J. Phys. Chem. 1993,97,5447-5450
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Dynamics of C,o in the Lowest Excited Triplet State at Low Temperatures Masahide Terazima,' Keita Sakurada, and Noboru Hirota' Department of Chemistry, Faculty of Science, Kyoto University, Kyoto, 606 Japan
Hisanori Shinoharat and Yahachi Saito* Department of Chemistry for materials, Mi'e University, Tsu,514, Japan Received: March 16, 1993
The dynamic behavior of C70 in the lowest excited triplet state is investigated by the time-resolved EPR (TREPR) method in methylcyclohexane at low temperatures. From the line width of the TREPR spectrum, thedistributions of the shortest and middle radii of the distorted rugby ball shape are revealed to be inhomogeneously broadened although the longest radius is relatively constant. The observing time dependence of the spectrum after the laser excitation is examined on the basis of the model involving pseudorotation and molecular rotation. The time dependence calculated based on the pseudorotation around the longest axis fits the observed one well. The activation energy of the dynamic deformation is dgtermined.
Introduction
Experiments
The dynamic behavior of fullerenes has been a subject of much attention because of their unique structures.l4 For example, the motion of c60, which possesses z h (spherical) symmetry, has been investigated by NMR1-3and neutron scattering4 in solid phases at low temperatures. These studies revealed that this molecule rotates isotropically even at relatively low temperature. The rotational rates at several temperatures have been determined. In contrast to the high symmetry of C60in the ground state, the time-resolved EPR (TREPR) investigations by several groups have shown that the molecular structure is distorted in the lowest excited triplet (TI) ~ t a t e . ~ -All I ~ of these studies have reported dramatic temperature dependence of the TREPR spectrum and suggested some sorts of molecular motions at low temperatures in the T I state, although different views have been given to the nature of the motion. Similar to Cm, the molecular structure of C70 has high symmetry in the ground state (D5h symmetry). However, contrary to the extensive studieson c60, the dynamicsof C70 has been less studied. The motion in the ground state is only known to be anisotropic rotation in a solid phase at a low temperature by the NMR method.2 In the TI state, it is known to be also deformed from t h e & ,symmetry by the TREPR In a previous paper,8 we have reported the sublevel parameters of the TI state (such as the zero-field splitting (zfs), the relative populating and decay rates, fwhm, and so on) and the remarkable dependence of the spectrum on the delay time between the photoexcitation and the EPR observation. This dependence has been phenomenologically interpreted in terms of an anisotropic spin-lattice relaxation (SLR). In this Letter, we discuss the motion of the c 7 0 in the TI state at low temperatures in more detail. The previously reported spectra are now analyzed by a model involving anisotropic discrete hopping, which suggests the dynamic Jahn-Teller distortion. An activation energy of the hopping is determined from the temperature dependence of the hopping rate, and it is found to be similar to that obtained from the temperature dependence of the TREPR spectrum in the C ~cOa ~ e . ~These ~J~ findings indicate that the dynamic Jahn-Teller distortion plays an important role in the dynamics of C ~ as O well as c60.
The experimental setup for TREPR measurements has been reported elsewhere.8 Briefly, a sample in a quartz tube was excited by an excimer laser (Lumonics Hyper 400) with XeCl operation. The EPR signal is detected by an X band microwave unit (JEOL Co.) without field modulation and fed into a boxcar integrator (PAR 160). Temperature was controlled by an Oxford FSR900 continuous flow cryostat. The fullerene C70 has been prepared and purified by the same method as described in a previous paper.* Spectrogradesolvents (methylcyclohexaneand toluene) were used without further purification.
