Transient Effect in Fluorescence Quenching by Electron Transfer. 2

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J. Phys. Chem. 1995, 99, 5354-5358

Transient Effect in Fluorescence Quenching by Electron Transfer. 2. Determination of the Rate Parameters Involved in the Marcus Equation Shigeo Murata,* Sanae Y. Matsuzaki, and M. Tachiya" Department of Physical Chemistry, National Institute of Materials and Chemical Research, Tsukuba, Ibaraki 305, Japan Received: July 20, 1994; In Final Form: January 17, 1995@

Transient effect in fluorescence quenching in solution was measured and analyzed to study electron transfer reactions. In the analysis, the dependence of the rate constant on the donor-acceptor separation was taken into account on the basis of the Marcus equation. The diffusion equation with a distance-dependent sink term was solved numerically, and the solution was used to calculate the fluorescence decay curve. The convolution of the calculated decay curve and the instrument response function was fitted to the observed fluorescence decay curve in order to determine the electron transfer rate parameters involved in the Marcus equation. Fitting was made by a nonlinear least-squares method based on the Marquardt algorithm. It was found that the decay curves can be much better reproduced by this method than by the method based on the Collins-Kimball model. The rate parameters were determined for several donor-acceptor pairs in a viscous solvent, ethylene glycol, and compared with those determined by other methods.

1. Introduction In a previous paper,' we reported the analysis of the transient effect in fluorescence quenching by electron transfer for a variety of donor (D)-acceptor (A) pairs in tetrahydrofuran (THF). Our analysis was based on the Collins-Kimball model of diffusioncontrolled reactions, which assumes that the reaction occurs at a particular D-A distance (called the reaction radius) with an intrinsic reaction rate. It was found that the reaction radius increases as -AG of the reaction increases. This is consistent with the prediction from the Marcus theory of electron transfer. At the same time, it was found that as long as we adopt realistic values of diffusion coefficients, the experimentally obtained fluorescence decay curves and the changes in stationary fluorescence intensity with quencher concentration cannot be satisfactorily reproduced by this model, whatever values of the parameters are assumed. This failure in reproducing the fluorescence decay curves and the changes in stationary fluorescence intensity is probably attributable to the model used for the analysis. Needless to say, electron transfer reactions occur over a range of distance. However, as mentioned above, the Collins-Kimball model assumes that the reaction occurs only at the reaction radius. A more elaborate model seems necessary in order to improve the agreement between experimental and calculated fluorescence decay curves. Several attempts have been made to take into account the distance dependence of the rate. Eads et aL2 analyzed their experimental result with a model proposed by Szabo3 in which the reaction rate is assumed to be constant over a certain range of distance. They have found that this model gives better agreement compared to the Collins-Kimball model. Numerical fits based on a model in which the rate is assumed to depend exponentially on the distance were also tried but the authors claim that the quality of fits obtained with this model is not so good as that obtained with the Szabo model. Kakitani et a1.4 compared the Collins-Kimball model, the Szabo model, and a model in which the rate is expressed by an equation similar to the Marcus equation. Their conclusion is that the first two models can reproduce the fluorescence decay curves @

Abstract published in Advance ACS Abstracts, March 15, 1995.

equally well compared with the last one. Fayer et al.5-7 assumed that the rate constant decreases exponentially with distance and obtained the rate parameters by comparing the calculated decay curves with experimental results. In this paper we measure and analyze the transient effect in fluorescence quenching by electron transfer. The rate of electron transfer has often been assumed to vary exponentially with distance. However, according to the Marcus equation, the dependence changes with the value of AG of the In the present analysis, we use the Marcus equation in order to take into account the distance dependence of the electron transfer rate more precisely.

2. Experimental Section 9-Cyanoanthracene (CA, fluorescer), 9,lO-dicyanoanthracene (DCA, fluorescer), and p-anisidine (ANS, quencher) were purified by repeated recrystallization from appropriate solvents. N,N-Dimethylaniline (DMA, quencher) and aniline (ANL, quencher) were vacuum distilled. Ethylene glycol (EG, solvent) for chromatographic use was used as received. The optical and the static dielectric constants of this solvent are 2.047 and 37.7, respectively.1° The solutions were not deoxygenated, since the concentration of the quencher was always higher than 200 mM, while that of 0 2 dissolved in EG is less than 1 mM. Fluorescers (CA and DCA, both are electron acceptors) are hardly soluble in EG, and their concentration was always lower than M. This eliminates the possibility of energy transfer between fluorescer molecules. Fluorescers were excited at wavelengths where quenchers do not absorb. Absorption spectra show that the ground-state complexes are formed between some donors and acceptors at high donor concentrations. Of course, the extent of complexation depends on the pair, but, generally speaking, the absorption of the complex can be detected for some pairs at quencher concentrations slightly lower than those shown in Table 1. Weak fluorescence due to the complexes was detected at longer wavelength side of the spectrum. The decay curves were measured at shorter wavelengths where the fluorescence of the complexes was not detected. The absorption of the ground-state complexes is extremely weak in this region and quenching by excitation energy transfer is not expected to occur.

