al.r Chemical Physics 232 (1998) 75–94

the greater degree of hyperconjugation present in fullerene derivatives. Of all molecular properties, vibrations and electronic states are of special interest because their alteration, for example as a response to doping, or change in carbon atom count, may presage macroscopic behaviour with potential for practical applications. In complementary infrared and Raman spectroscopies which are used to explore vibrational states there exist underlying electronic contributions that can be explicated in terms of the derivatives of the dipole moment Žin infrared. or the polarisability tensor Žin Raman.. For systems of the size of C 60 H 36 , the observed spectra can be difficult to interpret unless supplemented by other tools or information, in particular since the caged structure of fullerenes makes it possible for a very large number of isomers to be formed, at least theoretically, for any particular species. Usually only a few isomers are predicted to be molecules of low energy, with relatively little difference in their relative energies. Thus, synthetic techniques often produce several isomers of a given fullerene, Že.g., three isomers in the case of C 78 w3x, two isomers for C 84 w4x., and these require further separation techniques in order to identify them. The initial objective of the present study was to identify the particular isomer or isomers in our samples of C 60 H 36 and, if possible, in samples that have been prepared by other chemical procedures. As has been suggested elsewhere w5x, different preparative techniques could give rise to different isomers or mixtures of isomers of C 60 H 36 . Indeed, that a mixture of isomers can be formed is indicated by the 3 He-NMR spectra of 3 He@C 60 H 36 samples, recently measured by Billups et al. w6x, in which hydrogenation of the starting material, 3 He@C 60 , was carried out by the same transfer hydrogenation method that we used w7,8x, as well as by a Birch reduction w9x. With the present wide availability of computers, the natural adjunct to the interpretation of any spectroscopic measurement is the quantum chemical simulation of the spectra, which it is possible to carry out at several levels of theory. For fullerenes, semiempirical methods of the MNDO type w10x have been successful in a variety of tasks w11x and can be used to calculate the vibrational properties of interest in order to gain adequate insight into the origin of their vibrational mode activities.

In the present work, we have prepared C 60 H 36 by the transfer hydrogenation technique w7,8x and have measured its infrared absorption and Raman spectra. The IR results have been compared with published infrared spectra of samples synthesized by other methods. No previous Raman spectra of C 60 H 36 have been reported. In order to aid analysis of the vibrational spectra of C 60 H 36 , we have simulated the infrared and Raman spectra of five possible isomers, using the MNDO method as recently extended to allow the calculation of Raman activities w12x. Our theoretical calculations, and the experimental results, confirm the existence of an ‘exclusion principle’ that clearly separates Raman and infrared activities, even when the C 60 H 36 isomer is not centrosymmetric, as in the case of the T symmetry isomer. Comparison of the various experimental and calculated vibrational spectra of C 60 H 36 , carried out in the present work, supports the conjecture that the carriers of the various spectra contain more than one isomer and that their relative proportions vary with different techniques of synthesis.

2. Experimental 2.1. Preparation Several samples of the hydrogenated fullerene C 60 H 36 were synthesised by the technique of transfer hydrogenation of C 60 w7,8x. A number of variants in material quantities, reaction duration and subsequent sublimation of anthracene derivates were employed. The procedure used for the sample whose spectra were reported previously w5x was as follows. The starting material was C 60 , 5 mg Ž7 mmol. of which was heated with 150 mg of 9,10-dihydroanthracene Ž833 mmol. in a glass ampoule sealed under a nitrogen atmosphere. The ampoule was placed in liquid tin at 3508C for 25 min. The initially dark violet melt turned rust-brown, ruby-red, orange, yellow and finally became almost colourless. During the first 10 min the reaction mixture was shaken every 2 min in order to redistribute any initially undissolved C 60 . After the reaction mixture had been cooled, the anthracene derivatives were sublimed off at 808C Ž0.2 Torr. for about 4 h. The hydrogenated fullerene C 60 H 36 was isolated as a white product.

R. Bini et al.r Chemical Physics 232 (1998) 75–94

Two recent samples of C 60 H 36 were prepared under the following conditions: 50 mg of C 60 was heated with 1878 mg of 9,10-dihydroanthracene ŽDHA. in a glass ampoule Žsealed under N2 . for 20 min at 3508C. After the reaction mixture had been cooled, the anthracene derivatives were sublimed at 968C for 4 h Žfirst sample. and an additional sublimation was carried out at 1438C for 4.5 h Žsecond sample.. Hydrogenated fullerene samples thus synthesized contained some residual impurities introduced, or formed, by the technique of transfer hydrogenation. The impurities, observed by UV absorption spectroscopy or identified by their fluorescence excitation spectra and by gas-chromatography andror mass spectrometry were anthracenic materials Ž4–5% in the recent samples., mainly anthracene, DHA and small quantities of 2,2X-dianthracene and 1,2,3,4-tetrahydroanthracene. EI–MS spectra of the recent samples showed that the only hydrogenated fullerene produced was C 60 H 36 . 2.2. Infrared and Raman spectroscopy Infrared spectra of C 60 H 36 in KBr disks were measured at room temperature between 400 and 3500 cmy1 with Fourier Transform Infrared Spectrometers ŽIFS-88, IF S66V and HR-120 Bruker instruments.. The spectrum shown in Fig. 1 corresponds to one of the two recent samples. In Table 1, the IR frequencies Žcmy1 . and relative intensities of this sample ŽI. are compared with that of an earlier sample ŽII. of C 60 H 36 w5x, also prepared by the transfer hydrogenation technique but having a greater proportion of anthracenic impurities. Table 1 also contains similar data for C 60 H 36 samples whose spectra ŽIII and IV. are published in the literature and which have been prepared by high pressure hydrogenation of C 60 w13x, and zinc reduction of C 60 in aromatic solvents w14x, respectively. In Table 1, the data for the latter are taken from the literature; frequencies not reported by these authors w13,14x were estimated from their published infrared spectra and are considered to be accurate to within a few wavenumbers. Data on the infrared spectrum of anthracene, taken from a standard compilation w15x, are also given in Table 1, where they are placed under the band numbers closest to the anthracene frequencies. Anthracene data, for both infrared and Raman

77

Fig. 1. Infrared absorption spectrum of a C 60 H 36 sample synthesized by the transfer hydrogenation technique. KBr matrix; T s 300 K.

