Radiationless Decay in Exciplexes with Variable Charge Transfer

Jun 14, 2007 - Transition from Charge-Transfer to Largely Locally Excited Exciplexes, from Structureless to Vibrationally Structured Emissions. Ralph ...
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J. Phys. Chem. B 2007, 111, 6782-6787

Radiationless Decay in Exciplexes with Variable Charge Transfer† Ian R. Gould* Department of Chemistry and Biochemistry, Arizona State UniVersity, Tempe, Arizona 85287-1604

Samir Farid* Department of Chemistry, UniVersity of Rochester, Rochester, New York 14627 ReceiVed: December 30, 2006; In Final Form: January 31, 2007

Rate constants for radiative decay, radiationless decay, and intersystem crossing are reported for a series of excited states formed by reaction of cyanoanthracene acceptors with alkylbenzenes as donors in several solvents of moderate to low polarity. The excited states have widely varying degrees of charge transfer, from essentially pure electron transfer states to pure locally excited states. The data illustrate the fundamental factors that control the contrasting relative efficiencies of radiative and radiationless processes in electron transfer compared to locally excited states. The radiationless decay rate constants can be described quantitatively as a function of the extent of charge transfer using weighted contributions from a locally excited decay mechanism and a pure electron-transfer type mechanism. The factors that control the rate constants for radiationless decay in excited states with intermediate charge-transfer character are discussed.

1. Introduction

SCHEME 1

The theories of electron-transfer reactions in homogeneous fluid solution are now well-established and provide an excellent description of the rate constants for a wide variety of such processes.1 Photoinduced electron-transfer reactions have provided much important experimental data in this regard. Measurements of the rate constants for bimolecular reaction between excited acceptors and donors to form exciplexes and radicalion intermediates clearly demonstrated the driving force dependence of electron-transfer reactions,2 although diffusion and formation of excited-state products and different kinds of ion pairs masks the inverted region effect in these bimolecular quenching reactions.3 The inverted region, however, can be clearly observed in the return electron-transfer reactions.4 The products of photoinduced bimolecular electron-transfer reactions can be considered to be excited states of the bimolecular donor/ acceptor system.5 Indeed, much of the experimental work on photoinduced bimolecular electron-transfer reactions is based on the pioneering observations of Weller and Mataga on bimolecular exciplex emissions.5 Although exciplexes were originally described as the excited states formed as a result of photoinduced bimolecular reaction between electron acceptor and donor molecules,5 the definition has been extended to linked donor/acceptor systems, where the charge separation and recombination reactions are intramolecular.6 The term exciplex, both intermolecular and intramolecular, has historically been used to refer to excited states with variable degrees of charge transfer (CT) character.7 The varying CT is understood as arising from varying extents of mixing of locally excited, pure electron-transfer and pure ground states.7 This is illustrated in eq 1 for the case of an electron acceptor (A) and an electron donor (D). In this example, the locally

Ψ(Ex) ) c1Ψ(A*D) + c2Ψ(A•-D•+) + c3Ψ(AD) (1) †

Part of the special issue “Norman Sutin Festschrift”. * Corresponding authors. E-mail: [email protected].

excited-state of the acceptor (A*) is lower in energy than that of the donor (D*), and the pure ET state is a radical-ion pair (A•-D•+). Usually, (c1 + c2) is much greater than c3, and the exciplex may be described qualitatively as a resonance mixture of locally excited and electron transfer states, Scheme 1. The photophysical processes that characterize exciplexes are the same as those of excited states in general, i.e., radiative decay (kf), intersystem crossing (kisc), and nonradiative decay (knr), Scheme 1.8 In polar solvents, bimolecular exciplexes can also undergo a solvation process that may result in the formation of separated radical ions,9 and in other cases, chemical reactions may occur.10 When c2 approaches unity, the exciplex is essentially a radical-ion pair, and the radiationless decay corresponds to a “pure” electron-transfer reaction. The return electron-transfer reactions in radical-ion pairs proved to be excellent systems for testing electron-transfer theories under conditions where mixing with a locally excited state could be ignored.11 Although variable charge transfer has been recognized to be an important property of exciplexes since their first observations, there have been only a few quantitative studies of the extent of charge transfer in such systems.12 The magnitude of c2 is determined by the relative energies of the electron transfer and locally excited states and the magnitude of the electronic coupling matrix element. For the reactions of excited cyanoanthracene acceptors and alkylbenzene donors as an example, the exciplexes have largely (∼95%) radical-ion pair (i.e., nearly pure electron transfer) character when the energy of (A•-D•+) is lower than that of (A*D) by ∼ 0.2 eV.13 Therefore, when electron-transfer quenching is only mildly exothermic, the charge-transfer product is likely to be a mixed excited state with

