J. Phys. Chem. 1996, 100, 13399-13407
13399
Experimental and Theoretical Study of the Infrared, Raman, and Electronic Spectra of Two Isomers of C78 of C2W Symmetry Michael Benz,† Marianna Fanti,‡ Patrick W. Fowler,*,§ Dirk Fuchs,| Manfred M. Kappes,*,† Carolin Lehner,⊥ Rudi H. Michel,† Giorgio Orlandi,‡ and Francesco Zerbetto*,‡ Institut fu¨ r Physikalische Chemie und Elektrochemie der UniVersita¨ t Karlsruhe, D-76128 Karlsruhe, Germany, Dipartimento di Chimica “G. Ciamician”, UniVersita` degli Studi di Bologna, Via F. Selmi 2, 40126 Bologna, Italy, Department of Chemistry, UniVersity of Exeter, Exeter EX4 4QD, UK, Forschungszentrum Karlsruhe GmbH, Institut fu¨ r Nukleare Festko¨ rperphysik, P.O. Box 3640, D-76021, Karlsruhe, Germany, and Bruker Analytische Messtechnik, Postfach 210361, D-76021 Karlsruhe, Germany ReceiVed: January 24, 1996; In Final Form: May 8, 1996X
The two C2V isomers of C78 that satisfy the isolated-pentagon rule have been separated and studied by infrared, Raman (1064 nm excitation), and electronic spectroscopies backed up by semiempirical quantum chemical calculations. The structures have, respectively, 21 and 22 inequivalent atoms. The interplay between experiment and theory affords insight into the electronic and vibrational properties of the two molecules. In particular, through the comparison of the Raman and electronic spectra with their simulations, it is shown that the Raman spectra of the two isomers are different in nature. The spectrum of the isomer with 22 inequivalent atoms displays some preresonant character, while the spectrum of the other isomer does not. It is concluded that the properties of higher fullerenes must be treated on an individual basis, even when they share the same number of atoms and symmetry.
Introduction The discovery1 and subsequent preparation of macroscopic quantities of fullerenes2 have led to the investigation of the properties of C60 and its derivatives3 and to the attempt to isolate further related allotropic forms of carbon. While the characterization of the two smaller, more abundant, fullerenes C60 and C70 (which both exist in only one isomeric form) is well established, the intrinsic difficulty of isolation of the isomers of higher fullerenes has made them less available for general study. Consequently, although one might expect higher fullerenes to have interesting chemistry and physics, our present knowledge of them is still rather limited. Diederich et al. isolated and characterized, by 13C NMR and optical spectroscopy, two isomers of C78.4 The structures of these isomers belong to the D3 and C2V point groups, respectively. Interestingly, the isolated-pentagon rule5 allows for two C2V isomers that differ in the number of inequivalent atoms.6 The NMR spectrum of the C78 C2V cluster reported in ref 4 shows 21 inequivalent atoms. Subsequently, Kikuchi et al., under different experimental conditions, also obtained NMR spectral evidence for a C2V isomer with 22 inequivalent carbon atoms (designated as C2V′) by measurements on an isomeric mixture.7a In further work by the same group, the pressure dependence of relative C78 isomeric yields was studied in detail.7b Of all fullerene molecular properties, vibrations and electronic states are of special interest because their alteration, for example, as a response to doping or a change in carbon atom count, may presage macroscopic behavior with potential for practical applications. The reference techniques used to explore vibrational states are the complementary infrared and Raman spectro† Institut fu ¨ r Physikalische Chemie und Elektrochemie der Universita¨t Karlsruhe. ‡ Universita ` degli Studi di Bologna. § University of Exeter. | Institut fu ¨ r Nukleare Festko¨perphysik. ⊥ Bruker Analytische Messtechnik. X Abstract published in AdVance ACS Abstracts, July 1, 1996.