0022-365419512099-5354$09.00/0 0 1995 American Chemical Society

J. Phys. Chem., Vol. 99, No. 15, 1995 5355

Transient Effect in Fluorescence Quenching Fluorescence decay curves were measured with an apparatus already described elsewhere.' Briefly, the sample was excited by the second harmonic of the dye laser output which was synchronously pumped by a mode-locked Nd:YAG laser, and the resulting fluorescence was measured by time-correlated single-photon counting using an MCP-PMT. A combination of a Babinet-Solei1 compensator and a polarizer was used to eliminate polarization effects. The fwhm of the response function of the apparatus is about 60 ps. One should take enough care in the measurement to avoid distortion of the measured decay curve, since small distortion caused by, for instance, electric noise can change the result of the data analysis. Data were accumulated until the maximum reached 10 000 counts. Fitting was made from a channel of about 5000 counts in the rise-up region. The time shift between the measured decay curve and the instrument response function also affects the result of analysis, as has been reported by Penasamy et al." It was adjusted so that the convoluted curve best reproduces the rise-up region of the decay curve. Measurements were all made at 25 "C. 3. Data Analysis

dependence of the Marcus equation can be expressed as follows:

(3) In eq 3, the transfer integral has been assumed to decrease exponentially with r:16 JOis its magnitude at r = ro and p is its attenuation coefficient. The reorganization energy I. also depends on r: (4) cop and cs are the optical and the static dielectric constants, respectively, and a and b are molecular radii of D and A. The dependence of eq 3 on r has already been analyzed in detail: l s 8 the dependence changes with the value of AG of the reaction. Anyway, by substituting eqs 3 and 4 in eq 2, we can incorporate the complicated distance dependence of k(r) in the calculation of fluorescence decay curves. The following initial and boundary conditions are appropriate in the present case:

U(r,O) = 1

Suppose D and A are in solution and fluorescence of D or A is quenched by A or D. Then, the fluorescence decay function P(t) is theoretically expressed by eq 1:12 P(t) = exp(-r/to - 4 n c h m [ l - U(r,t)]r2 dr)

Here to is the fluorescence lifetime in the absence of the quencher, c the quencher concentration and d the sum of the molecular radii of donor and acceptor. U(r,t) stands for the survival probability of a D*-A or D-A* pair at time t which was initially (at time 0) separated by distance r. The initial distribution of the D-A distance has been assumed to be completely random. This assumption is not strictly valid, since ground state complexes are detected for some D-A pairs. However, because we measure the fluorescence of uncomplexed A*, we have only to take into consideration the distribution of uncomplexed D and A. In this paper, we assume that the distribution of the distance between uncomplexed D and A is random and use eq 1 without any correction. The possible nonrandomness of the distance distribution is a problem of a future work. It is necessary to know U(r,t) in order to calculate P(t). In solution, D and A undergo mutual diffusion and in that case it has been shown that U(r,t) satisfies the diffusion equation of the form:12J3

at

U(r,r) - k(r) U(r,r)

V(-,t) = 1

(1)

(2)

D is the sum of the diffusion coefficients of donor and acceptor and k(r) the first-order quenching rate constant. The last term is the sink term which takes into account that the D-A pair (either D*-A or D-A*) is removed from the system by the reaction. In the analysis based on the Collins-Kimball model, the reaction was assumed to occur at a fixed distance. Here we assume a more reasonable distance dependence for k(r). Since we are studying fluorescence quenching by electron transfer, we use the Marcus e q ~ a t i o n ' ~for . ' ~k(r). The distance

(7)