spectra Žsee later., will be used for assessment of the presence of anthracenic impurities in the various C 60 H 36 samples. In addition to the C 60 H 36 infrared spectrum given in Fig. 1, recorded with an IFS-66V instrument at room temperature, spectra were also measured at both room temperature and at 18 K, using a Bruker HR-120 FTS instrument. Part of the 18 K spectrum is shown in Fig. 2. At 300 and 18 K, the spectra were identical. In particular, there were essentially no modifications of band profiles on lowering the temperature. This indicates that inhomogeneous broadening due to KBr matrix interactions dominate over homogeneous broadening resulting from coupling between vibrational energy levels Žsee later.. Raman spectra Ž300 scans. of C 60 H 36 at 4 cmy1 resolution were measured with a FT–Raman instrument ŽIFS 66rFRA 106., using a 270 mW Nd:YAG laser at 1064 nm as excitation source and a Ge-diode detector. The Raman spectrum is shown in Fig. 3 and tabulated frequencies and relative intensities of the principal Raman bands are given in Table 2 where they are compared with similar data obtained on our previous sample of C 60 H 36 w5x. Also in Table 2, the frequencies and relative intensities of anthracene Raman bands taken from the standard compilation w15x are given. Raman spectra of C 60 H 36 have not been reported previously in the literature, except for our earlier sample prepared by transfer hydrogenation w5x. 3. Theoretical background In this work, we simulate the infrared and Raman spectra of five isomers of C 60 H 36 with the MNDO

R. Bini et al.r Chemical Physics 232 (1998) 75–94

78

Table 1 Infrared spectra of C 60 H 36 and of anthracene: Frequencies Žcmy1 . and relative intensitiesa,b Band No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

Transfer hydrogenation sample of C 60 H 36 I Present study

Transfer hydrogenation sample of C 60 H 36 II w5x

High-pressure hydrogenation sample of C 60 H 36 III w13x

Zn reduction sample of C 60 H 36 IV w14x

2911 vs 2849 vs 2829 vs vw features in 1750–1540 region

2912 vs 2851 vs 2826 vsŽsh. 1731 m

2912 vs 2847 vs 2827 vs

2913 vs 2849 vs unresolved 1725 s

1641 w 1607 m 1511 m

1640 ms

1635 ms

1489 s 1452 ms 1422 m

1334 m 1315 m 1286 w 1273 m

1452 w 1423 w 1384 vw

1448 m

1384 w

1230 m

1174 m

1170 vw

1105 vw

wbf 1100–900

1239 m 1182 m 1155 vw 1119 w

1456 ms

1198 m 1176 m

1256 m

c 1620 w

1510 s 1490 s 1448 ms

1369 w 1327 w 1314 w 1297 w 1278 vw 1259 w 1235 w

1314 w

Anthracene w15x

1314 w 1273 s Žbr.

1272 vw

1123 m

1089 w 1039 w 958 w 953 w 940 w 922 w 896 w 878 w 869 vw 863 w 828 vw 819 vw 816 vw 791 vw 776 vw 755 mŽbr. 729 m 718 vw 699 vw 670 vw

1078 m 1038 w

1035 w 956 s

949 w 918 w 889 w

938 w 919 w 897 w

910 w Žbr. 884 s

865 w Žbr. 840 vw

810 vw

745 m 720 m 693 vw

817 w 792 vw 777 vw 742 w 713 w Žbr.

730 ms Žbr.

691 w q 661 w q

700 w

594 vw

595 w Žbr.

652 vw 635 vw 608 w 601 vw

739 s 726 s

R. Bini et al.r Chemical Physics 232 (1998) 75–94

79

Table 1 Žcontinued. Band No. 50 51 52 53 54 55 56

Transfer hydrogenation sample of C 60 H 36 I Present study 571 vw 553 w 517 w 501 vw 482 w 458 vw 421 vw

Transfer hydrogenation sample of C 60 H 36 II w5x

553 vw 523 vw 477 w 454 vw 422 w

High-pressure hydrogenation sample of C 60 H 36 III w13x

Zn reduction sample of C 60 H 36 IV w14x

575 vw 548 vw 526 w q 507 vw 470 w q 440 w Žbr. 425 vw

Anthracene w15x

474 s 465 ms

a

Relative intensities of infrared bands: vs s very strong, s s strong, ms s medium strong, m s medium, w s weak, vw s very weak. q indicates additional strength, e.g., w q ) w. b sh s shoulder; wbf s weak broad featureŽs.; br s broad. c H 2 O infrared band.

model w10x. This model has been widely used in fullerene chemistry and physics for a variety of applications which range from infrared spectral simulations to superconductivity and reactivity w11x. The use of MNDO for modelling off-resonance Raman spectra is in its infancy. In recent work w12x, we have extended the computer programme that we use for this type of calculation w16x so as to include the Raman cross-sections. Since the calculation of the force fields is already performed partially numerically, we simply add a calculation of the polarisability at each step along the lines described in Ref. w17x. Numerical differentiation and subsequent projection of the Cartesian derivatives of the polarisability into the normal modes allows the calculation of the Raman intensities. Applications agree well with experiments, and the programme has been used to model

Fig. 2. Portion Ž600–1000 cmy1 . of the infrared absorption spectrum of a C 60 H 36 sample synthesized by the transfer hydrogenation technique. KBr matrix; T s18 K.

the spectra of C 60 , C 70 w12ax and two isomers of C 78 that have C 2v symmetry w12bx. The infrared and Raman spectral lines, calculated by the MNDO model, can then be broadened by multiplication with a Gaussian lineshape function, 2

G Ž n . s exp y Ž n y n 0 . ra2 rap 0 .5

Ž 1.

where n is the excitation wavenumber, n 0 is the MNDO calculated vibrational mode wavenumber, and a is a constant, all in cmy1 . Both homogeneous and inhomogeneous broadening are present in the samples of C 60 H 36 whose spectra have been measured. At present we cannot identify the source of homogeneous broadening in terms of the density of vibrational states that are degenerate with each spectroscopically active fundamental. In molecules as large as fullerenes and their derivatives, the density of states due to overtones and combination levels grows very rapidly. In these cases it is reasonable to make the empirical assumption that the constant a of Eq. Ž1. takes the energy-dependent form a Ž E . s 1 q 0.5 ln N Ž E . Ž 2. Ž . where N E is the vibrational density of states at

Fig. 3. Raman spectrum of a C 60 H 36 sample synthesized by the transfer hydrogenation technique.

