- Email: [email protected]
Orientational behavior of C70 molecules in chlorobenzene
CHEMICAL
26 January 1996
PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 249 (1996) 101-104
Orientational behavior of C70 molecules in chlorobenzene Igor V. Rubtsov l, Dmitrii V. Khudiakov, Alexander P. Moravskii, Victor A. Nadtochenko Institute of Chemical Physics, Russian Academy of Sciences, 142432 Chernogolooka, Moscow region, Russian Federation Received 7 September 1995
Abstract
The orientational behavior of C70 singlet excited molecules in a chlorobenzene solution has been measured at room temperature by the picosecond transient grating technique. A two-stage decay signal was observed: a fast part (~-= 12 + 5 ps) which is comparable with the corresponding signal of C6o in chlorobenzene (r = 8 _ 2 ps), and a slow part (~-= 30 + 5 ps). The data obtained are analyzed in terms of the rotation of C7o molecules. The influence of the dielectric friction on the C7o rotation is reported.
1. Introduction The rotational dynamics of the fullerenes attract great interest due to their unique shape and large delocalized ~-conjugated electron system [1-8]. Thin C60 and C70 films have been studied using the third harmonic generation method [1] and time-resolved degenerate four-wave mixing technique [2]. In solutions, the C60 rotation has been measured by ~3C-NMR [3-5], EPR [6], and fluorescence depolarization spectroscopy [7]. The orientational time of C60 in solutions measured by ~3C-NMR technique was 15.5 ps in tetrachloroethane at 283 K [1], 16 ps in carbon disulfide at 298 K [2], and 16.9 ps in deuterated toluene at 303 K [3]. To our knowledge
E-mail: [email protected] Elsevier Science B.V. SSDI 0009-261 4(95)0 1375-X
there are no works where the orientational behavior of C 70 in solution was detected. Recently we have studied orientational dynamics of C60 excited molecules in four different solvents by the picosecond transient grating technique [8]. It was shown that the orientation relaxation was very fast and could not be described by the hydrodynamic Stokes-Einstein-Debye (SED) theory. The prediction of a microscopic rough sphere fluid theory [9] for C60 rotation in toluene, o-dichlorobenzene, chlorobenzene, and decalin agree with our experimental data. The C60 rotation in decalin and to some extent in toluene is so fast that it is not diffusional but is governed by inertia. Our orientational time of C6o in toluene is approximately two times less than the value measured by NMR technique in deuterated toluene [3]. Perhaps the electron polarization of C60 excited molecule is not completely associated with the molecular skeleton.
102
I.V. Rubtsov et a l . / Chemical Physics Letters 249 (1996) 1 0 1 - 1 0 4
In this work, we will discuss the C7o orientational behavior in chlorobenzene in comparison with the C60 orientationai motion.
Experiments were performed in a 1.0 mm cavity at a temperature of 23 _+ I°C. The concentrations of C60 and C7o were 3 x 10 -3 and 1.7× 10 -3 M, respectively.