10.1021/jp069053e CCC: $37.00 © 2007 American Chemical Society Published on Web 06/14/2007

Radiationless Decay in Exciplexes

J. Phys. Chem. B, Vol. 111, No. 24, 2007 6783

TABLE 1: Photophysical Parameters for Exciplexes Formed between 9,10-Dicyanoanthracene (DCA) as Acceptor and Alkylbenzenes as Donors νavc donora solventb 103 cm-1 CHX dur CHX PMB CHX HMB CHX CTC dur CTC PMB CTC HMB CTC TCE dur TCE PMB TCE HMB TCE diox dur diox PMB diox HMB diox FB dur FB PMB FB HMB FB toluene p-xylene

22.27 20.33 19.80 18.97 21.88 19.83 19.25 18.46 21.63 19.42 18.82 18.02 21.58 18.99 18.21 17.31 21.57 18.71 18.04 17.08 21.44 21.23

fCTd

τ, nse

Φff

Φiscf

11.5 0.915 0.012 0.517 37.5 0.880 0.044 0.673 49.5 0.824 0.074 0.809 70.4 0.675 0.175 11.3 0.920 0.012 0.666 39.0 0.805 0.150 0.774 44.3 0.638 0.297 0.857 40.3 0.345 0.530 11.2 0.90 0.023 0.748 39.7 0.70 0.20 0.825 48.1 0.55 0.35 0.885 41.0 0.26 0.58 12.8 0.924 0.012 0.807 67.7 0.727 0.133 0.874 78.5 0.520 0.169 0.917 69.9 0.292 0.223 12.3 0.906 0.014 0.836 69.4 0.731 0.098 0.884 78.3 0.546 0.135 0.924 68.5 0.32 0.18 13.3 0.91 0.006 15.3 0.90 0.007

Φnrf

knr,g 106 s-1

0.073 0.076 0.102 0.150 0.068 0.045 0.065 0.125 0.077 0.10 0.10 0.16 0.064 0.140 0.311 0.485 0.080 0.171 0.319 0.50 0.084 0.093

6.35 2.03 2.06 2.13 6.02 1.15 1.47 3.10 6.88 2.52 2.08 3.90 5.00 2.07 3.96 6.94 6.47 2.46 4.08 7.30 6.32 6.08

a No entry refers to 9,10-dicyanoanthracene in the absence of an added donor, dur, PMB, and HMB refer to durene, pentamethylbenzene, and hexamethylbenzene, respectively. b CHX, CTC, TCE, diox, and FB refer to cyclohexane, carbon tetrachloride, trichloroethylene, 1,4dioxane, and fluorobenzene, respectively. c Average emission frequency, determined as described in ref 13. d Fractional charge transfer of the exciplex, calculated from νav using eq 9, see text. e Exciplex lifetime, in ns, from ref 13 and current work. f Quantum yields for fluoresecence (Φf), intersystem crossing (Φisc), and radiationless decay (Φnr) from refs 13 and 15 and the current work (see Experimental Section). g Rate constant for radiationless decay, determined using eqs 2-4.

less than 100% charge transfer. Under these conditions, neither the reaction that forms the charge-transfer state nor the radiationless decay process of the excited state is a pure electrontransfer reaction, and thus neither may be properly described using conventional electron-transfer theories. Interestingly, minimal exothermicity in the quenching reaction is required in order to store the maximum amount of light energy in, for example, solar energy conversion schemes.14 How are the quenching and, particularly, the radiationless decay processes of the excited intermediate states to be described under these conditions where electron transfer theories may not apply? This is the subject of the present work. 2. Systems To Be Studied Previously, we described a series of exciplexes formed between 9,10-dicyanoanthracene (DCA) and 2,6,9,10-tetracyanoanthracene (TCA) as the electron acceptors and various