S0022-3654(96)00228-6 CCC: $12.00
scopies. For systems of the size of C78, however, the study of the spectra may be awkward if not supplemented by other tools. With the present wide availability of computers, the natural adjunct of any spectroscopic measurement is a quantum chemical simulation of the spectra at one of several levels of theory. For fullerenes, semiempirical methods of the MNDO type8 have been successful in a variety of tasks9 and can be used to calculate the vibrational properties of interest. Besides the molecular vibrations and the related intensities, electronic states are also of interest. The CNDO/S method10 has also been used to study fullerenes.11-13 In particular, it has been found to be remarkably successful in the analysis of the vibronic structure of the S0-S1 transition of C60,11 in the simulation of the circular dichroism spectrum of C76,12 and in the simulation of the frequency-dependent, second-order polarizability of fullerenes.13 In this work, we have prepared fullerene-containing carbon soot by the standard Kra¨tschmer-Huffman method, we have isolated and separated the two components of the C78 fraction of the soot extract that correspond to the C2V isomers, and we have then measured their infrared, Raman, and electronic spectra. Further, we have simulated the vibrational spectra with the MNDO and QCFF/PI methods and the electronic spectra with the CNDO/S method. In the process, it was necessary to extend the MNDO program used by us to allow the calculation of the Raman activities. For a better simulation of the spectra, we have attempted to link the density of vibrational states with the spectroscopic line width. The different character of the Raman spectra of the two C2V isomers of C78 is discussed in the light of both the experimental results and the quantum chemical calculations. Experimental Section Preparation. Three isomers of C78 were generated as a part of fullerene- and metallofullerene-containing carbon soot by using the Kra¨tschmer-Huffman carbon-arc method modified © 1996 American Chemical Society
13400 J. Phys. Chem., Vol. 100, No. 32, 1996 for the production of La@C82. Details of production, extraction, and HPLC separation are described elsewhere.14 Briefly, after the removal of C60 and C70 from the raw soot by washing in room temperature toluene, a fraction enriched in higher and endohedral fullerenes was produced by refluxing in an azeotropic mixture of carbon disulfide/methanol (84:16 vol %). This extract was dried and redissolved in xylene at a concentration of 5 mg/mL. Multicycle HPLC purification was performed by using a Cosmosil column (10 × 250 mm, Nacalai Tesque Inc.) with toluene as eluent (5 mL/min) to efficiently prepare pure C2V′ and highly enriched C2V isomers. In the first cycle, C78 was part of the fourth fraction eluting from this column. This fraction contained C76 (25%), C78 (30%), C82 (10%), and C84 (30%), as well as some residual C60 and C70, as determined independently by HPLC and laser-desorption time-of-flight mass spectrometry. A second cycle of purification resulted in five fractions containing predominantly C60/C70, C76, C78(C2V/D3), C78(C2V′), and C82/C84 in their respective order of elution. After a third purification cycle, we obtained two C78 fractions [∼3 mg of C78 (I), ∼4 mg of C78(II)], which were used for further study. Fraction compositions based on 13C NMR study measurements were as follows: (I) 90% C2V, 8% D3; (II) 98% C2V′. Fractions I and II were contaminated to 98%, as confirmed by mass spectroscopy and HPLC analysis where applicable. In the following, we will refer to fraction I as C78(C2V) and to fraction II as C78(C2V′). Note that in our case, in contrast to earlier reports using different carbon-arc setups, both isomers have roughly the same abundance after extraction.7 Complete separation of all three isomers of C78 is possible by using a polymeric ODS column, but at significantly lower throughput than the method used here. IR Spectroscopy. As only small amounts of each isomer were isolated, we used the following method to obtain IR spectra with a good signal-to-noise ratio: a toluene solution was concentrated to the saturation limit and introduced dropwise onto a KBr window. Between each drop the solvent was removed by using a fan. Care was taken that C78 was spread as evenly as possible to reduce scattering effects. After fullerene application onto the KBr window, residual toluene was removed by drying in an vacuum oven at 0.3 mbar and 100 °C for 5 h. IR absorption measurements on the resulting 10 µm crystallites were performed by using a Bruker IFS 28 FTIR spectrometer. A total of 400 scans at 4 cm-1 resolution (5 cm-1 in case of the C2V isomer) was recorded. Spectra are reported after correction for the KBr cutoff below 430 cm-1, as well as for H2O vapor absorption. Features beyond 1500 cm-1 are due to incomplete water subtraction rather than due to fullerene vibrational modes. Only intense vibrational features are listed in the table. Spectra at lower signal-to-noise ratios were also taken at 2 cm-1 resolution and showed identical results within experimental accuracy. Raman Spectroscopy. The microcrystalline solid dried from toluene solution was sealed in a quartz tube under vacuum. Raman spectra were taken at 4 cm-1 resolution with a Bruker FT-Raman RFS 100 spectrometer using a Nd:YAG laser at 1064 nm in back-scattering geometry. The laser intensity was 140 mW and the spot was defocused. A single measurement with 200 scans is sufficient to obtain all features with intensities >15% of the strongest line. We averaged five of these spectra to increase the signal-to-noise ratio. All spectra show a strong luminescence background, which was subtracted (by fitting a polynomial) for clarity. Frequencies and intensities were determined in both the corrected and the uncorrected spectra. No correction was performed for the wavelength-dependent sensitivity of the detector and the optics. An estimate of the