2. Experimental details 3. Results and discussion Experimental details of the picosecond transient grating technique were given elsewhere [8,10]. In the present study to eliminate the contribution of thermal grating, a crossed grating technique was used [1 1]. Briefly, the light of an Nd3+-glass mode-locked laser (it = 1055 nm, '/'(fwl.n)= 6.2 ps) and its harmonics (528 nm) were the source of short pulses. The excitation of C60, C70 solutions by two coherent timecoincident pulses with perpendicular polarizations at 528 nm forms phase grating. The third beam (h = 1055 nm) with the 45 ° polarization relative to the pump beam diffracts at this phase grating and probes the grating with various time delays. The diffraction efficiency 7/~ (/Xn) 2, where An = n°5 n°_45, n°45 and n°45 are the refraction indices for polarization directions at 45 ° and - 4 5 ° versus pump polarizations, respectively. The diffracted light energy was detected by a photodiod. Typical energies of a single pulse focused into the sample were about 1-5 txJ in each of two pump beams and the energy of the probe beam was approximately 10 times lower. The spot sizes of the pump and probe beams were 250-300 p~m and --- 200 txm, respectively. In addition, intensities of pump and probe pulses were measured for each detected point. The signals from photodetectorSby a computer.Were amplified, digitized, and treated The C7o is much less convenient than C6o for probing at 1055 nm wavelength. The extinction coefficient°fC7° singlet excited state at 1 0 5 5 n m ( r s ' ) is rather small (~< 2 × 10 3 (M cm) - I ) [12,13]. The extinction coefficient of C7o triplet state at 1055 nm (r v) is approximately two times larger than rsl [12,13], in contrast to C6o for which rs~ is much larger than r. r [14]. So to minimize the thermal grating we use the crossed grating technique for C7o investigation. The experiment for C60 in chlorobenzene has been also performed in crossed grating setup for comparison with C70, but the more accurate data for C6o w e r e obtained in the ordinary grating polarization configuration (zzzz, zzyy) [15].
Since the two pulses used to form the grating have perpendicular polarizations, the two fields do not interfere and, hence, there is no spatial modulation of the total incident light intensity. No transient population grating can be formed. However, there is a spatial variation in the orientations of these excited states, which acts as a grating to diffract a polarized probe beam [10,11]. The time dependencies of the diffracted signal at a probe wavelength of 1055 nm measured for solutions of C70 and C60 in chlorobenzene are shown in Fig. 1. There is a contribution of the nonlinear signal from chlorobenzene to the signal from C70 excited molecules. It is known that the nonlinear signal from chlorobenzene exhibits two stages: a fast electron component (r < 1 ps) and a slow orientational part with characteristic time of = 6.3 ps [15,16]. Nevertheless, starting from the time delay of = 10 ps, the signal is almost completely determined by the excited C70. The signal of C60 is nearly exponential, while the nonlinear signal from C70 has two components: a fast part and a slow part. Considering that the C70 molecule is a prolate
1.o I
~
1.ooo~
,
o.1oo .~B ~ -1 .~6 .~ ] .4
02
/
\
/
°°I° l
I
~/V
"~
o.ool/ ........................ o 1o 2o 3o 4o .~
~
!)
oo :~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -10
0
"10
Time, (On)
20
30
Fig. 1. Time dependence of the transient grating signal for (1) C6o and (2) C7o in chlorobenzene. Aoump= 528 nm, Aorobe = 1055
nm.
I.V. Rubtsov et a l . / Chemical Physics Letters 249 (1996) 101-104
ellipsoid, one can expect that the orientational relaxation will consist of two parts: one part arising from the orientational relaxation around the main axis of the ellipsoid and another part connected with the relaxation around the axis perpendicular to the main axis. The diffraction efficiency is equal to r/(t) ~ [ a exp( -t/'r I ) ×exp(-2t/%),
+ b exp( -t/'r 2)]2 (1)
where ~ ' l = ( 4 D l + 2 D 2 )-~ and I"2=(6D2) -I are the characteristic times of rotation around short and long axes, respectively; D l and D 2 are the proper diffusion coefficients; a and b are constants; and ~s is the lifetime of the excited state, which is much greater than T 1 and 7"2 ( 7 " s = 550 ps [12,13]). We have made the theoretical fitting using Eq. (1) and have obtained the following values: T 1 = 12 + 5 ps, ~'2 = 30 ___5 ps, and a / b = 3 _+ 0.5. These data were checked by various theories. For calculation of orientational times the values of 5.15 and 5.85 ,~ were used for short and long semi-axes, respectively. According to the SED theory [17] assuming stick boundary conditions, for the rotation of C70 (prolate ellipsoid) in clorobenzene one can obtain the values ~'1 = 124 ps and ~'2 = 131 ps, which are too large. The microscopic rough sphere fluid theory (HKW - Hynes, Kapral, and Weinberg) [8,9] gives the values of ~'1 = 13 ps and T2 = 15 ps that coincide better with the experimental values, although with the invalid ratio of Tj/~-:. Unlike C60 there is a distribution of slight charge polarization in C70 [18,19]. This charge distribution causes additional dielectric friction that can drastically change the orentational times [20]. The C70 molecule has D5h symmetry, so the dielectric friction will be only for the rotation around the short axes. The solvent in this approach is treated as a continuous dielectric medium with dielectric constant e~. The dielectric friction coefficient [20] is given by
8 (,s-l)
N N
~:= a (2 ~ + 1)2 r Dj Z =l
Z
i=1
L (2L+l L~= 1 M =ZI
× ( L +--~! M 3qi qj ×P~(cos
Oj) cos( M~bji).
