J . Phys. Chem. 1994,98, 7933-7935
7933
Preresonance Raman Spectrum of Cla Y. Achiba,t K. Kikuchi,? M. Muccini,* Giorgio Orlandi,g C. Ruani,* C. Taliani,* R. Zamboni? and Francesco Zerbetto*i Department of Chemistry, Tokyo Metropolitan University, Hachi-oji Tokyo, 192-03, Japan: Istituto di Spettroscopia Molecolare, Comiglio Nazionale delle Ricerche, Via Gobetti 101, 401 29, Bologna, Italy: and Dipartimento di Chimica "G. Ciamician". Universitb di Bologna, Via F. Selmi 2, 401 26 Bologna, Italy Received: March 17, 1994: In Final Form: July 8, 1994"
Through a joint spectroscopic and theoretical study, we discuss the effect of electron excitation on the equilibrium position of the intramolecular phonons in C76.
Introduction The discovery' and subsequent preparation of macroscopic quantities of fullerenesZhave led to fast pace developments. Such developmentshave entailed both the investigation of the properties of C a and its derivatives3 and the attempt to isolate further allotropic forms of carbon. Recently, Ettl et al.4 have reported the partial spectroscopic characterization of an isomer of c 7 6 . Comparison of the I3C NMR spectrum4 with the theoretical suggestionSshowed that the structure of c 7 6 belongs to the DZ point group symmetry. The lack, in this group, of rotoinversion axes makes C76 a chiral molecule. Very recently, its two enantiomers have been separated and their circular dichroism spectra recorded.6 This experiment provides definitive evidence of the chiral nature of c 7 6 . Chirality sets (276 apart from the two other more abundant fullerenes and could have practical applications. In fact, because of its low-lying electronically excited states, c 7 6 should have high values of x@) and x ( ~ ) In , principle, the combination of the ability of the enantiomers of c76 to rotate polarized light and the nonlinear optical properties of c 7 6 itself could be used to make devices operating with light. It is the purpose of this Letter to provide spectroscopic and theoretical information on the lowest electronically excited states to C76. In particular, we seek to understand the effect of the electronic excitation to the three lowest electronic states on the equilibrium position of the intramolecular phonons. We achieve this through a joint Raman and quantum chemical study.
1000
500
1500
Raman shift (cm-I) Figure 1. Experimental preresonance Raman spectrum of a C76 polycrystalline sample. The spectrum was corrected for the detector response, and the background was subtracted. The excitationwavelength was h = 1064 nm.
The calculations were performed with the quantum consistent force field for ?r electrons (QCFF/PI).* This model employs an empirical potential for the u-electron framework and uses a quantum chemical scheme for the ?r electrons. The u bonds are simulated by harmonic and Morse oscillators. Three- and fourbody classical potentials describe bending deformations together with pyramidalization and torsional contributions. The ?r-electron Results and Discussion We isolated C76 by a multiple-step procedure described b e f ~ r e . ~ ; ~ system is simulated by a self-consistent-fieldprocedure followed by configurationinteraction. Both the oneelectron (tor hopping) HPLC wasused to separate thedifferent fullerenes. Mass spectra integrals and the two-electron (U or Coulomb) integrals are showed that fraction I11 is constituted only by Cs4 isomers, while functions of the interatomic distances. This model has been quite fraction I v contains c 7 6 and '278. h i r e c76 was obtained by successfulin predicting the ground state frequenciesof C70,IO performing preparative HPLC on fraction IV. The mass spectra and c76" and is used here to calculate the minimum-energy of the isolated stable microcrystallinec 7 6 material was 99%clean structures of the first three electron singlet states of c76. of all other carbon molecules. The onset of the electronic transition in c76 is located slightly Near-infrared-excited Raman spectra were obtained in a above 900 nm;4the laser wavelength of 1064 nm used by us falls backscattering configuration on an IFS 100 Bruker FT-Raman about 2000 cm-1 short of the S&, transition. In theseconditions, spectrometer with a resolution of 4 cm-1. The excitation source the Raman spectra are preresonant. The unraveling of all the was a Nd:YAG laser (A = 1064 nm). A Ge detector cooled at contributions to the Raman cross sections is made more liquid nitrogen temperature was used to collectthe scattered Stokes radiation (60-3500 cm-I) and the scattered anti-Stokes radiation complicated by the fact that above S1 there are two electronically (80-2100 cm-1). The laser beam power impinging on the sample excited states for which the S&. (n = 2, 3) transition is more was kept at 40 mW within a spot of 0.3 mm in diameter. The intense than the S&, transition.4Jl The larger energy gap spectra were corrected for the detector response, and the between the energy of the exciting beam and the energy of Sz and background luminescence was subtracted. S3 would make the corresponding electronic transitions less important for the Raman spectrum than that to SI.However, t Tokyo Metropolitan University. once the gaps are combined with the larger transition dipole Istituto di Spettroscopia Molecolare. moments, their contributions are similar to that of SI.The first 8 Universita di Bologna. three singlet excited states must therefore be considered if one Abstract published in Advance ACS Abstrocts, August 15, 1994.