Equation 6 is the reflecting boundary condition which shows that D and A cannot approach each other closer than d and are mutually "reflected back" at d. It is seen from these equations that P(t) depends on three parameters, 0,Jo,and p (see below for u and b). Equation 2 was solved numerically by the Crank-Nicholson method. In the calculations, both the temporal and spatial regions were divided into about 1000 steps. Since U(r,t) changes faster at earlier times, smaller temporal step sizes were employed at earlier times compared to the later times. Decreasing the numbers of steps to 300 or increasing them to 5000 did not change the calculated decay curves. The integral in eq 1 (and also eq 8 below) was calculated by the trapezoidal rule. ro was taken to be 6 A. The observed decay curve is different from P(t), since the instrument response is not infinitely fast. It is expressed by the convolutionf(t) of P(t) and the instrument response function dt): At) =

h'g(f) P(r - r') dr'

The function f ( t ) calculated from eq 8 was fitted to the observed decay curves in order to determine the values of the parameters. The values of the parameters corresponding to the best fits were determined by nonlinear least-squares method based on the Marquardt algorithm. The derivatives offlt) with respect to the fitting parameters which are needed in the calculation were replaced by the approximate forms using the finite differences. This is sufficient for practical purposes if the calculation is made in double precision." As already mentioned, three parameters are involved in the fitting. (Actually, there is another parameter, Le., the scaling factor which is to equalize the maximum value of the convoluted curve to that of the measured decay curve, but it will be omitted in the later discussion, since it has no physical meaning.) Of the three

5356 J. Phys. Chem., Vol. 99, No. 15, 1995

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1

x

3

. I

in

0.5 Y

c

c.l

0.5

1

1.5

t I ns Figure 1. Calculated fluorescence decay curves for two different sets of JO and p values. Quencher concentration = 1OOmM. D ( ~ 3 . 7 7x cm2 SKI)is the sum of the diffusion coefficients of DCA and A N S in THF. parameters, D was estimated from the Stokes-Einstein equation:l8

D = kT/nnqr,

(9)

where n is a constant, and 7 and r, are the viscosity of the solvent and the radius of the molecule, respectively. r, was estimated following EdwardIg and Bondi.22 The values of r, thus estimated are (in angstroms) CA 3.6, DCA 3.7, ANS 3.1, DMA 3.2, and ANL 2.9. These values were used for a and b in eq 4 and to calculate d in eq 1. The method of analysis described above is similar to that employed by Fayer et aL-' but is different from theirs in two respects. First, we use the Marcus equation for k(r), while they assumed that k(r) decreases exponentially with r. The transfer integral in the Marcus equation has been shown to decrease exponentially with r, but the r dependence of the whole equation is not exponential, as already pointed out. Second, we make the fitting by a least-squares method in order to determine the parameter values more accurately.

4. Results and Discussion A. Influence of Solvent Viscosity on the Decay Curve. We first investigate the dependence of the decay curve P(t) on the parameters D, Jo, and p. This will be useful in revealing the conditions under which JO and p can be accurately determined from experiment. Figure 1 shows the calculated decay curves for two different sets of J? and p values, 30 cm-' and 0.78 A-l and 500 cm-' and 3.68 A-l, respectively. (The values of p were obtained by fitting eq 8 with a fixed JO value (30 or 500 cm-') to the observed decay curve of DCA fluorescence quenched by 100 mM ANS in THF. D = 3.77 x lom5cm2 s-l from eq 9.) Surprisingly, two sets with much different JO and p values give very similar decay curves, as demonstrated in Figure 1. Actually, the sets which give very similar curves are not limited to these two. For an arbitrary value of JO in the range between the values shown in Figure 1, we can find a value of p which gives a curve very similar to those in Figure 1, Le., a wide range of JO and ,8 values give essentially the same decay curves. To determine the parameter values from experiment we use in the fitting procedure the convolutionflt) of the decay function P(t) with the instrument response function g(t) rather than P(t) itself. Since g(t) has a fwhm of about 60 ps, the convolutions of these

2

4

6 8 10 t I ns Figure 2. Calculated fluorescence decay curves for two different sets of JO and p values. Quencher concentration = 10 mM. All the other parameters are the same as those in Figure 1. The two curves are 0