R. Bini et al.r Chemical Physics 232 (1998) 75–94

80

Table 2 Raman spectra of C 60 H 36 prepared by transfer hydrogenation, and Raman data of anthracene. Frequencies Žcmy1 . and relative intensities Band No.

C 60 H a36 I Present study

C 60 H a36 II w5x

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

2913 vs 2853 vs q 2830 vs Žsh. 1736 m 1714 m 1605 w

2911 s 2852 vs 2829 sŽsh.

1508 w 1462 m

1600 w 1558 m 1497 vw 1481 m 1462 m 1402 s

Anthraceneb w15x

1554 Ž7.5 . 1480 Ž 4 . 1400 Ž 47 .

1386 w 1276 m 1262 w

1257 Ž 5 .

1213 w 1186 w 1163 w

1183 Ž 9 . 1160 Ž 5 .

1212 m

1154 w 1039 w 1015 w

1039 w

484 m 448 w

1008 w 753 m 484 m 458 vw 444 vw 395 m

395 w 313 w 264 w 211 s 175 w 136 vw 85 w q

239 w 207 m 180 w 128 w

1004 Ž 5 . 750 Ž 10 .

394 Ž 12 .

122 Ž 5 .

a

Relative intensities of Raman bands of C 60 H 36 : vs s very strong, s s strong, m s medium, w s weak, vw s very weak. q indicates additional strength, e.g; vs q ) vs; w q ) w. sh s shoulder. b Anthracene Raman spectral data: relative intensities Žin italics. and frequencies of bands from w15x.

energy E. The calculation of the density of states can be carried out using the extended algorithm of Stein and Rabinowitch w18x, based on the calculated n 0 values. Although the above treatment provides the possibility to estimate the extent of homogeneous broadening, this can only be tested by fitting to observed band profiles if the inhomogeneous broadening component is relatively small. Since the IR spectra of our samples of C 60 H 36 showed no change in band profiles in going from room temperature to 18 K, as mentioned earlier, it was clear that inhomogeneous broadening due to KBr matrix interactions

dominates the band profiles at all frequencies, thus making it unprofitable to carry out lineshape calculations in this case.

4. Results and discussion 4.1. Low energy isomers of C6 0 H36 4.1.1. Thermodynamic considerations In this study, the two standard techniques of infrared and Raman vibrational spectroscopies are

R. Bini et al.r Chemical Physics 232 (1998) 75–94

81

Fig. 4. Structures of five low energy isomers of C 60 H 36 , represented: Ža. as 3D space-filling and Žb. by Schlegel diagrams. Black balls stand for bare C atoms, white balls for CH groups; their radii are arbitrary. Table 3 MNDO results: Electronic energy differences, cmy1 , zero point energy ŽZ.P.E.. differences, cmy1 , and total energy differences, cmy1 , of the five isomers studied Isomer

Electronic energy difference

ZPE difference

Total energy difference

D 3d ŽC,K. T S6 Th D 3d

0 1170 1193 2527 13 508

0 y355 73 317 123

0 815 1266 2844 13 631

R. Bini et al.r Chemical Physics 232 (1998) 75–94

82

Table 4 ˚ 4ramu. cross-sections of the D 3d ŽC–K. isomer. The Calculated vibrational frequencies Žscaled, cmy1 and IR Žkmrmol. and Raman ŽA harmonic frequencies were scaled by a factor of 0.9

n

R

n

– – – – – –

3 52 2 20 79 3039

367 754 1121 1229 1739

– – – – –

10 26 40 16 333

409 811 1154 1246 2880

– – – – –

1 – – – –

425 733 1120 1246

– – – –

– – 2 2

– – – – – – – – – –

23 6 8 36 5 23 41 2 211 1292

216 457 695 911 1088 1164 1224 1304 2878 2904

– – – – – – – – – –

– – – – 1

– – – – –

283 720 1115 1231 2897

4 8 12 2 1

– – – – –

– 1 1

– – –

IR

R

n

– – – – –

– 7 16 74 189

491 911 1177 1268 2888

466 845 1134 1293

– – – –

– – – –

15 1 54 9 14 8 27 31 69 1402

329 521 726 958 1103 1170 1243 1318 2881

– – – – – – – – –

– 11 – 1 –

– – – – –

499 811 1122 1304

287 821 1142 1228 2880

1 1 8 7 1

– – – – –

288 488 687

– 1 1

– – –

IR

n

R

R

n

– – – – –

4 1 31 21 612

513 948 1188 1334 2894

– – – – –

72 – 18 1 109

546 963 1149 1339

– – – –

– – – –

612 1035 1185 2882

– – – –

– – – 75

14 – 17 1 23 210 3 22 160

369 570 767 971 1121 1186 1252 1447 2888

– – – – – – – – –

10 11 35 4 35 21 22 13 291

415 634 794 1046 1138 1194 1262 1631 2892

– – – – – – – – –

7 1 36 15 17 55 24 20 276

– – – –

– – – –

566 854 1148 1338

– – – –

– – – –

607 966 1170 1702

– – 3 –

– – – –

508 840 1165 1248 2887

1 4 – 5 4

– – – – –

538 892 1174 1265 2895

– – – 13 3

– – – – –

589 1053 1192 1309 2905

– 2 4 6 67

– – – – –

311 504 719

– 1 26

– – –

371 528 764

– – 10

– – –

399 555 826

7 2 –

– – –

IR

IR

IR

R

A 1g 186 597 1069 1208 1485 2905

A 2g 404 667 1065 1234 2897 Eg 204 419 641 853 1081 1150 1215 1284 1712 2899

A 1u 265 697 1094 1197 2882

A 2u 231 706 1104 1204 1485

Eu 266 439 600

R. Bini et al.r Chemical Physics 232 (1998) 75–94

83

Table 4 Žcontinued.

n

IR

R

n

IR

R

n

IR

R

n

IR

R

n

IR

R

1 – – 2 1 1 19

– – – – – – –

889 1088 1161 1234 1300 2878 2904

1 1 4 5 – – 101

– – – – – – –

970 1098 1173 1243 1329 2881

– 1 36 26 3 4

– – – – – –

991 1119 1194 1252 1447 2889

– 12 – 5 5 22

– – – – – –

1023 1133 1210 1261 1631 2892

2 – 10 3 – 1

– – – – – –

Eu 875 1064 1144 1215 1289 1731 2899

used to study C 60 H 36 . Because of the size of this hydrogenated fullerene system, determination of skeletal structure from analysis of the spectra is backed up by semiempirical quantum calculations

performed at the MNDO level. The choice of the bond connectivity of this molecule Žwhich could theoretically have over 10 14 possible isomers. does pose a significant problem which, however, is not