Benz et al. influence of the wavelength-dependent sensitivity can be obtained by comparison of two published Raman spectra of C7615,16 (with the same laser excitation wavelength but corrected response in the case of ref 15). Electronic Spectroscopy. Toluene was removed and both isomers were dried at 100 °C in a vacuum of 0.3 mbar for 5 h. They were subsequently redissolved in CS2 (spectroscopic grade). Measurements of these solutions were carried out by using a Varian Cary 5E UV-vis NIR spectrometer with a scan rate of 900 nm/min and a resolution of 1.0 nm. The spectra are reported relative to pure CS2 measured in the same cell under the same conditions. Theoretical Background In this work, we first simulated the infrared and Raman spectra of the two C2V isomers of C78 with the MNDO8 model. This model has been widely used in fullerene chemistry and physics for a variety of applications, ranging from superconductivity to stability and reactivity.9 To the best of our knowledge, MNDO has not yet been used to simulate Raman cross sections of fullerenes. One of the reasons for this could be that the most common computer packages that contain the MNDO model do not allow such calculations. We decided to extend the computer program that we use17 to include the Raman cross sections. The upgrade was carried out by a combination of analytical and numerical techniques. Since the calculation of the force field is already partially performed numerically, we simply added a calculation of the polarizability at each step along the lines described in ref.18 Numerical differentiation and subsequent projection of the Cartesian derivatives of the polarizability onto the normal modes allow the calculation of the Raman intensities. The infrared and Raman spectral lines, calculated by the MNDO model, are then broadened by multiplication with a Gaussian line shape function:
e-(ν-ν0) /a aπ0.5 2
G(ν) )
2
(1)
where ν is the excitation wavenumber in cm-1, ν0 is the MNDOcalculated vibrational mode frequency in cm-1, and a is a constant in cm-1 that accounts for the broadening, both homogeneous and inhomogeneous. In the samples used in the measurements, both types of broadening are present. Presently we cannot identify the source of inhomogeneous broadening; however, we can try to model the homogeneous broadening in terms of the density of vibrational states at the wavenumber of each spectroscopically active fundamental. In molecules as large as fullerenes, the density of states due to overtones and combination levels grows very rapidly. At the energy E, we empirically assumed the constant a of eq 1 to take the form
a(E) ) 1 + 2 ln(N(E))
(2)
where N(E) is the vibrational density of states. Implicitly, if the simulation is successful, the form of this empirical equation must account for the inhomegeneous broadening. The calculation of the density of states is carried out by using the extended algorithm of Stein and Rabinovitch19 based on the calculated ν0 values. Equation 2 is amenable to improvement and does not account for any inhomogeneous broadening that might be present in the spectra. The comparison of the experimental and quantum chemical results forced us to consider the possibility of preresonance in the Raman spectrum of the C2V′ isomer. A simulation of the preresonant Raman spectrum was carried out by using the quantum consistent force field for π electrons (QCFF/PI)
Study of Two C2V Isomers of C78
Figure 1. Infrared spectra of isomer 2 (C2V) of C78: top, experimental spectrum; bottom, MNDO simulation. The intensity is in arbitrary units.
Figure 2. Infrared spectra of isomer 3 (C2V′) of C78: top, experimental spectrum; bottom, MNDO simulation. The intensity is in arbitrary units.
model20 along the lines described for C76,15 where three lowlying electronically excited states contribute to the scattering. In the present case, there is only one preresonant state and the sum over states is limited to its contributions. In simple terms, to calculate the resonant contributions, one needs to optimize the geometries, Qi, i ) 0, 1, of the electronic states that are involved in the virtual transition. The difference in angstroms of geometry, ∆0i, projected along the mth normal modes gives the Bm displacement parameters:
Bm ) 0.172νm1/2[Q1 - Q0]M1/2Lm ) 0.172ν01/2∆m (3) where ν is in cm-1, Q is in angstroms, the atomic mass matrix, M, is in daltons, and Lm is the mth normal mode eigenvector. The Raman cross section for each mode can be taken to be proportional to γm ) 1/2Bm2. Results The isolated-pentagon rule allows for five distinct fullerene isomers of C78.6 Two of these have D3h symmetry and have never been observed experimentally. Of the remainder, one has D3 and two have C2V symmetry. The C2V isomers are distinguishable by 13C NMR where they show 21 and 22 distinct peaks, respectively. Several numbering schemes for these
J. Phys. Chem., Vol. 100, No. 32, 1996 13401
Figure 3. Raman spectra of isomer 2 (C2V) of C78: top, experimental spectrum; bottom, MNDO simulation. The intensity is in arbitrary units.
Figure 4. Raman spectra of isomer 3 (C2V′) of C78: top, experimental spectrum; bottom, MNDO simulation. The intensity is in arbitrary units.
isomers have been used in the literature;4-6 for convenience, we shall use the lexographic spiral ordering,5 which is the basis for IUPAC proposals for fullerene nomenclature. In this system, the D3 isomer is number 1, the C2V isomer with 21 distinct atoms is 2, the C2V′ isomer with 22 distinct atoms is 3, and the D3h isomers are 4 (the leapfrog of C26) and 5. (In the scheme used in ref 6, the same five isomers were labeled 3, 4, 5, 1, and 2.) The spectroscopic measurements and the calculations are performed on isomers 2 and 3. The purpose is to emphasize differences and similarities between the two isomers that share the same number of atoms and the same symmetry. Their vibrational properties should be very similar: in principle, there are 172 infrared active modes for isomer 2 and 173 for isomer 3, while in the Raman spectrum, there are 228 active modes for both isomers. In Figures 1-4, we show the experimental and scaled infrared and Raman spectra of isomers 2 and 3. For convenience, a list of the most intense experimental peaks is given in Tables 1 and 2. The MNDO frequencies together with their infrared intensities and Raman activities are shown in Tables 3 and 4. It is apparent that experimentally the number of intense bands is far smaller than that allowed by group theory. This is a feature that has already been pointed out for C76.15 Computa-
13402 J. Phys. Chem., Vol. 100, No. 32, 1996
Benz et al.