0022-365419412098-7933$04.50/0 0 1994 American Chemical Society
1934 The Journal of Physical Chemistry, Vol. 98, No. 33, I994
Letters
TABLE 2 Displacement Parameters, in amuoJA, for the %-SI,S,&, and S o 4 3 Transition8 freq, cm-l so41 so42 5053
Figure 2. Atom numbering for the first 49 atoms of
(276.
6
TABLE 1: Calculated S, lAg), Sl(lBs), S2(lB2), and S3(1BI) Bond Lengths, in ,of the 30 Symmetry-Independent Bonds of C,S’ bond
atoms
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
1-2 1-5 1-9 2-3 2-12 3 4 3-15 4-5 4-18 5-6 6-7 6-20 7-8 7-22 9-10 10-1 1 10-26 11-12 11-29 12-1 3 13-14 13-30 14-15 17-18 17-37 18-19 19-20 19-39 28-29 2849
So(lA,) 1.462 1.465 1.412 1.476 1.398 1.450 1.428 1.466 1.441 1.392 1.469 1.479 1.416 1.459 1.473 1.402 1.449 1.468 1.448 1.463 1.439 1.444 1.491 1.418 1.417 1.483 1.434 1.489 1.420 1.492
Sl(lB3) 1.463 1.467 1.410 1.464 1.407 1.461 1.430 1.458 1.439 1.397 1.471 1.471 1.416 1.458 1.475 1.397 1.453 1.468 1.454 1.452 1.437 1.458 1.489 1.421 1.462 1.48 1 1.438 1.487 1.428 1.484
Sz(lB2) 1.462 1 A65 .. .-“
1.414 1.469 1.405 1.453 1.434 1.464 1.441 1.395 1.471 1.473 1.416 1.458 1.472 1.401 1.449 1.461 1.456 1.461 1.432 1.454 1.493 1.423 1.462 1.478 1.444 1.484 1.427 1.487
S3(1Bl) 1.461 ~~
1461 *._“I
1.414 1.468 1.407 1.458 1.428 1.459 1.445 1.396 1.467 1.477 1.425 1.456 1.477 1.399 1.449 1.470 1.449 1.452 1.441 1.455 1.489 1.415 1.470 1.482 1.437 1.487 1.423 1.488
is to obtain meaningful information from the preresonant Raman spectrum shown in Figure 1. The depolarization ratios of the vibrational bands showed that only those at 1451 and 436 cm-l may be non totally symmetric. In the calculations, we decidedto neglect the non totally symmetric bands and focus only on the a1 bands which provide direct information on the geometry changes upon excitation. In fact, these phonons appear in the Raman spectrum because their equilibrium positionsin the initial and in the preresonant electronic states are different (vide infra). If one makes use of the algebra of the harmonicoscillator,l*thevibrational part of the preresonant Raman scattering cross section can be written in terms of the Franck-Condon integral between the initial vibrationless ground state and the preresonant vibrational states of the electronically excited state. The preresonant Raman scattering cross section for the fundamental of the mth totally symmetricvibration, F,( l), is therefore proportional to13