Table 5 ˚ 4ramu. cross-sections of the T isomer. The harmonic Calculated vibrational frequencies Žscaled, cmy1 and IR Žkmrmol. and Raman ŽA frequencies were scaled by a factor of 0.9

n

R

n

– – – – –

3 – – 4 165

410 755 1126 1217 2867

– – – – –

21 5 10 20 15

2 – – – 3 – – 1 10 8 27 – – 9

7 4 1 3 4 – 1 20 113 10 4 – 10 198

IR

R

n

– – – – –

1 – 10 2 266

488 825 1141 1228 2894

– – – – –

44 2 2 5 1138

518 862 1166 1261 2912

294 723 1109 1255 2872

– – – – –

11 3 14 48 128

379 762 1131 1269 2889

– – – – –

1 33 27 32 291

261 421 541 663 828 945 1087 1135 1180 1225 1272 1450 2867 2893

– – – 2 1 – 3 1 4 1 – 10 1 73

– – – – 1 1 6 5 – 45 17 2 19 571

290 431 545 674 848 972 1108 1146 1182 1236 1274 1452 2872 2902

– – – 13 1 – 3 1 1 12 – 1 – 9

– 2 1 12 – 1 7 – 12 – 6 13 23 295

IR

IR

n

R

R

n

– – – – –

65 – 1 2 1636

583 939 1172 1341

– – – –

1 1 18 –

442 930 1160 1295 2911

– – – – –

3 1 30 11 1792

508 983 1187 1450

– – – –

6 11 85 4

334 473 569 719 860 993 1115 1151 1196 1238 1284 1484 2872 2903

6 1 1 – 1 5 17 3 2 11 – 1 7 11

9 1 14 4 2 – 8 47 9 36 15 32 253 383

355 504 613 747 875 1008 1117 1158 1199 1252 1294 1630 2888 2911

1 – – 1 – – – 9 1 2 – – – 82

10 – 9 42 2 1 19 5 18 22 1 16 24 1

IR

IR

R

A 233 702 1107 1196 1485

E 206 670 1077 1197 1632

T 176 414 522 653 786 934 1077 1124 1165 1216 1254 1334 1631 2889

R. Bini et al.r Chemical Physics 232 (1998) 75–94

84

Table 6 ˚ 4ramu. cross-sections of the S 6 isomer Calculated vibrational frequencies Žscaled, cmy1 and IR Žkmrmol. and Raman ŽA

n

R

n

– – – – – – – – – –

4 17 2 7 1 2 8 32 401 1850

346 496 671 909 1091 1153 1214 1304 2867 2920

– – – – – – – – – –

27 5 6 40 4 30 23 21 109 995

1 2 4 6 – 5 3 7 1 9

– 4 7 2 1 7 17 5 – 82

IR

R

n

– – – – – – – – – –

8 14 4 7 17 50 5 2 157 665

365 509 720 948 1112 1159 1232 1330 2879 2920

225 459 701 944 1100 1163 1229 1326 2867

– – – – – – – – –

11 2 22 1 4 70 67 33 241

– – – – – – – – – –

280 544 699 887 1103 1158 1217 1301 2867 2924

– – 2 4 – 1 3 4 5 12

– – – – – – – – – –

287 485 671 916 1088 1163 1232 1327 2867 2920

1 – 1 4 2 5 9 3 10 19

IR

R

n

– – – – – – – – – –

10 31 32 1 16 51 1 27 100 858

392 579 761 973 1121 1178 1248 1370 2886 2924

330 526 718 965 1111 1177 1237 1366 2879

– – – – – – – – –

9 15 17 6 37 18 12 7 31

– – – – – – – – – –

305 569 722 896 1116 1169 1225 1328 2879

2 4 4 – 3 – – 5 1

– – – – – – – – – –

303 502 734 978 1108 1177 1239 1369 2879

– – 13 2 3 1 16 3 7

IR

R

n

– – – – – – – – – –

– 30 35 – 14 20 36 11 78 746

425 627 801 1053 1127 1194 1262 1439 2895

– – – – – – – – –

– – 8 4 1 16 1 85 619

372 581 757 970 1120 1195 1252 1438 2886

– – – – – – – – –

2 7 11 9 57 8 16 12 329

422 601 800 1018 1136 1200 1264 1600 2895

– – – – – – – – –

9 16 48 2 22 48 52 36 902

– – – – – – – – –

323 595 778 979 1123 1174 1230 1366 2886

1 1 2 – 6 7 7 2 –

– – – – – – – – –

450 631 815 1007 1144 1192 1255 1439 2895

5 – – 1 2 14 35 – 48

– – – – – – – – –

– – – – – – – – –

336 539 756 990 1116 1194 1257 1438 2886

2 – 10 2 2 9 4 5 15

– – – – – – – – –

406 575 829 1036 1129 1201 1267 1600 2895

5 1 4 – 11 2 1 – 16

– – – – – – – – –

IR

IR

R

Ag 188 460 647 852 1087 1144 1204 1283 1671 2902 Eg 201 435 640 866 1075 1147 1217 1268 1667 2901 Au 229 518 685 850 1101 1150 1203 1266 1665 2901 Eu 266 447 609 872 1072 1144 1216 1280 1670 2901

R. Bini et al.r Chemical Physics 232 (1998) 75–94

within the scope of the present paper. We have assumed that previous studies of the distribution of 36 CH bonds on the surface of C 60 w19,20x have been complete enough to generate a set of the most pertinent low energy isomers of C 60 H 36 . These are five in number ŽFig. 4., one or more of which should correspond to the isomers synthetically available. We have thus performed calculations of the energies

85

ŽTable 3. and infrared and Raman spectra ŽTables 4–8. of an isomer of T h symmetry ŽTable 7., an isomer of T symmetry ŽTable 5., an isomer of S 6 symmetry ŽTable 6. and two isomers of D 3d symmetry ŽTables 4 and 8.. In agreement with Clare and Kepert w20x we find that the most stable structure has D 3d symmetry. In Table 3, we report the energies of the optimised