/
-I Lt + 1
P~ (cos 0~) (2)
103
where a is the radius of the spherical cavity, determined from the C?0 volume, ~'D is the dielectric relaxation time of the solvent, P ~ are the Legendre polynomials, Sji = ~ b j - (hi, and the rotating molecule is a collection of N point charges q~ with coordinates r i, 0 i, chi. We have calculated the dielectric contribution to the orientation time for two models of charge distribution of C70 according to the works of Tanaka and co-workers [18] and Harigaya [19]. These contributions to the orientation time of C70 rotation around the short axes in chlorobenzene (e s ~ 5.7) are equal to 5 and 7 ps, respectively. When we add the value for dielectric friction to the value predicted by the HKW theory we obtain the value of 20-22 ps for rotation around the short axes, which is in a reasonable agreement with the experimental value (30 _+ 5 ps). Very large orientational times from the hydrodynamic SED theory and the better agreement of the HKW theory predictions allow one to conclude that slip boundary conditions appropriate better for the orientational motion of C70 in clorobenzene. This confirmation agrees with a data of investigation of C60 and C70 translational diffusion in solution [21] which follow the predictions of the Stokes-Einstein equation only under slip boundary conditions. In conclusion, the two stage signal for C70 excited state polarization decay was observed. A fast part (12 _+ 5 ps) can be attributed to the C70 rotation around the long axes, the slow part (30 _+ 5 ps) around the short axes. The rough sphere fluid theory predicts a correct value for the C70 rotation across the long axes. The dielectric friction affects the rotation around the short axes. Taking in to account the dielectric friction we obtain a good approximation for C70 rotation across the short axes. The slip boundary conditions are exhibited for C 70 rotation.
Acknowledgement The financial support by the International Science Foundation (Grant NJH000), the International Science Foundation and the Russian Government (Grant NJH300), and the Russian Foundation of Fundamental Researches (Grant 95-03-08247a) is gratefully acknowledged.
104
I.V. Rubtsov et a l . / Chemical Physics Letters 249 (1996) 101-104
References [1] F. Kajzar, C. Taliani, R. Danieli, S. Rossini and R. Zamboni, Phys. Rev. Letters 73 (1994) 1617. [2] J.M. Rosker, H.O. Marcy, T.Y. Chang, J.T. Khoury, K. Hansen and R.L. Whetten, Chem. Phys. Letters 196 (1992) 427. [3] R.D. Johnson and C.S. Yannoni et al., Science 255 (1992) 1235. [4] D. Canet, J.B. Robert and P. Tekely, Chem. Phys. Letters 212 (1993) 483. [5] V.K. Jones and A.A. Rodriguez, Chem. Phys. Letters 198 (1992) 373. [6] A. Regev, D. Gamliel, V. Meiklyar, S. Michaeli and H. Levanon, J. Phys. Chem. 97 (1993) 3671. [7] M. Rou and S. Dorasvamy, Chem. Phys. Letters 225 (1994) 181. [8] L.V. Rubtsov, D.V. Khudiakov, V.A. Nadtochenko, A.S. Lobach and A.P. Moravskii, Chem. Phys. Letters 229 (1994) 517. [9] J.T. Hynes, R. Kapral and M. Weinberg, J. Chem. Phys. 69 (1978) 2725; J.L. Dote, D. Kivelson and R.N. Schwartz, J. Phys. Chem. 85 (1981) 2169. [10] H.J. Eichler, P. Gunter and D.W. Pohl, Laser-induced dynamic gratings (Springer, Berlin, 1986);
[11] [12] [13]
[14] [15] [16] [17] [18] [19] [20]
[21]