TABLE 1: Frequency (cm-1) and Relative Peak Heights of the Experimental Raman and Infrared Spectra of Isomer 2 of C78 Raman
activity
1649 1589 1570 1534 1480 1468
14 67 50 60 8 18
1445
68
1421
5
1391 1370 1343 1323s 1316 1296 1279
15 20 26 43 48 10 5
1244 1229 1213
55 17 25
1173
36
infrared
1465 1458 1446 1437 1429 1420s 1413 1396 1367 1340
1261
1148 1134 1119
11 5 5
1057
5
1024
7
1005 932 898 818
9 9 5 18
791
12
intensity
50 52 38 38 52 29 23 7 10 10
Raman
activity
725 720 708s 699
5 5 10 23
683
37
619
17
573
5
20 540
5
504 494
5 9
1211 1203
9 7
1155 1147s
26 9
1121 1108 1101 1096s
14 9 7 5
473
12
446 432
6 100
1039 1020 1012
5 9 9
808 800 792 781 768 741
9 63 45 10 10 8
396 380 372s 332 309 297 282 247s 240 211 182
21 10 8 14 9 8 7 30 60 59 5
tionally, there is a strong overestimation of the infrared intensity in the high-frequency region. Remarkably, MNDO appears to be doing a better job on the Raman activity, although some overestimation is still present. The infrared spectra of both molecules can be divided into three regions: (i) a system of narrow bands between 400 and 800 cm-1; (ii) a remarkable almost flat region up to nearly 1200 cm-1; and (iii) a system of broad bands that extends up to about 1600 cm-1. In the first and the last regions, the two isomers present bands that are very different in intensity and position and can be taken as fingerprints. The Raman spectra can also be divided into three regions: (i) a system of bands in the lowfrequency region between 200 and 500 cm-1; (ii) a nearly flat region up to nearly 1200 cm-1; and (iii) a system of broad bands that extends up to about 1600 cm-1. Interestingly, the intensitydeprived region seems to be common to all isolated empty cage fullerenes for which there are analogous measurements available. A similar region also appears in the spectra of C7615,16 and in the infrared21 and Raman25 spectra of C82. The MNDO simulation of the vibrational frequencies and infrared spectra of C78 has already been carried out.22 Since at the time no experimental counterpart was available, the previous spectra were published without any line widths. In this work, the calculated frequencies are multiplied by 0.9. This standard
infrared
intensity
725 717s 705 698 692 687
33 12 16 18 11 14
679 659 652 644 636 631 621 616s
8 9 27 56 38 7 23 7
565 559 554 545 538 532 524 519 505 494 488 482 467 461 444 435s 419
41 33 14 100 63 24 51 25 44 28 29 10 5 8 34 8 10
practice23 in ab initio and semiempirical Hartree-Fock calculations brings theory and experiment into closer agreement. To evaluate the overall quality of the simulation, the stick spectrum must be broadened to account for both homogeneous and inhomogeneous broadening. The broadening must also account for the empirical observation that the line width increases with frequency. Apart from the intrinsic disorder of the samples, which contributes to the inhomogeneous width, the line width has a homogeneous source that derives from the interaction of the fundamental of each vibrational mode with the multiple-quantum dark states. By using the scaled MNDO frequencies, we calculate that, in the two isomers of C78, the density of vibrational states per cm-1 goes from 1 at around 200 cm-1 to more than 10 000 slightly above 1600 cm-1. In other words, above the latter threshold 1 cm-1 contains at least 10 000 vibrational states. Insofar as the harmonic approximation holds, they are all dark states and are not responsible for absorption or scattering. Small cubic and quartic anharmonic interactions, however, mix them with the fundamentals so that the one-quantum level of each vibrational mode effectively becomes quite spread. This intrinsically large width is then increased further by the inhomogeneous interactions. It is not the purpose of this work to assess the interplay between these two phenomena. After the discovery of the enormous variation
Study of Two C2V Isomers of C78
J. Phys. Chem., Vol. 100, No. 32, 1996 13403
TABLE 2: Frequency (cm-1) and Relative Peak Heights of the Experimental Raman and Infrared Spectra of Isomer 3 of C78 Raman
activity
1593
33
1562 1547 1532
49 11 28
1516
9
1491 1462
18 32
1438
7
1389 1377
11 15
1348
23
1329
100
1277 1254
36 37
1219
30
1194 1174 1156
5 5 29
1138 1059 1037
8 20 8
1009 967 872 818
14 5 15 5
infrared 1595 1590s
intensity 11 7
1522 1516 1509s 1493 1458 1445 1439 1434s 1418
10 27 15 10 15 100 79 28 27
1375 1370 1352 1348 1340 1329 1319 1313
13 10 6 7 17 21 9 8
1256 1230 1221 1207 1201
12 6 7 8 13
1171 1153 1142 1138
9 13 7 6
1041 1032 1028 1020 1007
6 5 5 9 5
798
29
in the density of states, we decided to broaden each active band by using eqs 1 and 2. One should notice that eq 2 is empirical and may not be transferable to other fullerenic systems. Further work on closely related molecules may allow the determination of a more general relation between the density of states and the line width. At this stage, it is instructive to compare the experiments and calculations. Infrared Spectra. Experimentally, in the low-frequency region (400-800 cm-1), the C2V isomer has the most intense peak at 545 cm-1 while the C2V′ isomer has the most intense peak at 635 cm-1. Computationally, we obtain very reasonable agreement with the experiment. In particular, isomer 2 has four normal modes, whose frequencies range from 525 to 546 cm-1, that contribute to the most intense peak located at around 530 cm-1. As for the spectrum of isomer 3, it has the most intense infrared vibration calculated at 619 cm-1; for this band, however, the line width law that we have used makes its peak height lower than that of some of the lower frequency modes. This must be taken as an indication that the present empirical relation between the density of states and line width is open to refinement in further work. It is interesting to notice that the intense pillar-like band located at 800 cm-1 in both spectra appears in the calculations. In the medium-frequency region, the calculations reproduce the lack of intensity of the experimental spectra.