Table 7 ˚ 4ramu. cross-sections of the Th isomer Calculated vibrational frequencies Žscaled, cmy1 and IR Žkmrmol. and Raman ŽA

n

R

n

– – –

22 – 493

426 1193 2885

– – –

2 5 286

518 1233 2909

– – –

14 316 467

368 1184 2886

– – –

12 17 295

– – – – – – –

22 22 92 2 – 19 26

363 608 877 1090 1178 1313 2904

– – – – – – –

– – –

– – –

579 1122

– – –

– – –

– 1 – 2 – 2 1 106

– – – – – – – –

IR

R

n

– – –

43 1 3419

796 1251

– –

2 –

921 1359

– –

3 2

670 1213 2908

– – –

6 44 602

723 1249

– –

34 3

908 1312

– –

3 121

2 3 138 – 28 29 27

375 627 959 1103 1197 1338 2905

– – – – – – –

11 9 5 – 22 – 427

414 675 988 1126 1201 1363 2907

– – – – – – –

2 1 5 1 17 2 1676

464 726 1045 1129 1234 1689

– – – – – –

1 16 – 30 3 22

– –

– –

712 1193

– –

– –

828 120

– –

– –

959 1325

– –

– –

434 1139

– –

– –

547 1165

– –

– –

702 1244

– –

– –

995 1355

– –

– –

300 568 867 1089 1196 1302 2871

– 1 19 2 1 53 2

– – – – – – –

309 606 897 1114 1206 1337 2886

– 2 26 29 16 3 30

– – – – – – –

419 686 972 1126 1224 1358 2904

13 – – 4 8 25 3

– – – – – – –

492 749 1046 1157 1247 1680 2906

– 49 5 – 3 1 6

– – – – – – –

IR

n

R

IR

IR

n

R

IR

R

Ag 425 1069 1710 Eg 198 1107 1681 Tg 214 517 791 1073 1156 1258 2871 Au 258 1096 2905 Eu 304 1070 2904 Tu 269 519 807 1077 1183 1260 1700 2908

R. Bini et al.r Chemical Physics 232 (1998) 75–94

86

Table 8 ˚ 4ramu. cross-sections of the D 3d isomer Calculated vibrational frequencies Žscaled, cmy1 and IR Žkmrmol. and Raman ŽA

n

R

n

– – – – – –

7 29 81 49 77 1808

325 731 1113 1251 1633

– – – – –

3 36 29 6 301

396 796 1158 1261 2859

– – – – –

2 4 11 24 23

408 905 1164 1278 2873

– – – – –

2 1 – – 57

414 777 1119 1262

– – – –

– – – 1

469 825 1130 1279

– – – –

– – – 13

– – – – – – – – – –

15 1 20 27 3 16 56 29 129 500

229 465 665 931 1082 1173 1229 1363 2856 2911

– – – – – – – – – –

18 1 4 2 30 83 30 9 55 1113

341 512 699 964 1112 1183 1238 1375 2867

– – – – – – – – –

– – – – –

– – – – –

339 725 1103 1226 2909

– 1 – – –

– – – – –

507 791 1145 1274

– 6 14 1 1

– – – – –

348 793 1126 1256 2855

4 – 1 14 2

– – – – –

1 – 1

– – –

288 497 703

– 3 11

– – –

IR

IR

n

R

R

n

– – – – –

14 1 62 3 132

508 948 1209 1381 2883

– – – – –

71 – 9 8 1829

585 984 1148 1366

– – – –

– – – –

644 1035 1181 2862

– – – –

– – – 9

14 8 11 17 35 101 16 17 172

395 586 740 973 1132 1191 1263 1429 2874

– – – – – – – – –

7 6 30 4 12 2 42 5 278

427 628 796 1040 1145 1206 1274 1578 2880

– – – – – – – – –

4 13 74 4 11 42 74 46 1074

– – – 1

– – – –

548 881 1155 1287

– – – –

– – – –

645 1002 1165 1372

– – – –

– – – –

471 818 1165 1275 2868

8 1 2 – 15

– – – – –

546 902 1197 1361 2879

1 19 7 11 6

– – – – –

611 1004 1218 1409 2911

1 1 10 – 22

– – – – –

304 511 727

1 – 7

– – –

321 517 736

– – 16

– – –

396 576 848

3 4 –

– – –

IR

n

R

IR

IR

R

A 1g 194 691 1103 1245 1409 2911

A 2g 404 663 1103 1199 2909

Eg 199 443 644 884 1070 1151 1224 1280 1635 2909

A 1u 278 663 1098 1181 2874 A 2u 232 686 1103 1222 1634

Eu 269 468 593

R. Bini et al.r Chemical Physics 232 (1998) 75–94

87

Table 8 Žcontinued.

n

IR

R

n

IR

R

n

IR

R

n

IR

R

n

IR

R

4 – 1 4 – – 4

– – – – – – –

921 1095 1163 1237 1365 2857 2911

4 – 9 19 – – 30

– – – – – – –

978 1120 1182 1247 1379 2864

3 6 1 – – –

– – – – – –

984 1127 1204 1263 1429 2873

2 – 10 2 8 2

– – – – – –

1036 1138 1210 1271 1578 2882

– 8 17 57 – 140

– – – – – –

Eu 866 1065 1142 1223 1277 1634 2909

structures relative to the most stable isomer of D 3d symmetry. The latter is the isomer referred to as D 3d ŽCK. in Ref. w5x and we will continue to use this designation in the present work; the other, less stable, D 3d isomer is not graced with an additional identifying symbol. The energy values of these five isomers agree precisely with those calculated by Buhl ¨ et al. w21x using MNDO. However, when the MNDO geometries were re-optimized at the SCFr321 G level, Buhl ¨ et al. w21x found the resulting relative energies of the D 3d ŽCK. and T isomers to be inverted with respect to the previous order, so that the T isomer becomes the most stable species at this ab initio level. We note that addition of the Žcalculated. zero-point energies decreases the energy gap between the most stable D 3d compound calculated at the MNDO level and the next most stable species, the T isomer ŽTable 3.. That the zero-point energy for the T species is smaller than for the other four isomers can be taken as an indication that the steric strain associated with the creation of the CH groups is smallest in the T isomer. Because the spread of the calculated energies of four of the isomers in Table 3 is less than 3000 cmy1 it is not possible, on the basis of these energies alone, to assign which isomer or isomers correspond to the measured spectra reported in Tables 1 and 2. One can nevertheless conclude from the calculated energies that thermodynamics appear to favour the D 3d ŽCK., T and S 6 isomers as being the most stable species. These will be seen to be the most significant isomers implicated by our vibrational analysis. 4.1.2. Centrosymmetry considerations Let us consider the number of bands that could, in principle, coincide in the two spectra Žinfrared and