A. Von Jena and H.E. Lessing, Opt. Quantum Electron. 11 (1979) 419. A.B. Myers and R.M. Hochstrasser, J. Quantum Electron QE 22 (1986) 1482. K. Tanigaki, T.W. Ebbesen and S. Kuroshima, Chem. Phys. Letters 185 (1991) 189. I.V. Vasil'ev, V.A. Nadtochenko, N.N. Denisov, A.C. Lobach and A.P. Moravskii, Zh. Fizich. Himii. (Russian) 67 (1993) 1880. T.W. Ebbesen, K. Tanigaki and S. Kuroshima, Chem. Phys. Letters 181 (1991) 501. D.V. Khudiakov, I.V. Rubtsov, A.S. Lobach and V.A. Nadtochenko, ICONO, June 1995, St. Peterburg, to be published. W.T. Lotshow, D. McMorrow, C. Kalponzos and G.A. Kenney-Wallace, Chem. Phys. Letters 136 (1987) 323. F. Perrin, J. Phys. Radium 5 (1934) 497. K. Tanaka, M. Okada, K. Okahara and T. Yamabe, Chem. Phys. Letters 202 (1993)394. K. Harigaya, Phys. Rev. B 45 (1992) 13767. D.S. Alavi and D.H. Waldeck, J. Chem. Phys. 94 (1991) 6196; T.W. Nee and R. Zwanzig, J. Chem. Phys. 52 (1970) 6353. R. Haselmeier, M. Holz, M.M. Kappes and R.M. Michel, Ber. Bunsenges. Physik. Chem. 98 (1994) 878.
26 January 1996
PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 249 (1996) 101-104
Orientational behavior of C70 molecules in chlorobenzene Igor V. Rubtsov l, Dmitrii V. Khudiakov, Alexander P. Moravskii, Victor A. Nadtochenko Institute of Chemical Physics, Russian Academy of Sciences, 142432 Chernogolooka, Moscow region, Russian Federation Received 7 September 1995
Abstract
The orientational behavior of C70 singlet excited molecules in a chlorobenzene solution has been measured at room temperature by the picosecond transient grating technique. A two-stage decay signal was observed: a fast part (~-= 12 + 5 ps) which is comparable with the corresponding signal of C6o in chlorobenzene (r = 8 _ 2 ps), and a slow part (~-= 30 + 5 ps). The data obtained are analyzed in terms of the rotation of C7o molecules. The influence of the dielectric friction on the C7o rotation is reported.
1. Introduction The rotational dynamics of the fullerenes attract great interest due to their unique shape and large delocalized ~-conjugated electron system [1-8]. Thin C60 and C70 films have been studied using the third harmonic generation method [1] and time-resolved degenerate four-wave mixing technique [2]. In solutions, the C60 rotation has been measured by ~3C-NMR [3-5], EPR [6], and fluorescence depolarization spectroscopy [7]. The orientational time of C60 in solutions measured by ~3C-NMR technique was 15.5 ps in tetrachloroethane at 283 K [1], 16 ps in carbon disulfide at 298 K [2], and 16.9 ps in deuterated toluene at 303 K [3]. To our knowledge
E-mail: [email protected] Elsevier Science B.V. SSDI 0009-261 4(95)0 1375-X
there are no works where the orientational behavior of C 70 in solution was detected. Recently we have studied orientational dynamics of C60 excited molecules in four different solvents by the picosecond transient grating technique [8]. It was shown that the orientation relaxation was very fast and could not be described by the hydrodynamic Stokes-Einstein-Debye (SED) theory. The prediction of a microscopic rough sphere fluid theory [9] for C60 rotation in toluene, o-dichlorobenzene, chlorobenzene, and decalin agree with our experimental data. The C60 rotation in decalin and to some extent in toluene is so fast that it is not diffusional but is governed by inertia. Our orientational time of C6o in toluene is approximately two times less than the value measured by NMR technique in deuterated toluene [3]. Perhaps the electron polarization of C60 excited molecule is not completely associated with the molecular skeleton.