Present address: Department of Chemistry, Faculty of Science, Nagoya University, Nagoya, 464 Japan. Department of Electronic Engineering, Mi'e University, Tsu,514 Japan. +
0022-365419312097-5447$04.00/0
Calculation Although the molecular structure of C ~ inO the ground state has D5h symmetry (one long axis ( z ) and two equivalent shorter a x e ~ ) , the ~ J structure ~ is distorted in the TIstate to have one long axis (z) and two shorter axes with different lengths (rx < ru;ri is the length of an i axis). At 3 K, the TREPR spectrum just after the laser excitation (0.2 MS) is exactly the same as recorded at 1 ms except for the polarity of the signal? This fact indicates that the molecular distortion is static at this temperature. On the other hand, at elevated temperatures above -30 K, the spectrum shape is extremely sensitive to the delay time between the laser excitation and the observing time. This delay time dependence has been interpreted based on the anisotropic SLR formula, which was phenomenologically derivedas Here we try to reproduce the spectra by taking into account the molecular dynamics directly to obtain further insight into the dynamics of fullerenes. Since C70 possesses the D5h symmetry in the ground state, the distorted molecule in the T I state has five equivalent sites (separated by an rotational angle 72') in a rigid matrix. Based on the pseudo-rotation model, the X and Yaxes are hopping to exchange among such equivalent sites (Figure 1). We assume that this hopping is random and that the spin polarization of an i sublevel after (n + 1)th hopping is expressed by a linear combination of the polarization after nth hopping (E)as
-
where Ci,, is determined by the relationship between the spin function of an j sublevel of the nth transferred state in a finite 0 1993 American Chemical Society
Letters
5448 The Journal of Physical Chemistry, Vol. 97, No. 21, 1993
I
2n/N
2 n/N
Figure 1. Schematic molecular dynamics of c70 based on (a) the pseudorotation model and (b) the molecular rotation model. The slightly distorted pentagons represent the cross section of C70 normal to the longest axis. In the pseudorotation model, the deformation moves to the five equivalent sites withequalprobability. In the rotationmodel, themolecule rotates a certain angle 2 r / N .
magnetic field (pn)) and that in the zero magnetic field (Ikn))
Here we implicitly assume that the spin polarization is conserved during the hopping process.Is The randomly oriented EPR spectrum is calculated after each hopping process. If the molecule is actually rotating, the deformation will move to the next stable site step by step. We calculate the spectrum in this case by the following procedure. First, the X-Y plane is divided into N sections, which represents the number of the stable sites in the matrix. From the starting point where the molecule is photoexcited, C70 moves to the next right or left stable site, or it stays in the same position with an equivalent probability (Figure 1). The polarization after the movement is also assumed to follow eq (1).
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MAGNET IC F IEl0hi
Results and Discussion The TREPR spectra of C70 in methylcyclohexane measured at various delay times are shown in Figure 2A. In our previous paper, we have shown the calculated TREPR spectrum of c70 at low temperature with parameters X = 4.0022 cm-I, Y = 4.001 1 cm-1, Z = 0.0033 cm-1, px-pr:py-pz = 0.7:1.0, and the fwhm AE = 0.9 mT.* The calculated spectrum consists of two sets of two peaks on the high- and low-field sides. The outer peaks are assigned to the Z stationary peaks and the inner peaks to the X and Ystationary points. For convenience, wedefine theintensities of these outer and inner peaks as I,,, and Ii,, respectively, throughout this paper. Although the calculated spectrum qualitatively agrees with the observed spectrum at 3 K, there are two major discrepancies of the calculated spectrum between these spectra. First, Iin/Zout is larger than that of the observed one. This discrepancy cannot be removed no matter how we adjust the populating rates or zfs. Second, the line width of the spectrum observed at sufficiently long time after the excitation at high temperatures is very narrow (0.4 mT) compared with the line width used for the calculation. It is reasonable to consider that the narrowest line width represents the intrinsic line width of C70 in the matrix. However, if we use AB = 0.4 mT in the calculation, the X and Y stationary peaks appear separately in the central portion, and the spectrum disagrees with the observed one seriously. We think that these discrepancies might reflect unique structural and dynamical properties of c70 in the TI state. First we consider the line width problem. The discrepancy can be removed if we assume that the line width of the signal around the central part (the X and Ystationaries) is broader than that at theouterpart (thezstationary). Infact,theobservedspectrum can be fitted better either by superimposing a number of spectra with slightly different zfs (Xand Y) or by phenomenologically broadening the spectrum depending on the X and Y characters
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MAGNETIC FIElD/mT Figure 2. (A) TREPR spectra of c70 in methylcyclohexane measured at (a) 3 K with a delay time 0.5 y and a t 77 K with a delay time of (b) 0.3,(c) 0.5, (d) 1.0, and (e) 2.0 ps. (B) Calculated TREPR spectra of c 7 0 at various delay times based on the pseudorotation model after (a) second hopping, (b) third hopping, (c) fourth hopping, and (d) eighth hopping.