overlapped. functions with g(t) are almost indistinguishable. This means that, under the present conditions, we cannot determine from experiment the values of JO and p simultaneously by the fitting procedure employed in this work. Let us examine how the situation changes when the quencher concentration is varied. At lower quencher concentrations where the transient effect is less distinct, the range becomes even wider, and the range shown in Figure 1 lies within this range. This can be seen in Figure 2 in which the decay curves corresponding to the two parameter sets shown in Figure 1 are depicted for a quencher concentration of 10 mM. In Figure 2 , the two curves are practically the same. Again, we can find between the two parameter sets a number of sets giving the same decay curve. So it is useless to lower the quencher concentration. The range should be narrower at higher quencher concentrations. However, an apparatus with higher time resolution is needed to measure the decay curves at higher concentrations. With time-correlated single-photon counting, it is almost impossible to measure the decay curve with higher time resolution than that shown in Figure 1. The fact that the wide range of Jo and p values give essentially the same decay curve is attributed to the fast diffusion of D and A in THF. If a more viscous solvent is employed, then the transient effect will be more prominent and we will see more clearly the differences in the decay curves that are caused by different JO and p values. This is shown in Figure 3 where the same parameter values are assumed as in Figure 1 except for the diffusion coefficient. In Figure 3, the diffusion coefficient was assumed to be 0.094 x cm2 s-', a typical value in a viscous solvent such as EG. It is apparent that EG is more suitable as a solvent for our purpose than THF, acetonitrile, etc., which are often used in the studies of electron transfer. For this reason we use EG as solvent in the present study. B. Comparison with the Collins-Kimball Model. Here we compare the present method with the method based on the Collins-Kimball model which was used in our previous paper.' Figures 4 and 5 show the observed decay of DCA fluorescence quenched by 200 mM ANS in EG solvent together with the best-fit curve to it simulated by the method based on the Collins-Kimball model and by the present method, respectively. The Collins-Kimball model cannot reproduce the rapid rise and decay of fluorescence: the x2 value of this fit is about 10. (The parameter values obtained are R = 10.8 %, and ET = 5.3 x lo1* M-' s-', and the method of estimating the diffusion

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Transient Effect in Fluorescence Quenching I

I

I

I

I

I

I

I

TABLE 1: Result of Analysis of the'Data of Figure 40 JO (cm-l)

I

5

10

20

40

50

100

200

/3(A-')0.4 0.7 0.9 1.1 1.1 1.3 1.6 X2 4.7133 1.7578 1.4570 1.3487 1.3598 1.5175 2.7852

F 9 0.5

a JO was fixed to an appropriate value and /3 was adjusted to give the best-fit curve to the observed fluorescence decay.

. I

in

Y

e

I

-0

4

6 8 10 t I ns Figure 3. Calculated fluorescence decay curves for two different sets of JO and /3 values. All the parameters are the same as in Figure 1 except D for which the value in EG was used (0.094 x cmz s-l).

10000

2

I t

01 0

1

I

I

I

I

1

I

2

4

t

I ns

Figure 4. Observed decay curve (dots) of DCA fluorescence quenched by 200 mM ANS in EG, and the best fit to it (full line) by the method based on the Collins-Kimball model.

10000

.-3 3e in

U

5000

:

I

"0

2

t

t

4

ns

Figure 5. Observed decay curve (dots) of DCA fluorescence quenched by 200 mM ANS in EG, the best fit to it (full line) by the method described in the text, and the weighted residuals (upper dots).

coefficient has been described above.18) It is clear that the whole decay curve is much better reproduced by the present method. k2= 1.3487. See the next section for the obtained parameters.)

This was also true for all the other systems with different D-A pairs and different quencher concentrations. The reason the present method gives a better fit is, as described above, that we have employed a more realistic expression for the electron transfer rate, in particular for the distance dependence of the rate. C. Determination of the Rate Parameters. For the reason described above, we use EG as the solvent in the present work. Because of the high viscosity of the solvent, fluorescence quenching is not efficient and the fluorescence decay curve clearly deviates from the exponential function when the quencher concentration is high enough. The parameter values corresponding to the best fit in Figure 5 are JO = 40 cm-' (at 6 A) and p = 1.1 k 1 with x2 = 1.3487. As seen in Figure 5 , the measured fluorescence decay curve has a prominent second peak. This is caused by the instrument response function and is reproduced pretty well by the convolution. This peak is more clearly seen in the present study than in THF solvent reported previously.' This is because we are observing a more distinct transient effect than in the previous study, Le., the quencher concentration is higher and the initial decay of fluorescence is faster in the present study. This causes the structures in the instrument response to appear more clearly in the measured decay curve. Analysis is easier when we have a distinct transient effect. On the other hand, the structures in the decay curve cause poor agreement between the observed and calculated decay curves. The fitting range in our analysis includes a part of the rise-up region and also the peaks. In these regions, small experimental errors (for instance, the difference in geometry in measuring the instrument response and the decay curve) can cause larger errors in the result of analysis. This is probably the reason that the x2 values found in our analysis were sometimes larger (up to ~ 1 . 7 )than those found in usual analyses. We have shown in section 4.A that it is almost impossible to determine the JO and p values simultaneously from the analysis of a fluorescence decay curve measured in THF solvent. To see the situation in EG solvent, we have analyzed the same decay curve as in Figure 5 by fixing JO and treating p as an adjustable parameter. The p and x2 values corresponding to the best fit are shown in Table 1 for several JO values. Table 1 shows that x2 f i s t decreases with increasing Jo, reaches a minimum, and then increases again. It is clear that the parameter values obtained correspond to a real minimum which can be easily detected by the x2 value. The variation of x2 seems smaller than that expected from Figure 3. The reason for this discrepancy is that in Table 1 we compare the convolutions of the decay function and the instrument response function, while in Figure 3 the bare decay functions are depicted. Table 2 summarizes the parameter values obtained in this study. p values are all close to 1 A-1 and JO values also fall in a narrow range from 19 to 54 cm-'. Some dependence of JO on the quencher concentration is found within the same pairs in Table 2. We believe this is caused by errors in experiment and analysis. As described in the Experimental Section, the time shift between the measured decay curve and the instrument response which should be adjusted in the fitting procedure