Raman. of the five isomeric molecules. They are zero in the D 3d , T h and S 6 symmetry species, whereas in T symmetry the t vibrational modes can be active in both spectroscopies and so give rise to a maximum of 70 coincident infrared and Raman active modes. Inspection of our infrared and Raman spectra of C 60 H 36 ŽTables 1 and 2. measured for sample I and II, respectively, show no more than 3 or 4 lines whose frequencies are the same in both spectra. This observation appears to indicate a species in which infrared and Raman active modes are divided by symmetry, and therefore seems to favour a centrosymmetric structure, which would exclude the T isomer. But this inference is not totally conclusive since we will show that an apparent separation of infrared and Raman activity can exist even for the T isomer. We compiled a list of the normal modes of the T isomer that are calculated ŽTable 5. to have at least 4% of the intensity of the most active mode in both spectroscopies. If one excludes the C–H stretching region, where the density of states is very high, there are only ten bands that are expected to coincide in frequency. For all of them the absolute Raman and infrared intensities are very weak. The frequencies reported in Tables 4–8 are the calculated harmonic vibrational frequencies scaled by the conventional empirical factor of 0.9 w22x. The bands shared by the two spectra for the T symmetry isomer are calculated at 674, 747, 1151, 1165, 1182, 1199, 1225, 1238, 1252 and 1453 cmy1 . The most likely to be observable, from the intensity viewpoint, would be located at 1165 and 1238 cmy1 . These two bands are predicted to have about the same intensity in the infrared but 1165 cmy1 to be more than 3 times more intense than the 1238 cmy1 band in Raman. The nearest experimental Žcoincident pairs of. bands are

88

R. Bini et al.r Chemical Physics 232 (1998) 75–94

at 1155 and 1273 cmy1 in spectrum I, in adequate agreement with calculation Žscaling factors 0.89 and 0.93 would be needed in order to fit the 1155 and 1273 cmy1 bands, respectively., but the relative intensities in both infrared and Raman are not at all consistent with the calculated values. Spectrum II has only one band in this spectral region that is coincident in frequency in the infrared and Raman spectra. This is a weak band at 1038 cmy1 . Thus, the data in Tables 1 and 2 do not support the T isomer assignment. Although the T isomer appears to be excluded by this comparison between experimental and theoretical results, there is a point of general interest that arises from the results of the MNDO model calculations concerning the number of expected observable common IR and Raman bands for the T isomer. The prediction of a very small number of observable common bands, for a case where a maximum of 70 is theoretically possible, suggests that sphericity still plays a major role for the T symmetry species as far as infrared and Raman spectra of C 60 H 36 are concerned. The presence of an ‘IRrRaman exclusion rule’ has already been noticed empirically for another non-centrosymmetric fullerene species, the D 2 isomer of C 76 w3x. In a Herzberg–Teller scheme, infrared intensity is due to the mixing of the ground state with optically allowed states w23x, while the Raman intensity is brought about by the mixing of the latter states with other excited states w24x. In non-centrosymmetric molecules, the two sets of states can coincide. The result of the calculations and of the spectra of C 76 and of C 60 H 36 is taken to show that the roundness of fullerenes and their derivatives keeps these states separate even when mixing is formally allowed. 4.2. Comparison of experimental and calculated infrared and Raman spectra of C6 0 H36 4.2.1. Infrared spectra We first consider possible impurities manifest in the infrared spectra. The medium strong band at about 1635 cmy1 in spectra III and IV ŽTable 1., which correspond to C 60 H 36 samples produced by high pressure hydrogenation w13x and by Zn reduc-

tion w14x, respectively, exists as a weak feature in spectrum II and possibly in I, which are of C 60 H 36 produced by the transfer hydrogenation technique. This band is due to traces of water, as confirmed by further absorptions observed in the 3400 cmy1 region Žnot shown in Fig. 1., most strongly in spectra III and IV. Anthracenic impurities are not very marked in the spectra of Table 1. Although there are C 60 H 36 infrared bands at or close to frequencies of several anthracene bands ŽTable 1., inspection of this table shows that the relative intensities of these particular C 60 H 36 bands do not, in general, follow those expected for anthracene. Thus, anthracene is difficult to detect in these samples by infrared spectroscopy alone. A conservative conclusion is that the C 60 H 36 bands occurring at anthracene frequencies could have components of both anthracene and C 60 H 36 . We now compare the two infrared spectra I and II, detailed in Table 1, of C 60 H 36 produced by the transfer hydrogenation technique. A large number of the features have the same frequencies Žwithin experimental error. in the two spectra but a certain number are present only in one or the other, e.g., in I, 1489, 1334, 1286, 1239, 1155, 1119, 1089, 1039, 878, 863, 828, 791, 776, 670, 608, 601, 501 cmy1 ; in II, 1731, 1607, 1511, 1384, 1256, 1198, 1078, 652 cmy1 . It is remarkable that most of the bands just mentioned as appearing only in spectrum I and not in II are observed in the infrared spectrum III obtained for a sample of C 60 H 36 synthesized by high-pressure hydrogenation w13x, and that most of the bands detailed as being in II and not in I occur in the infrared spectrum IV of a sample of C 60 H 36 produced by Zn reduction w14x. In fact, there are great similarities between the infrared spectra I and III as far as frequencies are concerned, although relative intensities differ in some cases. The most striking differences between I and III are the existence of a medium intensity band at 1422 cmy1 in I, absent in III, whereas a weak band in III at 1369 cmy1 is not observed in I. There are also similarities between spectra II and IV, as mentioned above, although in general these spectra differ more than spectra I and III do. These differences between spectra II and IV were remarked in an earlier study w5x. The global results indicate that spectra I and III correspond to similar isomers or isomeric mixtures,