Raman
activity
793
9
780
8
722 712
14 7
693
11
685s
7
654
8
636
5
621
7
484
10
476s 463
7 6
432 394 382 363 336 280 241 234s 214
29 13 9 14 52 6 47 35 59
infrared
intensity
793 787 781 777 767 725 708 696
40 48 7 7 5 51 15 23
690 683 678s 658 652 646 640 635 629 621 582 552 544 528 507 503 498 491 486 480 473 463 457 442 436
17 25 11 10 27 13 11 81 15 13 23 26 28 40 31 42 8 7 6 11 15 10 5 15 5
In the high-frequency region above 1200 cm-1, the C2V isomer presents a broad system with two major peaks at 1425 and 1460 cm-1. The C2V′ isomer has a single very intense peak at 1445 cm-1. Computationally, MNDO finds far too much intensity in the high-frequency region, although there is qualitative correspondence with the experiment. The line width calculated for this region is too large, again probably a shortcoming of the very simple equation chosen to link it with the density of vibrational states. Raman Spectra. Experimentally, the low-frequency region (200-500 cm-1) for isomer 2 shows a doublet at 211 and 240 cm-1 together with a very intense line at 432 cm-1, while isomer 3 has a similar doublet followed by an isolated band at 336 cm-1. A very broad system of medium-sized bands is also found below and around 500 cm-1. The calculation is quite successful for isomer 2 despite some overestimation of the frequency of the most intense band. For isomer 3, the calculation reproduces the low-frequency doublet, while some further problems with the line width exist for the broad band at 500 cm-1, which is predicted to be very sharp in the simulation. A possible explanation for the sudden rise of the line width in this region could be sought in the presence of large-amplitude breathing modes. Interaction between adjacent fullerene molecules in the solid, which experience different environments, might result in the dispersion of the normal mode frequency of the isolated fullerene over several tens of wavenumbers.
13404 J. Phys. Chem., Vol. 100, No. 32, 1996
Benz et al.
TABLE 3: Scaled MNDO Frequencies (cm-1), Infrared Intensities (IR), and Raman Activities (R) of Isomer 2 of C78 freq
IR
R
freq
IR
R
freq
IR
R
freq
IR
R
a1
186 302 425 476 583 678 737 819 1059 1167 1245 1320 1381 1477 1567
0 0 0 0 0 0 0 0 0 0 3 3 3 1 4
27 2 5 56 1 4 26 12 30 36 179 701 523 257 47
219 351 440 525 642 695 751 905 1080 1191 1261 1342 1414 1494 1590
0 0 0 5 1 1 0 0 1 9 0 1 4 5 4
23 2 1 2 21 9 58 17 15 39 69 43 110 50 636
257 359 457 547 664 696 756 947 1097 1211 1304 1350 1446 1512 1600
0 0 0 3 0 0 0 0 0 0 0 1 1 3 3
1 3 2 1 0 4 9 14 71 24 145 304 496 915 291
272 368 474 567 668 720 798 1025 1149 1231 1314 1367 1462 1549
0 0 0 0 0 0 1 1 0 11 1 0 0 1
1 4 55 2 0 1 35 79 17 3 78 11 226 422
a2
214 356 475 551 648 701 759 812 945 1165 1239 1329 1412 1514
0 0 0 0 0 0 0 0 0 0 0 0 0 0
26 4 1 0 6 2 19 1 2 45 25 2 2 96
267 365 480 566 658 709 769 823 1059 1197 1266 1343 1452 1517
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 6 2 11 12 15 1 2 43 125
289 413 499 588 667 725 778 844 1085 1215 1294 1356 1464 1543
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 9 1 0 6 1 2 10 13 0 51 2 17 22
340 439 503 626 697 752 802 868 1152 1230 1314 1366 1475 1558
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 2 2 0 64 4 0 6 3 121
b1
186 341 446 536 634 699 782 836 1086 1203 1263 1341 1412 1518
0 0 0 3 5 0 0 8 0 1 2 27 4 2
27 0 0 0 1 3 20 37 6 32 10 59 5 64
260 351 449 567 672 714 785 915 1132 1207 1288 1361 1424 1532
0 0 0 3 1 0 0 1 3 1 0 15 1 0
0 1 1 0 14 2 10 4 22 6 15 14 15 30
280 437 478 571 680 735 804 959 1143 1231 1304 1363 1471 1548
0 0 0 0 0 0 0 0 5 7 7 1 28 1
0 13 1 0 6 4 0 1 1 17 4 1 16 1
308 442 497 599 690 752 818 1059 1174 1238 1324 1397 1487 1599
0 0 1 0 1 0 0 1 8 0 1 13 0 11
0 0 4 1 0 0 0 10 14 29 31 2 84 24
b2
211 348 449 533 609 710 747 841 1030 1160 1266 1311 1400 1506 1572
0 0 0 5 0 0 0 6 0 9 0 1 0 6 0
29 0 0 1 1 0 4 9 13 1 2 3 12 8 26
272 361 469 577 654 731 774 851 1089 1203 1272 1335 1442 1510
0 0 1 0 0 0 1 0 1 3 0 0 28 7
0 7 0 0 1 0 2 0 0 1 1 16 5 5
290 424 489 582 682 733 787 913 1114 1219 1285 1344 1461 1522
0 1 1 0 1 0 0 2 0 10 0 0 12 1
0 2 0 0 11 2 3 0 68 0 27 6 0 8
340 431 509 604 701 743 794 917 1148 1234 1296 1389 1490 1553
0 0 1 2 0 0 0 0 0 0 0 4 2 10