based on the following expression
AB = AB'+ AB"(CAi)+ Cy(i))(C#)+ Cy(j)) (3) where Cdi)and Cy(i)denote the fraction of the x and y characters in the i sublevel, respectively, and AB' and AE" are adjustable
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The Journal of Physical Chemistry, Vol. 97, No. 21, I993 5449
'*t 0
0
2
4
6
8 times
b) lin
'1
0
0
O 0 o
10
20
00
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Figure 3. (a) Calculated I,,/Io,, against the number of the hopping times based on the pseudorotation model (solid line). The experimentally observed values in MCH a t 77 K are shown by circles. (b) Calculated Iin/lout against the number of the rotation steps based on the molecular rotation model (solid line). The experimentally observed values in MCH at 77 K are shown by circles.
parameters for the line width. The various line widths are rationalized by a serious inhomogeneousbroadening at theXand Y stationary points due to the presence of many geometrically different molecules with slightly different radii along the X and Y axes. In this paper, eq 3 is used to reproduce the observed spectrum (AB' = 0.4 mT and AB" = 0.8 mT). The smaller intrinsic line width of the C70 spectrum than that of C ~supports O the interpretation of the observed broad line width in the c 6 0 case:8 the inhomogeneous line broadening. Considering the line widths, we conclude that the structural fluctuation in the TI state of c60 is more than that of C70. Before considering the problem of smaller Zin/Zout in the calculated spectrum, we calculate the effect of the axis hopping (pseudorotation) or the molecular rotation in the TREPR spectrum. Figure 2B shows the calculated spectrum with the pseudorotation model. After several hopping steps, the spectrum starts to change drastically; the central peaks become weaker, and finally only a pair of sharp peaks at the z stationary points remain. The calculated spectra reproduce the delay time dependence of the TREPR spectra very well. As a convenient measure of the number of hoppings, we use the value of Zin/ZOut. This value decreases monotonously with the hopping times as shown in Figure 3a.
't
I
Figure 4. Temperature dependence of the hopping rates (w/s-I) of C70 in MCH.
The delay time dependence can also be reproduced by the molecular rotation model. Figure 3b shows a similar plot of Zin/Zout with N = 20. When we change the dividing step N, the scale of the abscissa will change. Now wecan deduce theoriginof the smalllin/Zout in the observed TREPR spectrum even at very low temperature and at higher temperatures with very short delay time. A probable interpretation is that C70 moves very rapidly just after the creation of the TI stateand thenrotatesuniformly withaconstant ratedetermined by the temperature. This spikelike movement after the photoexcitation might reflect a microenvironmentaltemperature effect around the excited c70. After c70 is excited in the excited singlet state, it should release a part of the electronic energy as heat to go down to the TI state. Then, the microscopic temperature around the excited c70 becomes hot instantaneously. Due to that heat energy, the deformation of the triplet C70 will move. After some short time, the environment cools down and C70 moves uniformly in time. The random hopping and molecular rotation predict different behavior of the time dependence Of Zin/Zo"ts In the pseudorotation case, Zin/Zout decays to zero nearly exponentially after the second step, whereas in the case of the molecular rotation model, Zin/Zou, decays rapidly first and then slowly. We now examine which model explains the observation better. In Figure 3a,b, the measured Zin/Zout values