R. Bini et al.r Chemical Physics 232 (1998) 75–94

somewhat different from those of spectra II and IV. Since the C 60 H 36 sample of spectrum III was found in X-ray and electron diffraction studies w25x to be most closely modelled by a structure having D 3d symmetry, with possibly some admixture of a component of S 6 symmetry w13,25x, we will consider initially that these assignments are valid for the carrier of spectrum I and we will examine whether the calculated infrared spectrum supports this conjecture. An important difference between spectra I and III concerns the C–H stretch region Žbands No. 1, 2, 3 of Table 1.. The order of their relative intensities is markedly different for spectra I and III. In spectrum I Žand II. the apparent intensity order is 3 ) 2 ) 1, whereas in III it is 1 ) 2 ) 3 Žand in IV it is 2 ) 1, band 3 being unresolved.. A plot of the calculated infrared C–H stretch frequencies and intensities given in Tables 4–8 for the five C 60 H 36 isomers, shows that these features can be grouped quite naturally to form three bands Ž1, 2 and 3. for each isomer. These plots give the following expected intensity order of the CH region bands: D 3d ŽCK.: 1 ) 3 G 2; T: 1 ) 2 4 3; S 6 : 2 ) 3 G 1; T h : 1 ) 2 4 3; D 3d : 2 ) 1 4 3. Thus, the observed order in spectrum III is most consistent with that predicted for the D 3d ŽCK. structure, whereas the order observed in spectra I, II and IV is less well predicted by the calculations, the closest match being to S 6 . It should be remarked, however, that the predicted intervals between bands 1 and 2, for D 3d ŽCK. Žf 7 cmy1 ., T Žf 20 cmy1 ., S 6 Žf 24 cmy1 ., T h Žf 22 cmy1 . and D 3d Žf 29 cmy1 . are much less than the 60 cmy1 observed, whereas the predicted intervals of 10–20 cmy1 between bands 2 and 3 of the various isomers are much closer to the observed value, 20 cmy1 . Thus, there is some uncertainty as to whether the pattern of the calculated CH stretch frequencies can be correlated with the observed order as we have done above. Furthermore, the relatively small interval Ž20 cmy1 . observed between bands 2 and 3, as compared with their combined FWHM of about 67 cmy1 makes the relative intensities of the two underlying components somewhat conjectural. However, fitting the CH stretching region of spectrum I with 3-component ŽGaussian plus Lorentzian. features indicated that the relative intensities of these component peaks is indeed in the

89

order 1 ) 3 ) 2, i.e., in agreement with the predictions for the D 3d ŽCK. isomer. Concerning the general validity of calculated infrared intensities we remark, as a word of caution, that even for well studied molecules such as benzene, simulation of the infrared intensities of CH stretches is remarkably complicated w26x and requires terms of order higher than the quadratic used here. Furthermore, MNDO simulation of infrared intensities has been found to be less accurate than that of Raman activity w3,12x, so that we will eventually examine the latter for a more consistent picture. Nevertheless, it is gratifying that the relative intensities of the C–H stretch bands in spectrum III match those predicted for one of the D 3d isomers since, as mentioned above, the major component of the spectrum III C 60 H 36 sample has a structure of D 3d symmetry as determined by X-ray and electron diffraction studies w25x. An attempt was made also to choose between the various isomers by comparing the calculated bands in the spectral region 400–2000 cmy1 with the experimental frequencies and relative intensities. For the simulated infrared spectrum ŽTables 4–8., the comparison was limited to those bands calculated to have an intensity greater than about 8 kmrmol. A comparison carried out in detail for spectra I and III showed that, with few exceptions, experimental bands can be found for both spectra within 20 cmy1 of calculated band frequencies of all five isomers ŽFig. 5., with average differences between experimental and calculated frequencies in the range 6–10 cmy1 . This density of calculated band frequencies precluded firm assignment of the infrared spectra I and III for comparison with calculated band frequencies and intensities, apart from the C–H stretch region discussed earlier. A similar conclusion was drawn from spectra II and IV. 4.2.2. Raman spectra The frequencies and relative intensities of the C 60 H 36 Raman spectrum of Fig. 3 are given in Table 2 as spectrum I. The corresponding data for the C 60 H 36 sample studied in Ref. w5x are indicated as spectrum II in Table 2. Comparison of frequencies with those of anthracene ŽTable 2. show that the carrier of Raman spectrum II is contaminated with anthracene, as previously established on the basis of

90

R. Bini et al.r Chemical Physics 232 (1998) 75–94

electronic spectroscopy w5x. In particular, the strong band in II at 1402 cmy1 is a very characteristic anthracene band w15x. The absence of this band in Raman spectrum I shows that there is much less anthracenic impurity in this sample of C 60 H 36 , in agreement with other analytical determinations, and confirms that the apparent bands of anthracene in infrared spectrum I ŽTable 1., discussed above, are largely due to vibrations of C 60 H 36 itself. We next examine the C–H stretch region of the

Raman spectra of C 60 H 36 . The bands numbered 1, 2 and 3 in Table 2 have the relative intensity order 2 ) 1 ) 3 in both Raman spectra I and II. Theoretical calculations ŽTables 4–8. predict the following intensity orders for the various isomers: D 3d ŽCK., T, D 3d : 1 ) 2 ) 3; S 6 : 2 ) 1 ) 3; T h : only two bands predicted, for which 1 4 2. The predicted interval between the first two bands is only about 18 cmy1 , instead of the 60 cmy1 observed, while the calculated interval between the second and third band is

Fig. 5. Calculated infrared absorption spectra Žstick spectra. of five isomers of C 60 H 36 .

R. Bini et al.r Chemical Physics 232 (1998) 75–94

more satisfactory. Caution similar to that expressed above in comparing experimental and simulated infrared bands in the CH stretch region is called for here. With all due caution we can, nevertheless, conclude that our CH stretch Raman band intensity results favour S 6 as an important isomeric component in the carriers of both Raman spectra I and II. We now examine the rest of the Raman spectra. Quite intense Raman bands are predicted for the S 6 species at 1671 and 1667 cmy1 , and a weaker band

91

at 1600 cmy1 ŽTable 6 and Fig. 6.. Although a weak band exists in the 1600 cmy1 region in both Raman spectra I and II, the other two bands were not clearly observed; however, examination of both spectra indicates weak broad structures in this spectral region. There are no other regions of the calculated Raman spectra that would be distinctive for an S 6 symmetry species. A medium intensity band at 484 cmy1 in both spectra could correspond to one or more of the

Fig. 6. Calculated Raman spectra Žstick spectra. of five isomers of C 60 H 36 . For convenience, the intensities are cut off at a maximum of 10000 in arbitrary units in the CH stretch region. For calculated Raman cross-sections, see Tables 4–8.