4 5 0 0 1 3 4 8 13 8 5 5 42 0
Noticeably, the calculation predicts no intensity for the 336 cm-1 band (vide infra). The medium-frequency region is calculated to show little or no Raman scattering, in good agreement with the experiment. The high-frequency region presents a broad system for the C2V isomer and a single strong band at 1329 cm-1 for the C2V′ isomer. The MNDO calculations are rather successful in discerning between the two isomers. In particular, both the broad, intense system of bands of isomer 2 and the single most intense peak of isomer 3scalculated at 1335 cm-1sare present in the simulations. As observed for the infrared spectra, the line width calculated for this region tends to be too large, although, in the present
case, there is better agreement between experiment and simulation. Electronic Spectra. The electronic spectra of the two isomers of C78 are shown in Figures 5 and 6. It is interesting to assess them in the light of CNDO/S calculations. The results reported here are very similar to the INDO/S calculations that appeared when this work was nearing completion.24 In that work, the less extensive experimental spectra drawn from refs 27 and 28 are also shown pictorially. For the discussion of the electronic states one can refer to ref 24. Here, we focus on the first singlet excited state, S1. Comparison of the results presented in Figures 5 and 6 and in Tables 5 and 6 shows that the transition of lowest energy is well separated from the others
Study of Two C2V Isomers of C78
J. Phys. Chem., Vol. 100, No. 32, 1996 13405
TABLE 4: Scaled MNDO Frequencies (cm-1), Infrared Intensities (IR), and Raman Activities (R) of Isomer 3 of C78 freq
IR
R
freq
IR
R
freq
IR
R
freq
IR
R
a1
190 308 430 482 585 682 748 797 1041 1148 1222 1323 1379 1471 1520
0 0 0 0 0 1 1 0 6 0 1 26 1 4 2
30 3 14 3 5 8 59 63 248 9 56 2620 45 200 117
214 335 436 505 619 696 752 838 1069 1169 1258 1328 1402 1491 1540
0 0 0 2 7 0 0 11 5 6 1 5 22 16 0
26 2 4 3 6 3 85 68 25 13 129 333 259 480 345
259 349 447 566 641 700 774 921 1083 1200 1297 1340 1421 1491 1585
0 0 0 6 2 1 1 0 0 14 9 10 0 0 4
1 1 3 1 17 4 43 43 14 444 38 10 83 291 240
278 364 477 584 670 722 776 929 1121 1215 1305 1359 1458 1499 1603
0 0 0 0 3 0 1 0 1 0 2 40 0 2 7
0 2 101 2 21 3 25 7 87 3 100 70 815 681 841
a2
208 352 470 572 644 705 763 824 1025 1193 1274 1335 1423 1519
0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 13 0 0 0 1 7 11 136 1 4 6 2 22
272 363 472 579 662 711 773 842 1075 1214 1296 1343 1458 1545
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 1 0 1 6 3 25 18 8 4 11
301 430 488 582 691 728 782 857 1121 1230 1315 1370 1485 1564
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 2 0 0 11 9 2 1 224 2 3 4 139 13
336 436 492 598 694 744 789 909 1167 1241 1321 1397 1511
0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 3 0 1 8 33 2 21 2 3 6
b1
191 351 445 496 649 696 755 836 1067 1198 1257 1344 1410 1518
0 0 0 0 1 0 1 2 0 15 0 26 0 1
31 1 0 4 2 2 6 33 9 4 12 32 7 54
259 355 447 531 672 708 792 906 1096 1204 1303 1357 1427 1546
0 0 0 4 1 0 1 0 1 5 2 4 0 0
0 2 0 0 3 12 6 0 4 4 43 100 3 0
272 359 451 553 675 727 807 964 1154 1210 1322 1362 1477 1558
0 0 0 4 0 1 0 0 3 1 9 2 0 3
1 6 0 0 2 2 0 3 9 70 2 25 25 11
305 430 475 613 690 735 818 1059 1169 1243 1326 1393 1486 1604
0 0 0 0 3 0 0 1 5 10 0 2 4 2
1 3 0 0 4 15 2 3 2 8 4 3 95 297
b2
212 349 485 568 612 710 754 833 1049 1162 1259 1332 1406 1488 1547
0 0 1 0 0 0 0 15 1 0 1 0 2 22 9
26 1 0 1 0 0 18 21 71 75 1 11 9 17 5
268 419 492 578 642 717 771 845 1085 1184 1273 1338 1448 1510
0 0 0 2 0 0 0 1 1 16 1 0 62 1
0 4 1 0 2 5 4 6 0 26 9 98 4 129
286 434 506 590 670 737 801 912 1133 1228 1291 1354 1465 1517
0 1 1 0 2 0 2 5 0 4 1 2 2 0
0 0 1 0 10 0 26 0 127 17 5 1 2 33
333 447 543 593 703 748 809 940 1148 1234 1299 1379 1476 1520
0 0 2 4 0 0 0 0 0 4 0 1 11 1
0 0 0 0 3 6 2 16 15 6 20 37 84 193