102
I.V. Rubtsov et a l . / Chemical Physics Letters 249 (1996) 1 0 1 - 1 0 4
In this work, we will discuss the C7o orientational behavior in chlorobenzene in comparison with the C60 orientationai motion.
Experiments were performed in a 1.0 mm cavity at a temperature of 23 _+ I°C. The concentrations of C60 and C7o were 3 x 10 -3 and 1.7× 10 -3 M, respectively.
2. Experimental details 3. Results and discussion Experimental details of the picosecond transient grating technique were given elsewhere [8,10]. In the present study to eliminate the contribution of thermal grating, a crossed grating technique was used [1 1]. Briefly, the light of an Nd3+-glass mode-locked laser (it = 1055 nm, '/'(fwl.n)= 6.2 ps) and its harmonics (528 nm) were the source of short pulses. The excitation of C60, C70 solutions by two coherent timecoincident pulses with perpendicular polarizations at 528 nm forms phase grating. The third beam (h = 1055 nm) with the 45 ° polarization relative to the pump beam diffracts at this phase grating and probes the grating with various time delays. The diffraction efficiency 7/~ (/Xn) 2, where An = n°5 n°_45, n°45 and n°45 are the refraction indices for polarization directions at 45 ° and - 4 5 ° versus pump polarizations, respectively. The diffracted light energy was detected by a photodiod. Typical energies of a single pulse focused into the sample were about 1-5 txJ in each of two pump beams and the energy of the probe beam was approximately 10 times lower. The spot sizes of the pump and probe beams were 250-300 p~m and --- 200 txm, respectively. In addition, intensities of pump and probe pulses were measured for each detected point. The signals from photodetectorSby a computer.Were amplified, digitized, and treated The C7o is much less convenient than C6o for probing at 1055 nm wavelength. The extinction coefficient°fC7° singlet excited state at 1 0 5 5 n m ( r s ' ) is rather small (~< 2 × 10 3 (M cm) - I ) [12,13]. The extinction coefficient of C7o triplet state at 1055 nm (r v) is approximately two times larger than rsl [12,13], in contrast to C6o for which rs~ is much larger than r. r [14]. So to minimize the thermal grating we use the crossed grating technique for C7o investigation. The experiment for C60 in chlorobenzene has been also performed in crossed grating setup for comparison with C70, but the more accurate data for C6o w e r e obtained in the ordinary grating polarization configuration (zzzz, zzyy) [15].
Since the two pulses used to form the grating have perpendicular polarizations, the two fields do not interfere and, hence, there is no spatial modulation of the total incident light intensity. No transient population grating can be formed. However, there is a spatial variation in the orientations of these excited states, which acts as a grating to diffract a polarized probe beam [10,11]. The time dependencies of the diffracted signal at a probe wavelength of 1055 nm measured for solutions of C70 and C60 in chlorobenzene are shown in Fig. 1. There is a contribution of the nonlinear signal from chlorobenzene to the signal from C70 excited molecules. It is known that the nonlinear signal from chlorobenzene exhibits two stages: a fast electron component (r < 1 ps) and a slow orientational part with characteristic time of = 6.3 ps [15,16]. Nevertheless, starting from the time delay of = 10 ps, the signal is almost completely determined by the excited C70. The signal of C60 is nearly exponential, while the nonlinear signal from C70 has two components: a fast part and a slow part. Considering that the C70 molecule is a prolate
1.o I
~
1.ooo~
,
o.1oo .~B ~ -1 .~6 .~ ] .4
02
/
\
/
°°I° l
I
~/V
"~
o.ool/ ........................ o 1o 2o 3o 4o .~
~
!)
oo :~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -10
0
"10
Time, (On)
20
30
Fig. 1. Time dependence of the transient grating signal for (1) C6o and (2) C7o in chlorobenzene. Aoump= 528 nm, Aorobe = 1055
nm.