92

R. Bini et al.r Chemical Physics 232 (1998) 75–94

following predicted bands: D 3d ŽCK. at 513 cmy1 , S 6 at 509 cmy1 , T at 488 cmy1 . A notable observation is the existence of two medium intense bands at 1736 and 1714 cmy1 in spectrum I, respectively, absent in spectrum II. The only C 60 H 36 isomer to have calculated bands in this precise region is the D 3d ŽCK. species. This isomer is predicted to have reasonably intense bands at 1739 and 1712 cmy1 , respectively, ŽTable 4 and Fig. 6., which very closely match the observed bands in spectrum I. However, it is also possible to consider the two observed bands as being due to the S 6 isomer, which is calculated to have quite intense Raman bands at 1671 and 1667 cmy1 . To the 1671 and 1667 cmy1 frequencies would correspond factors of 0.86 and 0.88, respectively, for correcting the calculated harmonic frequencies. These values are very reasonable; we recall that we used a uniform scaling factor of 0.9 to produce the frequencies given in Tables 4–8. We further remark that the three Raman bands at 1630, 1631 and 1632 cmy1 , calculated to be the closest T isomer frequencies, are predicted to be weak bands. A comparison of the calculated Raman spectra of the D 3d ŽCK., S 6 and T isomers ŽFig. 6. indicates that it would be difficult to find distinctive assignment differences between the spectra of these isomers apart from the 1670–1750 cmy1 region discussed above. We note, for example, that the medium intensity Raman band observed in both spectrum I and II at 1462 cmy1 could nominally be assigned to either D 3d ŽCK. or T structures, for both of which a relatively intense Raman band is predicted at 1485 cmy1 , or, alternatively to the S 6 isomer for which bands are predicted at 1438 and 1439 cmy1 . Finally, we examine the low frequency region where are observed in spectrum I weak bands at 175, 264 and 313 cmy1 and a strong band at 211 cmy1 , and in spectrum II weak bands at 180 and 239 cmy1 and a medium intensity band at 207 cmy1 . The observed bands at 211 and 207 cmy1 could correspond to the strongest calculated bands in this spectral region, 204, 206 and 201 cmy1 for the isomers D 3d ŽCK., T and S 6 , respectively; the weak bands at 175 ŽI. and 180 cmy1 ŽII. could have as assignments the bands calculated at 186, 176 and 188 cmy1 for D 3d ŽCK., T and S 6 , respectively; 239 cmy1 ŽII. andror 264 cmy1 ŽI., the S 6 band at 225 cmy1

andror the T symmetry 233 cmy1 band; the 313 cmy1 band ŽI. could correspond to bands calculated at 329 cmy1 ŽD 3d ŽCK.., 334 cmy1 ŽT. andror 330 cmy1 ŽS 6 .. Comparison between calculated and observed Raman spectra gives the following global conclusions. First of all, it is clear that the results do not support assignment of C 60 H 36 to the T symmetry isomer. The principal conclusion is that the results are consistent with the two isomers, D 3d ŽCK. and S 6 , being present in each of the carriers of spectra I and II, with D 3d ŽCK. being the major component in spectrum I and S 6 in spectrum II. It is of interest that the C 60 H 36 sample studied in Raman spectrum II was previously assigned as having the S 6 isomer as an important component on the basis of both vibrational and electronic spectroscopy w5x. These conclusions are compatible with our infrared spectra results. They are also compatible with the 3 He-NMR spectra of 3 He@C 60 H 36 samples, recently measured by Billups et al. w6x, in which hydrogenation of the starting material, 3 He@C 60 , was carried out by the same transfer hydrogenation method that we used w7,8x. Billups et al. w6x observed two NMR signals which, of the 3 He chemical shift positions calculated for the five isomers of our interest, are closest to the values calculated for the D 3d ŽCK. and S 6 isomers. At present, it is not possible to make quantitative conclusions concerning the relative proportions of the D 3d ŽCK. and S 6 isomers in the various samples under discussion in our work.

5. Conclusion The task of identifying, by vibrational spectroscopy, the C 60 H 36 isomers synthesized by various methods has proved to be quite arduous, in part because of the almost inevitable presence of impurities resulting from the particular techniques of synthesis. It was also an intrinsically difficult task because of the complexity of the spectra and the probable presence of more than one isomer. Thus, it has been essential for analysis of the observed spectra to use the results obtained by semiempirical quantum chemical calculations of IR and Raman frequencies and band strengths on five low energy isomers of C 60 H 36 . Our IR and Raman data suggests that each

R. Bini et al.r Chemical Physics 232 (1998) 75–94

of two samples prepared by transfer hydrogenation contains a mixture of two principal isomers, of D 3d Žlowest energy form. and S 6 symmetries, the former being the major component in one, and the latter in the other, sample. From published IR spectra, we also conclude that the D 3d isomer is the major component of a sample of C 60 H 36 prepared by high pressure hydrogenation of C 60 w13x. Our analysis also allows us to conclude that C 60 H 36 prepared by zinc reduction of C 60 in aromatic solvents w14x contains the S 6 isomer as a major component. The results of the present study clearly demonstrate that different methods of synthesis prepare quantitatively different mixtures of isomers of C 60 H 36 . In these syntheses, the initial and subsequent hydrogen atom additions to C 60 may create some distortion of the fullerene cage, making some sites more reactive than others. The regioselectivity of subsequent addition of hydrogen could therefore, in a certain sense, be predetermined by previous addend sites. Thus, it is conceivable for these kinetically controlled addition reactions to produce mixtures of isomers. Detailed understanding of these processes requires more work on the reaction mechanisms, in particular concerning the interconversion of isomers of similar energy during the period of synthesis, as well as on the influence of experimental conditions on isomer production, with the objective of obtaining the most stable isomer as a unique product.

w5x

w6x

w7x

w8x w9x

w10x w11x

w12x

w13x w14x

w15x w16x

Acknowledgements We are grateful for support from the European HCM-Network Contracts CHRX-CT94-0614 and ERB FMRX-CT97-0126.

w17x w18x w19x

References w1x H.W. Kroto, J.R. Heath, S.C. O’Brien, R.F. Curl, R.E. Smalley, Nature 318 Ž1985. 162. w2x W. Kratschmer, L.D. Lamb, K. Fostiropoulos, D.R. Huff¨ man, Nature 347 Ž1990. 354. w3x R.H. Michel, H. Schreiber, R. Gierden, F. Hennrich, J. Rockenberger, R.D. Beck, M.M. Kappes, C. Lehner, P. Adelmann, J.F. Armbruster, Ber. Bunsenges. Phys. Chem. 98 Ž1994. 975. w4x D.E. Manolopoulos, P.W. Fowler, R. Taylor, H.W. Kroto,

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