J. Phys. Chem. 1985,89, 8-10
8
New Energy Gap Laws for the Charge Separation Process in the Fluorescence Quenching Reaction and the Charge Recombination Process of Ion Pairs Produced in Polar Solvents Toshiaki Kakitani* Department of Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464, Japan
and Noboru Mataga* Department of Chemistry, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan (Received: September 20, 1984)
Taking into consideration that the phonon frequency of the solvent surrounding a neutral solute molecule is much smaller than that surrounding a charged species, we have formulated a rate expression for an electron transfer reaction in polar solvents. Our theory can explain satisfactorily the insensitiveness of the rate constant of the fluorescence quenching reaction, A* + B AT + B’, in polar solvents upon the energy gap in the “inverted region” and the strong dependence of the rate of the recombination reaction, AT B* A B, upon the energy gap and the nature of the individual electron donor and acceptor.
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+
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Introduction Photoinduced electron transfer (ET) is one of the most important primary processes of a photochemical reaction and is a subject of lively investigations. Especially detailed investigations including a wide range of compounds have been made for the AT fluorescence quenching reactions due to ET, A* B B*, in polar solvents.’ Systematic experimental studies of the fluorescence quenching reactions and behaviors of the ion pairs produced in strongly polar solvents have revealed following facts concerning the relations between the ET reaction rate and the energy gap (AG) between the states before and after ET. Namely, (a) the bimolecular rate constant kq of the fluorescence quenching reaction A* + B ---f A*...B + AS?...&,’ +
+
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+
for many aromatic fluorescer-quencher pairs in acetonitrile solution shows a steep rise around zero energy gap toward the downhill side and it shows a constant, diffusion-controlled value even in the strongly downhill region.* This result shows the lack of an “inverted region”, which cannot be satisfactorily explained by the current theory of ET. On the other hand, (b) the behaviors of the ion pairs produced, ASF-BS*, have been investigated by picosecond and nanosecond laser photolysis methods. In contrast to the above charge separation type E T reaction from the fluorescent state, the charge recombination reaction shows a rather strong energy gap dep e n d e n ~ e . ~For example, typical exciplex systems like pyreneN,N-dimethylaniline (DMA) in strongly polar solvents show a high yield of dissociation into free i ~ n ~ ,while ~ ~ ,porphyrin~ v ~ q ~ i n o n e ~ ~and * g f*l~a v i n - i n d ~ l esystems, ~~ where the energy gap between the ion-pair state and the ground state is much smaller compared with that of the pyrene-DMA system, do not show the formation of free ions in strongly polar solvents due to ultrafast nonradiative deactivation to the ground state. Accordingly, any (1) (a) Mataga, N.; Ottolenghi, M. In “Molecular Association”, Foster, R., Ed.; Academic Press: New York, 1979; Vol. 2, p 1. (b) Mataga, N. In “Molecular Interactions”, Ratajczak, H.; Orville-Thomas, W. J., EMS.; Wiley: Chichester, 1981; Vol. 2, p 509. (2) (a) Rehn, D.; Weller, A. Isr. J . Chem. 1970,8, 259. (b) Rehm, D.; Weller, A. Ber. Bunsenges. Phys. Chem. 1969, 73, 834. (3) (a) Taniguchi, Y.; Nishina, Y.; Mataga, N. Bull. Chem. Sor. Jpn. 1972, 45, 764. (b) Hino, T.; Akazawa, H.; Masuhara, H.; Mataga, N. J . Phys. Chem. 1976,80, 33. (c) Masuhara, H.; Mataga, N. Arc. Chem. Res. 1981,14,312. (d) Mataga, N. Radiat. Phys. Chem. 1983, 21, 83. (e) Karen, A.; Ikeda, N.; Mataga, N.; Tanaka, F . Photochem. Photobiol. 1983, 37, 495. (f) Mataga, N. Pure Appl. Chem. 1984,56, 1255. (g) Mataga, N.; Karen, A.; Okada,T.; Nishitani, S.;Kurata, N.; Sakata, Y.; Misumi, S. J. Am. Chem. SOC.1984,106, 2442. (h) Mataga, N.; Karen, A,; Okada, T.; Nishitani, S.; Sakata, Y.; Misumi, S. J. Phys. Chem. in press.
0022-3654/85/2089-0008$01 S O / O
theory concerning the electron transfer quenching of the fluorescent state and the charge recombination reaction of the ions produced in strongly polar solvents must be able to explain results (a) and (b). However, no satisfactory interpretation of these results, especially result (a), has been given on the basis of current theory up to now. We have developed a new theory which can explain the above results, taking into consideration the important fact that the phonon frequency of the solvent surrounding a neutral solute is much smaller than that surrounding a charged species due to the strong solutesolvent interaction in the latter. The important role of the reorientational motion of polar solvent molecules accompanying the ET reaction was recognized already in the very early stage of the theoretical investigation^^^^ and the solvent phonon modes were incorporated into the theory together with the intramolecular quantum modes by way of the Franck-Condon factor in a recent quantum mechanical study.6 However, the large difference in the frequency of the solvent mode before and after ET has not been taken into account in those theoretical studies. In this report, we will show that this large frequency difference can cause a drastic effect upon the energy gap dependence of the rate of the electron transfer reaction.
Formulation We consider the following photoinduced charge separation (la) and the charge recombination ( l b ) processes: A*...B A-...B+
-+ A...B
-+ A- ...B+ or (3A*...B or A...3B*)
(la)
(1b)
The E T rate constant W can be written by a convolution formalism6 W ( M ) = Jmdt W,(AE - t) S(t) -OD
(2)
where AE is the energy gap and Wqis the rate constant obtained by considering obly the intramolecular quantum modes as follows:6 W , ( U - €) = d exp[-S(20 I)]I,,(~S[O(OI ) ] ’ / z ) [ ( ~ 1 ) / 0 ] ~ /(3) ~
+
+
B = [exp(h(w)/kT)
+
- 11-l
(4)
P = (AE - t ) / h ( w ) , S = 62/2
(5)
A = 2~l(ilHlf)(~/h*(w)
(6)
(4) Marcus, R. A. J. Chem. Phys. 1956, 24,966. (5) Levich, V. G.; Dogonadze, R. R. Collect. Czech. Chem. Commun. 1961, 26, 193. (6) Jortner, J. J . Chem. Phys. 1976, 64, 4860.
0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 1, 1985 9
Letters charge separation
1 0 ~ ~ ~ 10'2
!
_.... -.
.I
', I
charge recombination
+ coordinate x f o r solvent a r o u n d A
*
> coordinate y f o r solvent around
or A
€3
Figure 1. Potential energy curves for reactants and products in neutral
107
and charged states as functions of solvent coordinates.
where ( w ) , 6, and ( i J H l f ) are the angular frequency of the quantum mode, the displacement of the normal coordinate, and the electronic matrix element causing the ET reaction. ZI4 is the modified Bessel function. It is difficult to formulate quantum mechanically the Franck-Condon factor S(t) due to the solvent mode in eq 1 when the difference in frequencies before and after E T is very large. We can, however, formulate S(t) classically by the method of Hopfield.' In Figure 1, we show schematically potential curves for reactants as functions of solvent coordinates. ka,and k,, are phonon force constants of the solvent surrounding the reactant A in the charged and neutral state, respectively, and so on. X, and E,* are the displacement of the solvent coordinate and the energy difference between the neutral and charged states of the reactant A*, respectively, and so on. With these parameters, one can write S(c) for the charge separation reaction as $(E)
= X:D,(&Ea*) D