I.V. Rubtsov et a l . / Chemical Physics Letters 249 (1996) 101-104
ellipsoid, one can expect that the orientational relaxation will consist of two parts: one part arising from the orientational relaxation around the main axis of the ellipsoid and another part connected with the relaxation around the axis perpendicular to the main axis. The diffraction efficiency is equal to r/(t) ~ [ a exp( -t/'r I ) ×exp(-2t/%),
+ b exp( -t/'r 2)]2 (1)
where ~ ' l = ( 4 D l + 2 D 2 )-~ and I"2=(6D2) -I are the characteristic times of rotation around short and long axes, respectively; D l and D 2 are the proper diffusion coefficients; a and b are constants; and ~s is the lifetime of the excited state, which is much greater than T 1 and 7"2 ( 7 " s = 550 ps [12,13]). We have made the theoretical fitting using Eq. (1) and have obtained the following values: T 1 = 12 + 5 ps, ~'2 = 30 ___5 ps, and a / b = 3 _+ 0.5. These data were checked by various theories. For calculation of orientational times the values of 5.15 and 5.85 ,~ were used for short and long semi-axes, respectively. According to the SED theory [17] assuming stick boundary conditions, for the rotation of C70 (prolate ellipsoid) in clorobenzene one can obtain the values ~'1 = 124 ps and ~'2 = 131 ps, which are too large. The microscopic rough sphere fluid theory (HKW - Hynes, Kapral, and Weinberg) [8,9] gives the values of ~'1 = 13 ps and T2 = 15 ps that coincide better with the experimental values, although with the invalid ratio of Tj/~-:. Unlike C60 there is a distribution of slight charge polarization in C70 [18,19]. This charge distribution causes additional dielectric friction that can drastically change the orentational times [20]. The C70 molecule has D5h symmetry, so the dielectric friction will be only for the rotation around the short axes. The solvent in this approach is treated as a continuous dielectric medium with dielectric constant e~. The dielectric friction coefficient [20] is given by
8 (,s-l)
N N
~:= a (2 ~ + 1)2 r Dj Z =l
Z
i=1
L (2L+l L~= 1 M =ZI
× ( L +--~! M 3qi qj ×P~(cos
Oj) cos( M~bji).
/
-I Lt + 1
P~ (cos 0~) (2)
103
where a is the radius of the spherical cavity, determined from the C?0 volume, ~'D is the dielectric relaxation time of the solvent, P ~ are the Legendre polynomials, Sji = ~ b j - (hi, and the rotating molecule is a collection of N point charges q~ with coordinates r i, 0 i, chi. We have calculated the dielectric contribution to the orientation time for two models of charge distribution of C70 according to the works of Tanaka and co-workers [18] and Harigaya [19]. These contributions to the orientation time of C70 rotation around the short axes in chlorobenzene (e s ~ 5.7) are equal to 5 and 7 ps, respectively. When we add the value for dielectric friction to the value predicted by the HKW theory we obtain the value of 20-22 ps for rotation around the short axes, which is in a reasonable agreement with the experimental value (30 _+ 5 ps). Very large orientational times from the hydrodynamic SED theory and the better agreement of the HKW theory predictions allow one to conclude that slip boundary conditions appropriate better for the orientational motion of C70 in clorobenzene. This confirmation agrees with a data of investigation of C60 and C70 translational diffusion in solution [21] which follow the predictions of the Stokes-Einstein equation only under slip boundary conditions. In conclusion, the two stage signal for C70 excited state polarization decay was observed. A fast part (12 _+ 5 ps) can be attributed to the C70 rotation around the long axes, the slow part (30 _+ 5 ps) around the short axes. The rough sphere fluid theory predicts a correct value for the C70 rotation across the long axes. The dielectric friction affects the rotation around the short axes. Taking in to account the dielectric friction we obtain a good approximation for C70 rotation across the short axes. The slip boundary conditions are exhibited for C 70 rotation.