methylsubstituted benzenes as donors in solvents with varying polarity.13 Depending upon the particular acceptor/donor/solvent combination, exciplexes with varying extents of charge-transfer character are obtained, ranging from essentially zero (i.e., for the pure cyanoanthracene locally excited states, A*D) to nearly 100% as cyanoanthracene radical anion/alkylbenzene radical cation pairs, A•-D•+.13 The radiative rate constants (kf) decreased

smoothly with increasing charge-transfer character. A complete theoretical analysis of the data was possible, and from this a quantitative determination of the extent of charge transfer in each exciplex was obtained.13 Intersystem crossing in these exciplex systems has also been recently described.15 Qualitatively, intersystem crossing behaves like an electron-transfer reaction when the energy gap between the exciplex and locally excited triplet state is large and when the extent of CT is high. As the extent of CT character decreases, a smooth transition from electron-transfer-like to pure locally excited- like behavior was observed.15 This set of exciplexes represent perhaps the best characterized series of related systems that have controllable degrees of charge transfer. We now describe how the rate constants for radiationless decay in these systems depend upon the extent of charge transfer. 3. Radiationless Decay Rate Constants As indicated in Scheme 1, the exciplexes can undergo intersystem crossing, radiative decay, and radiationless decay. In the present work, we carefully selected reactant/solvent combinations to ensure that solvation to form solvent-separated radical ions could be neglected.9c,d The formation of chemical products in these systems can also be safely ruled out. The lifetime of the exciplex, τEx, is thus given by eq 2, where kf, kisc, and knr represent the rate constants for radiative decay, intersystem crossing, and radiationless decay, respectively.

τEx ) 1/(kf + kisc + knr)

(2)

Values for kf and kisc have already been reported for these systems, determined using eqs 3 and 4, where Φf and Φisc represent the quantum yields for fluorescence and intersystem crossing, respectively.13,15 Values for knr can be readily obtained using eq 2.

kf ) Φf /τEx

(3)

kisc ) Φisc/τEx

(4)

We have revisited the previously published fluorescence quantum yield data in ref 13 because, in this work, the emphasis is on the radiationless decay, and for many of the systems, knr is significantly smaller than (kf + kisc), especially when the extent of charge transfer becomes small. Under these conditions, small uncertainties in Φf result in negligible uncertainties in kf, but the uncertainties in knr could be large. We have remeasured some of the fluorescence quantum yields and have found very small differences compared to those reported previously (see Experimental Section). These differences have essentially no effect on the kf values but a modest effect on the knr values. Summarized in Tables 1 and 2 are the pertinent photophysical data, taken mainly from refs 13 and 15, with some additional data from current experiments. Shown in Figure 1 are the radiationless decay data from Tables 1 and 2, plotted as a function of the average emission frequency of the corresponding exciplex, νav.13 Also included are some additional data for radiationless decay for pure radicalion pairs in acetonitrile from other previous studies.16 Evaluation of νav is described in ref 13. It represents the vertical energy difference between the exciplex in its equilibrium geometry and the ground state at the same geometry. This energy is equal to the excited-state energy minus the reorganization energy for the excited-state to ground state transition. As explained previously,15 plotting the data in this way allows reactions in different solvents, with different solvent reorganization energies to be

6784 J. Phys. Chem. B, Vol. 111, No. 24, 2007

Gould and Farid

TABLE 2: Photophysical Parameters for Exciplexes Formed between 2,6,9,10-Tetracyanoanthracene (TCA) as Acceptor and Alkylbenzenes as Donors νavc donora solventb 103 cm-1 p-xy p-xy TMB dur PMB HMB TMB dur PMB HMB TMB dur PMB HMB

CTC TCE TCE TCE TCE TCE TCE diox diox diox diox diox FB FB FB FB FB

18.98 21.47 18.41 17.53 16.27 15.83 14.75 21.27 15.97 14.91 14.45 13.74 21.16 16.21 14.91 14.45 13.52

fCTd

τ, nse

0.808 49.8 11.8 0.860 51.8 0.908 54.8 0.944 46.6 0.952 26.2 0.965 12.2 6.93 0.949 16.8 0.963 8.7 0.968 5.2 0.973 2.6 15.7 0.945 14.7 0.963 7.2 0.968 4.6 0.974 2.1