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TABLE 2: Parameter Values Obtained from the Analysis of Fluorescence Decay Curves CA CA DCA DCA DCA DCA DCA DCA CA CA

ANS (300 mM) ANS (400 mM) ANS (200 mM) ANS (300 mM) DMA (250 mM) DMA (310 mM) ANL (260 mM) ANL (350 mM) DMA (250 mM) DMA (310 mM)

0.85

19

0.85

19 40 50 31 54 20

1.26 1.26 1.21 1.21 1.02 1.02 0.73 0.73

36 22 27

1.o 1.o 1.1 I .2 0.9 1.o 0.8 1.o 0.9 0.9

affects the result of analysis. This and the structures in the decay curve described above may account for the major part of the change in the obtained values of JO at different quencher concentrations (or in different experiments). Values of JO and p have been determined by various ways.23-29 ,b values thus determined are close to 1 A-1 being in good agreement with our results. On the other hand, JO values are generally larger than ours: 1900 cm-' at 6 A23, 10-65 C ~ - I , * and ~ 3.5-160 cm-1,26 respectively, at distances substantially longer than 6 A. These JO values have been determined for D-A pairs incorporated in a molecule and linked rigidly by chemical bonds. Closs et aLZ3stressed the importance of through-bond electronic interactions in electron transfer and pointed out that for intermolecular electron transfer JO should be smaller than these values. Our result is in qualitative agreement with their speculation. However, their value of JO for intermolecular electron transfer in rigid glass (300 cm-I at 6 A) is also much larger than ours. Very recently, Katz et aLZ9 calculated the JO values of ligand-to-ligand electron transfer in some rhenium complexes from the absorption spectra. Their values are 44, 51, and 61 cm-' at -6 A, which are in good agreement with ours. Up to now there seems to be no experimental values of JO that are widely accepted as accurate, and we do not know how large it is. Moreover, it may differ from one D-A pair to another. The discrepancy between the values obtained in this work and those in the literature are, therefore, not important. For this reason we do not discuss further the JO values we have obtained. Anyway, to our knowledge, this is the first determination of JOand ,b for electron transfer in liquid solution. (Song et al.637 assumed that the electron-transfer rate decreases exponentially with D-A distance, analyzed their experimental results in solution, and obtained a value for p which is somewhat different from ours.)

5. Concluding Remarks Electron-transfer parameters were successfully determined by analyzing the transient effect in fluorescence quenching on the basis of the Marcus equation of electron transfer and the solution of the diffusion equation. Our results seem to be consistent with those which have been derived by different methods. As is well-known, the transient effect appears only at initial stages of quenching. In this paper we measured the fluorescence decay curves by time-correlated single-photon counting with a time resolution of e 6 0 ps (fwhm of the instrument response function). This time resolution was not always sufficient, since the decay

curves at earlier times are more important. Measurements with higher time resolution seem necessary to study electron transfer in more detail. Work along this line is in progress in this laboratory and will be published in the near future.