at 77 K are plotted on the calculated curve. For the fitting, we adjust the rate so that Zin/Zout from t = 0 1.1s (which is assumed to 1.49 observed at 3 K) to 0.4 ps is reproduced by the calculated value. The observed values in the whole time range agree well with the calculated curve based on the pseudorotation model. On the other hand, the data seriously disgree with the ones calculated based on the molecular rotation model. Therefore, we believe that the pseudorotation is the mechanism which gives rise to the delay time dependence of the spectrum. According to the fitting, the hopping rate of C ~ inOMCH at 77 K is determined to be 3.6 X lo6s-l. This is the first quantitative measurement of the hopping rate of c 7 0 is the TI state caused by.the dynamic Jahn-Teller effect. Similarly, we can obtain the hopping rates at various temperatures. The Arrhenius type plot of the hopping rates is shown in Figure 4. Although the data are somewhat scattered because of the impurity signal in the central part of the spectrum,l6 the activation energy of the hopping is determined to be 250 f 50 cm-1. This activation energy is on the same order of magnitude with that determined from the temperature dependence of the TREPR spectra of (2.50 reported by Bennati et al. (137 cm-I)l2 and by Regev et al. (75-419 cm-I depending on the temperature range). I
5450 The Journal of Physical Chemistry, Vol. 97, No. 21, 1993
Acknowledgment. We thank Prof. H. Levanon for sending us a preprint of the paper on Cm. This work is supported by Scientific Research Grant-in-Aid for the Priority Area of ‘Molecular Magnetism” (Area No. 228/04242102) by the Ministry of Education, Science and Culture. References and Notes (1) Johnson, R. D.; Bethune, D. S.;Yannoni, C. S. Acc. Chem. Res. 1992, 25, 169. (2) Tycko, R.; Haddon, R. C.; Dabbagh, G.; Glarum, S.H.; Douglass, D. C.; Mujsce, A. M. J. Phys. Chem. 1991, 95, 518. (3) Yannoni, C. S.;Johnson, R. D.; Meijer, G.; Bethune, D. S.; Salem, J. R. J. Phys. Chem. 1991, 95, 9. (4) Neumann, D. A.; Copley, J. R. D.; Kamitakahara, W. A.; Rush, J.
J.; Cappelletti, R. L.; Coustel, N.; Fisher, J. E.; McCauley, Jr., J. P.; Smith, 111, A. B.; Creegan, K. M.; Cox, D. M. J . Chem. Phys. 1992, 96, 8631. (5) Jones, V. K.; Rodriguez, A. A. Chem. Phys. Lett. 1992, 198, 373. (6) Koga, N.; Morokuma, K. Chem. Phys. Letr. 1992, 196, 191. (7) Wasielewski, M. R.; ONeil, M. P.; Lykke, K. R.; Pellin, M. J.; Gruen, D. M. J. Am. Chem. SOC.1991, 113, 2114.
Letters (8) Terazima, M.; Hirota, N.; Shinohara, H.; Saito, Y . Chem. Phys. Lett. 1992, 195, 333. (9) Closs, G. L.; Gautam, P.; Zhang, D.; Krusic, P. J.; Hill, S. A.; Wasserman, E. J. Phys. Chem. 1992, 96, 5228. (10) Levanon, H.; Meiklyar, V.; Michaeli, A.; Michaeli, S.;Regev, A. J. Phys. Chem. 1992, 96,6128.
(1 1) Groenen, E. J. J.; Poluektov, 0.G.; Matsushita, M.; Schmidt, J.; van der Waals, J. H.; Meijer, G. Chem. Phys. Lett. 1992, 197, 314. (12) Bennati, M.; Grupp, A.; Mehring, M.; Dinse, K. P.; Fink, J. Chem. Phys. Lett. 1992, 200, 440. (1 3) During the preparation of this Letter, we have learned that Regev et al. have analyzed the TREPR spectra of C ~atOvarious temperatures based on a similar discrete jump model. Regev, A.; Gamliel, D.; Meiklyav, V.; Michaeli, S.; Levanon, H. J. Phys. Chem. 1993,97, 3671. (14) Taylor, R.; Hare, J. P.; Abdul-Sada, A. K.; Kroto, H. W. J . Chem. SOC.,Chem. Commun. 1990.20, 1423. (15) Mukai, M.;Yamauchi, S.;Hirota, N. J. Phys. Chem. 1992,96,3305. Nakamura, H.; Terazima, M.; Hirota, N. J. Phys. Chem., submitted. (16) The broad signal observed in the central part at 71 K spectrum with delay time 5 ps (Fig. 4 in ref 8) is due to an impurity contained in the C70 sample.