Acknowledgement The financial support by the International Science Foundation (Grant NJH000), the International Science Foundation and the Russian Government (Grant NJH300), and the Russian Foundation of Fundamental Researches (Grant 95-03-08247a) is gratefully acknowledged.
104
I.V. Rubtsov et a l . / Chemical Physics Letters 249 (1996) 101-104
References [1] F. Kajzar, C. Taliani, R. Danieli, S. Rossini and R. Zamboni, Phys. Rev. Letters 73 (1994) 1617. [2] J.M. Rosker, H.O. Marcy, T.Y. Chang, J.T. Khoury, K. Hansen and R.L. Whetten, Chem. Phys. Letters 196 (1992) 427. [3] R.D. Johnson and C.S. Yannoni et al., Science 255 (1992) 1235. [4] D. Canet, J.B. Robert and P. Tekely, Chem. Phys. Letters 212 (1993) 483. [5] V.K. Jones and A.A. Rodriguez, Chem. Phys. Letters 198 (1992) 373. [6] A. Regev, D. Gamliel, V. Meiklyar, S. Michaeli and H. Levanon, J. Phys. Chem. 97 (1993) 3671. [7] M. Rou and S. Dorasvamy, Chem. Phys. Letters 225 (1994) 181. [8] L.V. Rubtsov, D.V. Khudiakov, V.A. Nadtochenko, A.S. Lobach and A.P. Moravskii, Chem. Phys. Letters 229 (1994) 517. [9] J.T. Hynes, R. Kapral and M. Weinberg, J. Chem. Phys. 69 (1978) 2725; J.L. Dote, D. Kivelson and R.N. Schwartz, J. Phys. Chem. 85 (1981) 2169. [10] H.J. Eichler, P. Gunter and D.W. Pohl, Laser-induced dynamic gratings (Springer, Berlin, 1986);
[11] [12] [13]
[14] [15] [16] [17] [18] [19] [20]
[21]
A. Von Jena and H.E. Lessing, Opt. Quantum Electron. 11 (1979) 419. A.B. Myers and R.M. Hochstrasser, J. Quantum Electron QE 22 (1986) 1482. K. Tanigaki, T.W. Ebbesen and S. Kuroshima, Chem. Phys. Letters 185 (1991) 189. I.V. Vasil'ev, V.A. Nadtochenko, N.N. Denisov, A.C. Lobach and A.P. Moravskii, Zh. Fizich. Himii. (Russian) 67 (1993) 1880. T.W. Ebbesen, K. Tanigaki and S. Kuroshima, Chem. Phys. Letters 181 (1991) 501. D.V. Khudiakov, I.V. Rubtsov, A.S. Lobach and V.A. Nadtochenko, ICONO, June 1995, St. Peterburg, to be published. W.T. Lotshow, D. McMorrow, C. Kalponzos and G.A. Kenney-Wallace, Chem. Phys. Letters 136 (1987) 323. F. Perrin, J. Phys. Radium 5 (1934) 497. K. Tanaka, M. Okada, K. Okahara and T. Yamabe, Chem. Phys. Letters 202 (1993)394. K. Harigaya, Phys. Rev. B 45 (1992) 13767. D.S. Alavi and D.H. Waldeck, J. Chem. Phys. 94 (1991) 6196; T.W. Nee and R. Zwanzig, J. Chem. Phys. 52 (1970) 6353. R. Haselmeier, M. Holz, M.M. Kappes and R.M. Michel, Ber. Bunsenges. Physik. Chem. 98 (1994) 878.