and has different character in the two isomers. In isomer 2, the transition is higher lying and forbidden, while in isomer 3, it is lower lying, calculated to be at about 1.5 eV, and allowed. For fullerenes, it has been shown before11-13 that this type of calculation systematically overestimates the energy of the S0S1 transition by about 0.3 eV. One can therefore infer that the onset of the S0-S1 transition should lie at 1.2-1.3 eV (1033954 nm), in good agreement with the spectrum of Figure 6. The study of the lowest lying electronic transitions has consequences for the description of the Raman spectra.25 The exciting laser has an energy of 1064 nm, (1.16 eV) which makes it preresonant with the S1 state of isomer 3, but not with the forbidden and higher lying S1 state of isomer 2. The case of isomer 3 presents similarities with the case of C7615,16 in which
three electronic states contribute to the preresonant spectrum. We therefore decided to perform QCFF/PI calculations of the preresonant Raman activities of isomer 3 along the lines of those reported in ref 16. Interestingly, the calculated spectrum is very sparse. Only nine modes have values of γ larger than 0.01; they are calculated to be at 1650 cm-1 (γ ) 0.08), 1354 cm-1 (γ ) 0.04), 1265 cm-1 (γ ) 0.03), 1256 cm-1 (γ ) 0.03), 1218 cm-1 (γ ) 0.02), 1150 cm-1 (γ ) 0.02), 718 cm-1 (γ ) 0.04), 335 cm-1 (γ ) 0.12), and 233 cm-1 (γ ) 0.33). Two comments are in order: (i) the preresonance activity does not change the overall Raman pattern of a spectrum divided into three regions, of which the central one is almost flat; (ii) the largest part of the activity is concentrated in the low-frequency region with only two modes that are affected by the preresonance. These
13406 J. Phys. Chem., Vol. 100, No. 32, 1996
Benz et al. TABLE 5: CNDO/S Excitation Energies (eV) and Transition Dipole Moments of Isomer 2 of C78
Figure 5. Electronic spectrum of isomer 2 (C2V) of C78.
Figure 6. Electronic spectrum of isomer 3 (C2V′) of C78.
modes are located at 335 cm-1 and 233 cm-1. The question that arises is whether one can map QCFF/PI onto MNDO modes so as to find which bands are modified by this activity. Overlapping of the normal modes shows a substantial normal mode rotation between the two models in the high-frequency region. Fortunately, the two modes under scrutiny have a oneto-one correspondence with the scaled MNDO vibrations located at 214 and 308 cm-1. The first mode is part of the highest frequency band of the doublet located around 200 cm-1 that already appears in the spectrum. The preresonance activity simply redistributes its intensity: notice that the Raman activity due to off-resonance contributions can interfere positively or negatively with the (pre)resonance Franck-Condon activity; the second, 308 cm-1, mode is located in the region of the missing band discussed earlier. The failure of MNDO to predict sizeable intensity in the region around 300 cm-1 for isomer 3 is caused by the presence of preresonant contributions that are not included in the frequency-independent TDHF calculations. Discussion and Conclusion We have carried out measurements and calculations of the vibrational and electronic states of two isomers of C78. The present data have indications for future measurements and calculations. A case in point is the calculation of the Raman activities. If the first electronically excited states of the molecule under investigation were located several electronvolts above the ground state, one could safely consider the beam excitation energy to be zero. In turn, this would mean that frequency-
state
en
sym
Mx
My
Mz
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
1.81 2.05 2.25 2.38 2.38 2.39 2.39 2.56 2.60 2.62 2.62 2.64 2.66 2.73 2.70 2.78 2.79 2.84 2.84 2.89 2.95 2.95 2.97 3.04 3.05 3.06 3.07 3.08 3.14 3.15 3.23 3.28 3.30 3.32 3.33 3.35 3.37 3.37 3.40 3.41 3.42 3.46 3.46 3.48 3.50 3.56 3.58 3.58 3.60
A2 B2 B1 B1 B2 A2 A1 B2 B2 B1 B2 A2 A1 A1 A2 B1 B2 A1 A2 B1 A1 B1 A1 A2 B1 B2 A1 A2 B2 A2 A2 B1 B2 B2 A1 A2 B1 B2 B1 B1 A1 A2 A1 B2 A2 A2 B1 A1 B2
0.0000 0.0000 0.3937 -0.0978 0.0000 0.0000 0.0000 0.0000 0.0000 0.1671 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0179 0.0000 0.0000 0.0000 -0.1720 0.0000 0.2471 0.0000 0.0000 -0.3544 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.5806 0.0000 0.0000 0.0000 0.0000 0.2382 0.0000 -0.0626 0.1579 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.4293 0.0000 0.0000