1668 1668 1641 1635 1582 1561 1494 1487 1480 1468 1452 1428 1401 1375 1359 1349 1315 1308 1259 1231 1200 1191 1180 1096 1077 1039 1027 921 904 860 815 799 787 756 749 728 716 712 707 695 684 662 580 549 534 524 484 474 454 406 390 384 379 323 292 245 204
0.0044 0.0186 -0.0449 -0,0420 -0.0020 -0.0076 0.0187 -0.0095 0.0002 0.0068 0.0017 -0.0035 -0,0143 -0.0233 -0,0019 0.0133 -0.0121 -0.0043 0.0156 -0.0056 -0.0118 0.0340 0.0716 -0.0250 0.0182 0.0070 -0.0020 -0,0136 0.0032 0.0016 -0.0008 0.0004 0.0007 0.0038 0.0138 -0.0210 0.0224 0.0009 -0.0179 -0.0012 -0,0233 -0.0045 0.0122 -0.0034 -0.0157 -0,0184 -0.0160 0.0263 0.0017 -0.0172 0.0286 0.0333 0.0501 0.2041 -0.1267 0.1532 -0.0106
-0.0183 4.0041 -0.0346 -0.0327 -0.0074 -0.0035 0.0162 -0.0066 0.0019 0.0223 0.0044 0.0095 -0.0074 -0.0082 -0.0030 0.041 1 -0.0242 -0,0076 0.0114 -0.0016 -0.0123 0.0044 0.0482 -0.0040 0.0273 0.0152 0.0030 -0.0078 0.0066 0.0021 0.0077 0.0040 0.0012 0.0074 0.0002 -0.0213 -0.0055 -0.0036 -0.0030 -0.0116 0.0001 -0.0068 0.0078 -0.01 11 -0.0199 0.0090 -0.0102 0.0107 -0.0066 -0.0094 -0.0004 0.0195 0.0452 0.1969 -0.1352 -0.0265 0.0358
0.0101 0.0325 -0.0125 -0,0350 -0.0034 -0.0056 0.0138 0.0025 -0.0027 -0.0137 0.0075 0.0040 -0,0242 -0.0142 -0.0018 0.0288 -0.0074 0.0037 0.0059 -0.0022 -0.0027 0.03 16 0.0373 -0.0329 0.0094 -0.0076 -0.0091 -0.0024 0.0051 0.0044 -0.0030 -0.0021 -0.0058 -0.0028 -0.0028 -0.0373 0.0343 -0.0046 -0.0235 -0,0020 -0,0187 -0.0084 0.0157 -0.0095 0.0023 -0.0187 -0.0090 0.0112 -0.0041 -0.0031 0.0387 0.0216 0.0383 0.0950 -0.0480 0.1419 -0.1027
where i = 1,2,3 is the ith electronic state, umt is the vibrational quantum number of the preresonant level of the mth mode in the ith state, Bmfis displacement from the ground state equilibrium position, g, of the mth mode in the ith state, (#dog) is the FranckCondon integral, MBIis the electronic transition dipole moment between the ground state and the ith state, AE# is the excitation energy from the ground state to the ith state, and hv is the laser excitation energy. In practice, B,, is calculated as14J5
B,, = 0.172vm’/’[Q,- Qo]M”2L, = 0.172~,‘/~A~,(2) where V , (cm-1) and L, are the mth frequency and mth normal
Letters
The Journal of Physical Chemistry, Vol. 98, No. 33, 1994 7935
A
1
0
Figure 3. Simulated preresonance Raman spectrum of c76. The calculated stick spectrum was convoluted with a Gaussian line widths (a = 5 cm-1).