Φff

Φiscf

Φnrf

knr,g 106 s-1

0.676 0.78 0.41 0.29 0.15 0.065 0.027 0.40 0.054 0.017 0.01 0.0036 0.875 0.042 0.016 0.008 0.004

0.21 0.08 0.31 0.326 0.256 0.206 0.194 0.021 0.082 0.058 0.051 0.043 0.020 0.057 0.040 0.035 0.026

0.114 0.14 0.28 0.384 0.594 0.729 0.779 0.579 0.864 0.925 0.939 0.954 0.105 0.901 0.944 0.957 0.970

2.9 11.9 5.4 7.0 12.8 27.8 63.9 83.6h 51.4 106 181 367 6.7 61.3 131 208 462

a No entry refers to 2,6,9,10-tetracyanoanthracene in the absence of an added donor, p-xy, TMB, dur, PMB, and HMB refer to p-xylene, 1,2,4-trimethylbenzene, durene, pentamethylbenzene, and hexamethylbenzene, respectively. b CHX, CTC, TCE, diox, and FB refer to cyclohexane, carbon tetrachloride, trichloroethylene, 1,4-dioxane, and fluorobenzene, respectively. c Average emission frequency, determined as described in ref 13. d Fractional charge transfer of the exciplex, calculated from νav using eq 9, see text. e Exciplex lifetime, in ns, from ref 13 and current work. f Quantum yields for fluoresecence (Φf), intersystem crossing (Φisc), and radiationless decay (Φnr) from refs 13 and 15 and the current work (see Experimental Section). g Rate constant for radiationless decay, determined using eqs 2-4. h The radiationless decay rate constant is particularly large in this case and is due to chargetransfer quenching, which will be addressed in a separate paper. This point is not included in the figures.

directly compared, although small changes in the shape of a plot of rate versus energy gap measured this way will occur. The data generally exhibit a smooth decrease in knr with increasing νav. To support the assignment of the knr to radiationless decay in the exciplexes rather than, for example, a bimolecular quenching process, especially for the smaller values of knr, we also measured some deuterium isotope effects, Table 3. Electrontransfer-type radiationless decay in these systems is sensitive to deuterium substitution as a consequence of hyperconjugation in the radical cation of the pair.17 In each case, the measured isotope effects are between 2.5 and 3.0, Table 3, which are consistent with previously determined isotope effects in related electron-transfer systems.17 The knr data of Figure 1 exhibit a smooth decrease with increasing average emission frequency, reach a minimum at roughly 19.5 × 103 cm-1, and then increase somewhat to the values for the pure locally excited states. As discussed above, for these exciplexes, we have previously determined the quantitative relationship between the average emission frequency νav and the extent of charge transfer in the emitting species, as indicated in Figure 1.13 The energy of the pure radical-ion pair state (A•-D•+) increases with decreasing solvent polarity or with a donor of higher oxidation potential or an acceptor with a more negative reduction potential (i.e., DCA in place of TCA). Increasing the energy of the A•-D•+ state increases mixing with the locally excited state (A*D), which decreases the extent of charge transfer and also increases νav. For exciplexes with a νav smaller than ca. 17.5 × 103 cm-1, the fractional charge transfer is greater than 0.9, and they are thus essentially contact radical-ion pairs, (A•-D•+). The minimum value of knr occurs at ∼0.7 fractional charge transfer.

Figure 1. Plot of the logarithm of the rate constant for radiationless decay, knr, for the donor/acceptor systems summarized in Tables 1 and 2, vs (bottom) average emission frequency, νnr, and (top) fractional charge transfer, fCT.13 Note that the change in fCT with νav is described by a complex function, hence the uneven spacing between the tic marks. The closed black circles are for TCA as the acceptor in acetonitrile solvent (data from ref 16), the open black squares are for TCA as the acceptor, data from Table 2, and the red open circles are for DCA as the acceptor, data from Table 1. The curves through the data points are as described in the text.

The rate constants for radiationless decay processes are usually described using a Fermi golden rule expression, eq 5a, i.e., as the product of a coupling matrix element squared (V2) and a Frank-Condon weighted density of states (FCWD).18

knr )

4π2 2 V FCWD h

FCWD ) ∞

Fj(4πλskBT) ∑ j)0

-1/2

[

exp -

]

(∆E + jhνv + λs)2

Fj ) exp (-S) S)

(5a)

4λskBT Sj j!