0.0000 0.3345 0.0000 0.0000 -0.3428 0.0000 0.0000 0.2735 0.0547 0.0000 -0.1032 0.0000 0.0000 0.0000 0.0000 0.0000 0.6093 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0514 0.0000 0.0000 -0.4823 0.0000 0.0000 0.0000 0.2054 0.0944 0.0000 0.0000 0.0000 -0.2813 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0125 0.0000 0.0000 0.0000 0.0000 -0.3356
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0280 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0962 0.2693 0.0000 0.0000 0.0000 -0.0088 0.0000 0.0000 0.1074 0.0000 -0.2732 0.0000 0.0000 0.0000 0.2909 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.4616 0.0000 0.0000 0.0000 0.0000 0.0000 0.2386 0.0000 -0.2871 0.0000 0.0000 0.0000 0.0000 0.2471 0.0000
independent TDHF calculations were appropriate to evaluate the Raman response. In the case of higher fullerenes, however, the onset of the electronic absorption is very close to the energy of the radiation (1064 nm), and care should be taken to check whether a (pre)resonant contribution is present. For C76, we found that three states contribute to give (pre)resonant Raman activity. Simple considerations based on the size of the π system would indicate that the Raman spectrum of C78 isomers, taken under the same conditions, should show similar character. Yet we find that while the Raman spectrum of isomer 2 has no resonance contributions, at least two bands of the spectrum of isomer 3 can be positively assigned to be (pre)resonant. The implication is quite far reaching both in terms of the foreseeable complexity of the theory of the spectroscopy of fullerenes and in terms of properties of undoped and doped fullerenes, which can substantially differ from one another even for isomers of the same molecular weight and symmetry. In conclusion, we have reported the vibrational and electronic characterizations of two fullerene isomers in their uncharged states. Infrared and Raman data can be simulated qualitatively by MNDO calculations. A more accurate simulation requires,
Study of Two C2V Isomers of C78
J. Phys. Chem., Vol. 100, No. 32, 1996 13407 Formation, Stability and Photophysics of Fullerenes is acknowledged.
TABLE 6: CNDO/S Excitation Energies (eV) and Transition Dipole Moments of Isomer 3 of C78 state
en
sym
Mx
My
Mz
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 50 51
1.53 1.66 1.98 2.02 2.19 2.27 2.34 2.35 2.36 2.44 2.50 2.51 2.54 2.58 2.65 2.71 2.76 2.79 2.82 2.83 2.83 2.87 2.92 2.95 2.98 2.99 3.03 3.05 3.06 3.07 3.14 3.15 3.20 3.22 3.24 3.24 3.25 3.26 3.31 3.31 3.34 3.35 3.35 3.35 3.38 3.39 3.42 3.49 3.49 3.50 3.54
B2 A2 B2 A2 A2 B1 B1 B2 A1 B2 B2 B1 A2 A1 A2 B1 A1 A1 B2 A2 B1 A1 B1 A2 B1 A2 A1 B1 A2 B2 A2 B2 B2 B1 A2 B2 A1 A2 B2 B1 A1 B1 A1 B2 A2 A1 B2 B1 A1 B2 B1
0.0000 0.0000 0.0000 0.0000 0.0000 -0.1933 0.0347 0.0000 0.0000 0.0000 0.0000 0.2170 0.0000 0.0000 0.0000 0.0030 0.0000 0.0000 0.0000 0.0000 0.1985 0.0000 -0.1586 0.0000 0.0006 0.0000 0.0000 0.3364 0.0000 0.0000 0.0000 0.0000 0.0000 -0.7062 0.0000 0.0000 0.0000 0.0000 0.0000 -0.2641 0.0000 -0.0198 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0825 0.0000 0.0000 0.2467
0.4392 0.0000 0.4439 0.0000 0.0000 0.0000 0.0000 0.7823 0.0000 -0.0208 -0.2607 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.5931 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1631 0.0000 0.4062 -0.0023 0.0000 0.0000 -0.0200 0.0000 0.0000 -0.0003 0.0000 0.0000 0.0000 0.0000 -0.1367 0.0000 0.0000 -0.1461 0.0000 0.0000 -0.3532 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.5180 0.0000 0.0000 0.0000 0.0000 -0.3369 0.0000 0.0000 -0.0889 -0.1311 0.0000 0.0000 0.0000 0.2884 0.0000 0.0000 0.0000 0.0000 0.2824 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.6871 0.0000 0.0000 0.0000 0.3576 0.0000 -0.0876 0.0000 0.0000 -0.4797 0.0000 0.0000 -0.0011 0.0000 0.0000
among other things, a better understanding of the homogeneous and inhomogeneous line broadening in these systems. It is proposed that the most important source of homogeneous broadening occurs via Fermi interactions and can be modeled in terms of the density of vibrational states. Acknowledgment. Partial support from the Bundesministerium fu¨r Bildung und Forschung and from the European Union Human Capital and Mobility Scheme Network Project on
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