The Raman scattering is in arbitrary units. mode coordinate in the ground state, Mis the 3N X 3Ndiagonal matrix of atomic masses, in amu, and Qi and QOare the Cartesian coordinate vectors, in angstroms, of Si and SO. The QCFF/PI calculationsof the electronicexcitation energies confirmed the results of our previous calculation.ll The S1state is of B3 symmetry and is located at 1.73 eV, S2 is of Bz symmetry and is located at 2.22 eV, and S3 is of B1 symmetry and is located at 2.28 eV. In Table 1, we show the calculated SO,SI, Sz,and S3 bond lengths for the 30 symmetry-independent bonds of C76. Symmetry constraints were not imposed on the geometry. This shows that the molecular structures of the four electronic states considered in the present calculation belong to the Dz point group symmetry. The atom numbering can be found in Figure 2, where only 49 atoms are displayed. With respect to the ground state bond lengths, the changes are relatively small and differ from state to state. As a rule of thumb, one can notice that the short bonds tend, upon excitation, to elongate while the long bonds tend to shorten. This is in keeping with the notion that electronic excitation transfers electron density from short bonds to long bonds. A similar behavior is well-known for the oligomers of polyacetylene.15 In Table 2, we give the Amivalues for the three electronically excited states considered here. Because of their relatively small values, one can see that only the term with u = 0 contributes to the sum in eq 1. This makes possible to set the Franck-Condon integral (Od, tounity. ) Inother words, apart fromany numerical consideration, the values of Ami in Table 2 show that the only virtual vibroelectronic transition that contributes to the preresonance Raman cross section is that from the vibrationless ground state to the vibrationless electronically excited state. To simulate the spectrum, we need the values of Ma. We take them from the QCFF/PI calculation: Mgl = 0.15, M,z = 0.69, Mg3 = 0.74. The excitation energies are also taken from the present calculation (see above). These values are reasonable if compared with the experiment4 with our previous calculations.11 To make the simulation more adherent to reality, we scale the calculated frequencies according to the simple rule suggested before for the QCFF/PI frequencieslobJ6 (3) and convolutethe calculated stick spectrum (fundamental energies and cross sections) with a line shape. Such a line shape can be described by a Gaussian function. Each line calculated quantum chemically is then broadened by multiplying it by a function G(nh (4)
where v is thescattered Stokesradiation,incm-l, vois thevibration fundamental, in cm-l, and a is a constant, in cm-l, that accounts
for both homogeneous and inhomogeneous broadening. In the present simulation, we set a = 5 cm-1. In Figure 3, we show the result of the simulation of the Raman spectrum. Above 500 cm-l frequency region, the simulation is remarkably successful. This shows that the Raman scattering is mainly due to the mechanism described in eq 1. In particular, the simulation reproduces the three major patterns present in the spectrum, which are the following: (i) Two strong bands appear around 1600 and 1200 cm-l. In between these two bands, some medium to weak bands appear with the strongest one at 1300 cm-l. (ii) Between 500 and 1100 cm-l there is little scattering, with the strongest band around 700 cm-l and a doublet at 1100 cm-l. (iii) The region below 500 cm-l scatters the most; however, the very strong band at 436 cm-1 is absent in our calculation because it is non totally symmetric (vide supra). The partial success of the simulation for this spectral region is due to the presence of non totally symmetric bands and also to the fact that the QCFF/PI method is better suited to describe the modifications upon excitation induced by modes of the high-frequency region, namely, CC stretches, rather than those due to low-frequency vibrations, namely, CCC bendings. In conclusion, we have shown that the preresonance Raman spectrum of C76 is mainly due to totally symmetric modes which gather intensity from the three lowest energy electronictransitions through the Franck-Condon mechanism.
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Shiromaru, H.; Yamauchi, K.; Ikemoto, I.; Kuramochi, T.; Hino, S.;Achiba, Y. Chem. Lett. 1991, 9, 1607. (8) Warshel, A.; Karplus, M. J. Am. Chem. SOC.1972, 94, 5612. (9) Negri, F.\Orlandi,G.;Zerbetto, F. Chem. Phys. Lert. 1988,144,31. Negri, F.; Orlandi, G.; Zerbetto, F. Chem. Phys. Leu. 1992, 190. 174. (10) Negri, F.;Orlandi, G.; Zerbetto, F. J . Am. Chem. Soc. 1991, 113, 6037. Christides, C.; Nikolaev, A. V.; Dennis, T. J. S.; Prassidcs, K.; Negri, F.; Orlandi, G.; Zerbetto, F. J . Phys. Chem. 1993, 97, 3641. (1 1) Orlandi, G.; Zerbetto, F.; Fowler, P. W.; Manolopoulos,D. E. Chem. Phys. Lett. 1993, 208, 441. (12) Manneback, C. Physica (Utrecht) 1951, 17, 1001. (13) Siebrand, W.; Zgierski, M. 2.In Excited Srares; Lim, E.C., Ed.; Academic Press: New York, 1979; Vol. 4, p 1. (14) Zerbetto, F.; Zgierski, M. Z. Chem. Phys. 1988, 127, 17. (15) Orlandi, G.; Zerbetto, F.; Zgierski, M. Z . Chem. Reu. 1991,91,867. (16) Orlandi, G.; Zerbetto, F.; Fowler, P. W. J . Phys. Chem. 1993, 97, 13575.