Acknowledgment. The authors are grateful to Mr. Motoi Nishimura of Konica Corp., Tokyo, for experimental assistance. References and Notes (1) Murata, S.; Nishimura, M.; Matsuzaki, S. Y.; Tachiya, M. Chem. Phys. Lett. 1994, 219, 200. (2) Eads, D. D.; Dimer, B. G.; Fleming, G. R. J. Chem. Phys. 1990, 93, 1136. (3) Szabo, A. J. Phys. Chem. 1989, 93, 6929. (4) Kakitani, T.; Matsuda, N.; Denda, T.; Mataga, N.; Enomoto, Y. Ultrafast Reaction Dynamics and Solvent Effects; A I P Conference Proceedings 298; Gauduel, Y., Rossky, P. J., Eds.; American Institute of Physics: New York, 1993. (5) Dorfman, R. C.; Lin, Y.; Fayer, M. D. J. Phys. Chem. 1990, 94, 8007. (6) Song, L.; Dorfman, R. C.; Swallen, S. F.; Fayer, M. D. J. Phys. Chem. 1991, 95, 3454. (7) Song, L; Swallen, S. F.; Dorfman, R. C.; Weidemaier, K.; Fayer, M. D. J. Phys. Chem. 1993, 97, 1374. ( 8 ) Tachiya, M.; Murata, S. J. Phys. Chem. 1992, 96, 8441. (9) Kakitani, T.; Yoshimori. A.; Mataga, N. J. Phys. Chem. 1992, 96, 5385. (10) Riddick, J. A.; Bunger, W. B. Organic Solvents, Wiley-Interscience, New York, 1970. (11) Periasamy, N; Doraisawamy, D; Venkataraman, B; Fleming, G. R. J. Chem. Phys. 1988, 89, 4799. (12) Tachiya, M. Radiat. Phys. Chem. 1983, 21, 167. (13) Sano, H.; Tachiya, M. J. Chem. Phys. 1979, 71, 1276. (14) Marcus, R. A. J. Chem. Phys. 1956, 24, 966. (15) Marcus, R. A. Annu. Rev. Phys. Chem. 1964, 15, 155. (16) Logan, J.; Newton, M. D. J. Chem. Phys. 1983, 78, 4086. (17) Koyanagi, Y. Software for Numerical Calculations by Fortran 77; Watanabe, T., Natori, M., Oguni, T., Eds.; Maruzen: Tokyo, 1989 (in Japanese). (18) In the original Stokes-Einstein equation, the number n in the denominator in eq 9 is 6. This equation was derived for relatively large particles diffusing in a continuous medium. It has been shown19~20 that this number should be smaller than 6 if the solute and solvent molecules are of comparable sizes. Actually, this number should be about 4 to reproduce the experimental results of Miller et al.*' for the diffusion coefficients of anthracene, naphthalene, and biphenyl in acetonitrile. Although we were not able to find experimental values of diffusion coefficients in EG, n is considered to be smaller than 6 in EG. If the diffusion coefficients derived from eq 9 with n = 4 are used in the analyses, agreement between experimental and calculated decay curves becomes less good (with x2 > 2.5) than in the case with n = 5 . So we assume n = 5 in this paper, which gives reasonable values of x2. (19) Edward, J. T. J. Chem. Educ. 1970, 47, 261. (20) Birks, J. B. Photophysics of Aromatic Molecules; Wiley-Interscience: New York, 1970. (21) Miller, T. A,; Prater, B.; Lee, J. K.; Adams, R. N. J. Am. Chem. Soc. 1965, 87, 121. (22) Bondi, A. J. Phys. Chem. 1964, 64, 441. (23) Closs, G. L.; Calcaterra, L. T.; Green, N. J.; Penfield, K. W.; Miller, J. R. J. Phys. Chem. 1986, 90, 3673. (24) Finckh, P; Heitele, H; Volk, M; Michel-Beyerle, M. E. J. Phys. Chem., 1988, 92, 6584. (25) Kavamos, G. J; Turro, N. J. Chem. Rev., 1986, 86, 401 and references therein. (26) Zeng, Y; Zimmt, M. B. J. Phys. Chem., 1992, 96, 8395. (27) Clayton, A. H. A; Ghiggino, K. P.; Wilson, G. J.; Keyte, P. J.; Paddon-Row, M. N. Chem. Phys. Lett. 1992, 195, 249. (28) Osuka, A.; Kobayashi, F.; Maruyama, K.; Mataga, N.; Asahi, T.; Okada, T.; Yamazaki, I.; Nishimura, Y. Chem. Phys. Lett. 1993, 201, 223. (29) Katz, N. E.; Mecklenburg, S. L.; Graff, D. K.; Chen, P.; Meyer, T. J. J. Phys. Chem. 1994, 98, 8959. JP941856R