λv hνv

(5b)

(5c) (5d)

The usual form of the FCWD for electron-transfer reactions is given in eqs 5b-5d, where λs, λv, and νv represent the lowand high-frequency reorganization parameters, and the rest of the parameters have their usual meanings.1,19 Radiationless decay in an exciplex that is a pure radical ion pair, A•-D•+, is an example of a return electron-transfer reaction, in which case knr is k-et, V is V-et, the electronic coupling matrix element, and ∆E is replaced by ∆G-et, the free energy difference between ground and excited states.1,19 Equations 5 predict that k-et should decrease rapidly with increasing energy gap between the ground and the excited state. For a pure electron-transfer reaction, νav is given by eq 6.13

νav ) ∆G-et - (λv + λs)

(6)

Radiationless Decay in Exciplexes

J. Phys. Chem. B, Vol. 111, No. 24, 2007 6785

TABLE 3: Photophysical Parameters for Exciplexes of DCA and TCA with Hexamethylbenzene and Hexamethylbenzene-d18 and the Corresponding Deuterium Isotope Effects on the Rate Constant for the Radiationless Decay, knrh/knrd acceptor solventa DCA

FB

DCA

diox

TCA

diox

donorb

τc ns

Φfd

HMB 68.5 0.32 HMB-d18 103.0 0.49 HMB 69.9 0.29 HMB-d18 108.6 0.44 HMB 2.6 0.0036 HMB-d18 6.6 0.0093

knre knrh/ 6 -1 knrd s

Φiscd

Φnrd

0.18 0.21 0.22 0.30 0.043 0.070

0.50 7.30 2.51 0.30 2.91 0.49 7.01 2.93 0.26 2.39 0.953 367 2.62 0.921 140

10

a FB and diox refer to fluorobenzene and 1,4-dioxane, respectively. HMB and HMB-d18 refer to hexamethylbenzene and perdeuteriohexamethylbenzene, respectively. c Exciplex lifetime, in ns, from ref 13 and current work. d Quantum yields for fluoresecence (Φf), intersystem crossing (Φisc), and radiationless decay (Φnr) from refs 13 and 15 and the current work. e Rate constant for radiationless decay, determined using eqs 2-4.

b

Also shown in Figure 1 is the dependence of log k-et versus νav calculated using eqs 5 and 6 and parameters that were previously determined for return electron transfer in contact radical-ion pairs, i.e., V ) 750 cm-1, λv ) 0.25 eV, and νv ) 1500 cm-1.16 Although the νav corrects for the different energetics of the reactions in different solvents, the log k-et plots have slightly different shapes depending upon the particular value of λs, the reorganization energy associated with the solvent motion, and other low-frequency vibrations.20 Previous studies on λs for return electron transfer in radical-ion pairs suggest a range of ∼0.15-0.35 eV for the solvents included in the present study.11d The dashed line in Figure 1 is calculated using a value of 0.48 eV for λs, which was previously determined for contact radical-ion pairs in acetonitrile.16 This line provides the best fit to the acetonitrile points (filled circles), as expected. Taking an average value for λs of 0.25 eV11d for the solvents studied here generates a curve that fits the remaining data points that have high charge-transfer character reasonably well. Of course, at higher νav (lower charge-transfer), the experimental data deviate significantly from the electron transfer behavior predicted using eqs 5 and 6, and the data trend smoothly toward the values for the pure locally excited states. In the previous work on the radiative rate in these systems, it was found that the dependence of the radiative rate constant kf on the extent of charge transfer could be accurately described by calculating the transition dipole moment for the mixed state, M, according to eq 7.13 Here, fCT represents the fractional charge transfer in the mixed state

M2 ) fCT (MA-D+)2 + (1 - fCT) (MA*)2

(7)

and MA-D+ and MA* are the transition dipole moments for the pure radical-ion pair and locally excited states, respectively. In essence, the radiative process was considered to consist of weighted contributions from the pure LE and ET components to the mixed state. We wondered whether a similar approach might work for the corresponding rate constants for radiationless decay. The broad gray curve in Figure 1 is calculated according to eq 8, where k-et is the “electron transfer” contribution to knr for each exciplex, calculated according to eqs 5 and 6, i.e., the black curve in Figure 1, and (knr)A* represents the “locally excited” contribution to knr. (knr)A* is the rate constant for radiationless decay of the pure locally excited state, for which an average value of 6.5 × 106 s-1 is taken, Tables 1 and 2.21

knr ) fCTk-et + (1 - fCT) (knr)A*

(8)

Figure 2. Plot of the logarithms of the rate constants for radiationless decay (knr, black filled circles, this work), radiative decay (kf, red open squares, from ref 13), and intersystem crossing (kisc, blue open triangles, from ref 15) for the donor/acceptor systems summarized in Tables 1 and 2 vs (bottom) average emission frequency, νav, and (top) percentage charge transfer.13 Data points for intersystem crossing in chlorinated solvents, where a heavy atom effect is observed,15 are not included.

The fCT values are those indicated in Figure 1 and are derived from the previous analysis of the radiative rate data, i.e., using eq 9, where νA* refers to the average emission frequency of the pure locally excited state.13 The previously determined Vet (referred to as H12 in ref 13) for DCA and TCA are 1300 and 1350 cm-1, respectively. Because here we are using combined data from both acceptors, we use an average value of 1325 cm-1. Similarly, the values for νA* for DCA and TCA used previously are 21.8 and 21.6 × 103 cm-1, respectively, and here we use an average value of 21.7 × 103 cm-1.

1/fCT ) 1 + {Vet/(νA* - νav)}2

(9)

The dependence of log knr on νav, calculated using this method (the broad curve in Figure 1), describes the observed data remarkably well over the entire range of charge transfer. Compared in Figure 2 are the dependencies of kf, kisc, and knr on energy gap (νav) and degree of charge transfer. The behavior is complex due to changes in both energy gap and mechanism as the degree of charge-transfer changes, but the figure illustrates the important and contrasting photophysical behavior of locally excited and charge-transfer states in a very clear way. The kf for the pure locally excited states is significantly larger than both kisc and knr, and the fluorescence quantum yields for the LE states are high, as expected for rigid aromatic molecules.18 The extreme mismatch between the large energy gap and the small reorganization energy for the locally excited state is responsible for the relatively low values for knr. The reorganization energy for a locally excited state is much smaller than for a CT state, mainly due to significantly reduced solvent reorganization in the former case. Thus, radiationless decay occurs with unfavorable Franck-Condon factors and is relatively slow. For the current systems, the radiative rate constant for the pure LE is roughly an order of magnitude larger than the nonradiative rate constant and roughly 2 orders of

6786 J. Phys. Chem. B, Vol. 111, No. 24, 2007 magnitude larger than the intersystem crossing rate constant. At approximately 0.9 fCT , all three rate constants are nearly the same, and at >0.95 fCT, nonradiative decay becomes the dominant process. Radiationless decay dominates the pure ET states because the solvent reorganization energy increases substantially with increasing CT character. In addition, as the energy gap decreases, there is a better match between exothermicity and the required reorganization energy, resulting in more favorable Franck-Condon factors. As a consequence of the dominant knr for such ET states, emission is commonly observed to be relatively weak.1 Quite interesting behavior is observed at intermediate degrees of charge transfer, and it is useful to speculate on the way that this data should be interpreted. Extrapolation of the curve for the pure ET data in Figure 1 to the energy gap for the locally excited, i.e., νav ∼ 22 × 103 cm-1, gives a substantially smaller rate constant for decay by pure electron transfer (0.60), the influence of energy gap and reorganization apparently becomes more important, and “normal” energy gap, or inverted region-type behavior, is observed. Clearly, further theoretical development is required to properly describe and understand the trends observed here. 5. Conclusions The rate constants for radiationless decay for a series of excited states with fractional charge transfer ranging from 0.0

Gould and Farid (i.e., pure locally excited) to ∼1.0 (i.e., pure electron transfer) exhibit complex behavior that nevertheless can be described quantitatively in terms of weighted contributions from locally excited and pure electron-transfer states. An alternate explanation considers the relative contributions of the coupling matrix element and the Franck-Condon weighted density of states to the reaction rate constant. Comparison with corresponding rate constants for radiative decay and intersystem crossing provides a complete picture of the factors that control the photophysics of the excited states in these systems from pure locally excited to pure electron transfer. 6. Experimental The cyanoanthracenes, alkylbenzenes, and 9,10-diphenylanthracene were all available from previous studies.11,13,17a Exciplex, DCA, and TCA fluorescence spectra and lifetimes were taken from ref 13 or were measured using the methods described in that reference. The fluorescence quantum yields for DCA in the absence of added donor and in the solvents listed in Table 1 and for TCA with no added donor in fluorobenzene (Table 2) were obtained from the integrated fluorescence intensities vs wavelength in argon-purged solutions using 9,10-diphenylanthracene in cyclohexane (Φf ) 0.90)23 as an actinometer. The intensities were corrected for the difference in the index of refraction by multiplying by (nsolvent/ncyclohexane).2 The measurements were taken with excitation at several isosbestic points (usually 3 or 4) between 370 and 400 nm, with the optical densities between 0.03 and 0.06. The fluorescence quantum yields for these systems given in the Tables represent the average from measurements on three different samples and typically exhibit a deviation of (1%. The fluorescence quantum yields for the exciplexes given in Tables 1 and 2 were then determined relative to those of DCA and TCA in the absence of donor using the relative emission yields given in ref 13. Acknowledgment. We thank Ralph Young (Eastman Kodak Company) for valuable discussions. This work was supported by the NSF grant CHE-0213445. References and Notes (1) (a) Sutin, N. AdV. Chem. Phys. 1999, 106, 7. (b) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265. (2) See, for example: Rehm, D.; Weller, A. Isr. J. Chem. 1970, 8, 259. (3) See, for example: (a) Gould, I. R.; Young, R. H.; Mueller, L. J.; Farid, S. J. Am. Chem. Soc. 1994, 116, 8176. (b) Kikuchi, K. J. Phys. Chem. 1993, 97, 5070. (c) Tachiya, M. J. Phys. Chem. 1992, 96, 8441. (4) See, for example: Gould, I. R.; Ege, D.; Moser, J. E.; Farid, S. J. Am. Chem. Soc. 1990, 112, 4290. (5) (a) Weller, A. In The Exciplex; Gordon, M., Ware, W. R., Eds.; Academic Press: New York, 1975; p 23. (b) Mataga, N.; Ottolenghi, M. In Molecular Association, Vol. 2; Foster, R., Ed.; Academic Press: New York, 1979; p 1. (6) (a) Verhoeven, J. W. AdV. Chem. Phys. 1999, 106, 603. (b) Wasielewski, M. R. Chem. ReV. 1992, 92, 435. (7) (a) Murrell, J. N. J. Am. Chem. Soc. 1959, 81, 5037. (b) Beens, H.; Weller, A. In Organic Molecular Photophysics; Birks, J. B., Ed.; Wiley: New York, 1975; Vol. 2, Chapter 4. (c) Mataga, N. In The Exciplex; Gordon, M., Ware, W. R., Eds.; Academic: New York, 1975. (8) (a) Jones, G., III. In Photoinduced Electron Transfer, Part A: Conceptual Basis; Fox, M. A., Chanon, M., Eds.; Elsevier: Amsterdam, 1988; p 245. (b) Kuzmin, M. G.; Soboleva, I. V. Prog. React. Kinet. 1986. (9) (a) Weller, A. Pure Appl. Chem. 1982, 54, 1885. (b) Weller, A. Z. Phys. Chem. (Wiesbaden) 1982, 133, 93. (c) Arnold, B. R.; Noukakis, D.; Farid, S.; Goodman, J. L.; Gould, I. R. J. Am. Chem. Soc. 1995, 117, 4399. (d) Arnold, B. R.; Goodman, J. L.; Farid, S.; Gould, I. R. J. Am. Chem. Soc. 1996, 118, 5482. (10) See, for example: (a) Lewis, F. D. Acc. Chem. Res. 1979, 12, 152. (b) Mattes, S. L.; Farid, S. Science, 1984, 226, 917.

Radiationless Decay in Exciplexes (11) See, for example: (a) Gould, I. R.; Farid, S.; Young, R. H. J. Photochem. Photobiol., A 1992, 65, 133. (b) Gould, I. R.; Noukakis, D.; Goodman, J. L.; Young, R. H.; Farid, S. J. Am. Chem. Soc. 1993, 115, 3830. (c) Gould, I. R.; Noukakis, D.; Gomez-Jahn, L.; Goodman, J. L.; Farid, S. J. Am. Chem. Soc. 1993, 115, 4405. (d) Gould, I. R.; Noukakis, D.; Gomez-Jahn, L.; Young, R. H.; Goodman, J. L.; Farid, S. Chem. Phys. 1993, 176, 439. (12) (a) Soboleva, I. V.; Dolotova, E. V.; Kuz’min, M. G. High Energy Chem. 2002, 36, 29. (b) Davis, H. F.; Chattopadhyay, S. K.; Das, P. K. J. Phys. Chem. 1984, 88, 2798. (c) Watkins, A. R. Chem. Phys. Lett. 1976, 43, 299. (d) Van Haver, P.; Helsen, N.; Depaemelaere, S.; Van der Auwerer, M.; De Schryver, F. C. J. Am. Chem. Soc. 1991, 113, 6849. (e) Mataga, N. Radiat. Phys. Chem. 1983, 21, 83. (f) Adams, B. K.; Cherry, W. R. J. Am. Chem. Soc. 1981, 103, 6904. (g) Bixon, M.; Jortner, J.; Verhoeven, J. W. J. Am. Chem. Soc. 1994, 116, 7349. (h) Levy, D.; Arnold, B. R. J. Phys. Chem. A 2005, 109, 8572. (i) Morais, J.; Hung, R. R.; Grabowski, J. J.; Zimmt, M. B. J. Phys. Chem. 1993, 97, 13138. (j) Oliver, A. M.; PaddonRow, M. N.; Kroon, J.; Verhoeven, J. W. Chem. Phys. Lett. 1992, 191, 371. (k) Van der Auweraer, M.; Viaene, L.; Van Haver, P.; De Schryver, F. C. J. Phys. Chem. 1993, 97, 7178. (13) (a) Gould, I. R.; Young, R. H.; Mueller, L. J.; Albrecht, A. C.; Farid, S. J. Am. Chem. Soc. 1994, 116, 3147. (b) Gould, I. R.; Young, R. H.; Mueller, L. J.; Albrecht, A. C.; Farid, S. J. Am. Chem. Soc. 1994, 116, 8188. (14) See, for example: Blankenship, R. E. Molecular Mechanisms of Photosynthesis; Blackwell Science: Oxford, UK, 2002. (b) Gust, D.; Moore, T. A.; Moore, A. Acc. Chem. Res. 2001, 34, 40.

J. Phys. Chem. B, Vol. 111, No. 24, 2007 6787 (15) Gould, I. R.; Boiani, J. A.; Gailard, E. B.; Goodman, J. L.; Farid, S. J. Phys. Chem. A 2003, 107, 3515. (16) Gould, I. R.; Young, R. H.; Farid, S. J. Phys. Chem. 1991, 95, 2068. (17) (a) Gould, I. R.; Farid, S. J. Am. Chem. Soc. 1988, 110, 7883. (b) Lim, B. T.; Okajima, S.; Chandra, A. K.; Lim, E. C. Chem. Phys. Lett. 1981, 79, 22. (18) Turro, N. J. Modern Molecular Photochemistry; Benjamin Cummins: Menlo Park, CA, 1978. (19) (a) Hopfield, J. J. Proc. Natl. Acad. Sci. U.S.A. 1974, 71, 3640. (b) Van Duyne, R. P.; Fischer, S. F. Chem. Phys. 1974, 5, 183. (c) Ulstrup, J.; Jortner, J. J. Chem. Phys. 1975, 63, 4358. (d) Siders, P.; Marcus, R. A. J. Am. Chem. Soc. 1981, 103, 741. (e) Marcus, R. A. J. Phys. Chem. 1984, 81, 4494. (20) If a purely classical model for the electron transfer rates were used, the correction for differing solvents would be exact. (21) (knr)A* is obtained by averaging all of the knr values for TCA and DCA in the absence of added donors (Tables 1 and 2), excluding the low and high outlier points, which are DCA in dioxane and TCA in trichloroethylene, respectively. Also omitted is TCA in dioxane because radiationless decay in this case occurs via charge-transfer quenching, which will be the subject of a separate paper. (22) It is intriguing that the initial decrease in log knr is very similar to the initial decrease in log kf. (23) Hamai, S.; Hirayama, F. J. Phys. Chem. 1983, 87, 83.