J . Phys. Chem. 1991,95, 1941-1944
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3.5. Time-Resolved Microwave Conductivity (TRMC). The TRMC measurements were carried out as described fully elsewhere.35 The solute was photoexcited by using the 308-nm XeCl line of a Lumonics HyperEX-420 laser with a 5-11s FWHM pulse of approximately 10 mJ/cm2 integrated intensity. The change in microwave power reflected by the cell containing the solution of interest was monitored by using a Tektronix 7912 transient digitizer. Signal noise was reduced by averaging up to 64 single-shot traces. The pulse shape was monitored by using a subnanosecond time response photodiode. The time response of the microwave cavity, which was the limiting factor in the overall time response and equal to approximately 6 ns, was determined accurately by measurement of the reflection characteristics of the cavity containing the solvent of interest. Data analysis involved numerically solving the appropriate rate equations by the Runge Kutta method including the known pulse shape and time response and correcting for the variation of light intensity with penetration as described p r e v i ~ u s l y . ~ ~ Figure 6. Fluorescence decay, as measured by picosecond time correlated single photon counting, for ZnP[2] and ZnP[6]Q in tetrahydrofuran. Excitation at 593 nm, detection at 680 nm, channel width 10 ps.
In Figure 6 we show the experimental fluorescence decay curves of ZnP[2] and ZnP[6]Q in tetrahydrofuran. While the former can be fitted perfectly with a single lifetime (1 260 ps), the fit for the latter is significantly improved by biexponential fitting with a main component (90%) of 285 ps and a minor component of -1100 ps.
Acknowledgment. We thank the Australian Research Council for support. The present investigationswere furthermore supported by the Netherlands Foundation for Chemical Research (SON) with financial aid from the Netherlands Organization for the Advancement of Research (NWO) and by the Netherlands Ministry of Economic Affairs Innovation-oriented Research Programme on Polymer Composites and Special Polymers (IOP-PCBP). The valuable assistance of Ing. D. Bebelaar in the realization of the picosecond measurements is gratefully acknowledged.
Non-Arrhenius Temperature Dependence of Electron-Transfer Rates M. Bixon* and Joshua Jortner* School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel- Aviv University, 69978 Tel- Aviv, Israel (Received: June 7 , 1990)
A surprisingly weak temperature dependence of electron-transfer (ET) rates in a dense medium may be induced by vibrational excitations of high-frequency quantum vibrational modes of the donor and acceptor centers, which accompany ET. Practically activationless ET prevails over a broad range of the free energy gap within the inverted region for moderate values of electron-vibration coupling. The effects of intramolecular vibrational excitations on the primary ET and recombination rates in the photosynthetic reaction center are elucidated.
Introduction Weller made central contributions to our understanding of intramolecular and intermolecular electron-transfer (ET) processes in solution. A fascinating observation reported by Rehm and Weller in 1970' pertained to the rates of highly exoergic ET reaction, which were found to be independent of the thermodynamic driving force, Le., the free energy gap (-AG). This observation was in variance with an important prediction of the Marcus theory2 that the rate of highly exoergic ET reactions slows down with increasing -AG in the so-called inverted region. The work of Rehm and Weller initiated the exploration of quantum effects on ET processes, elucidating the role of high-frequency intramolecular vibrational modes of the donor and acceptor centers on ET dynamics.) These quantum effects are expected to not only modify free energy relationship for ET',' but also exert a dramatic ( I ) Rehm, D.; Weller, A. Isr. J . Chem. 1970, 8, 259. (2) (a) Marcus, R . A. J . Chem. Phys. 1956,24966. (b) Marcus, R. A. J. Chem. Phys. 1957,26,867. (c) Marcus, R. A. Discuss.Faroday Soc. 1960, 29, 21.
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effect on the temperature dependence of ET rates. The Marcus theory2 of electron transfer (ET) in solution, which constitutes the first quantitative description of a chemical reaction in a dense medium, resulted in the Arrhenius-type temperature (3) (a) Efrima, S.;Bixon, M. Chem. Phys. Lrrr. 1974,25, 34. (b) Kertnor, N. R.; Logan, J.; Jortner, J. J. Chem. Phys. 1974,78,2148. (c) Van Duyne, R. P.; Fischer, S.F. Chem. Phys. 1974, 5, 183. (d) Ulstrup, J.; Jortner, J. J . Chem. Phys. 1975,63,4358. ( e ) Efrima, S.;Bixon, M. Chcm. Phys. 1976, 13,447. (f) Fischer, S.F.; Van Duyne, R.P.Chem. Phys. 1977,26,9. (8) Webman, I.; Kestner, N. R. J . Phys. Chrm. 1979,83,451. (h) Kestner, N, R . J . Phys. Chem. 1980,84,1270. (i) Marcus, R. A. J . Chcm. Phys. 1984, 81, 4494. (4) (a) Miller, J. R.; Calcaterra, L. R.; Close, 0. L.J . Am. Chrm. Soc. 1984, 106, 3047. (b) Miller, J. R.;Bcitz, J. V.; Huddlerton, R. K. J . Am. Chem. Soc. 1984, 106, 5057. (c) Closs, G. L.; Calceterra, L.T.; Own, N. J.; Penfield, K. W.; Miller, J. R. J . Phys. Chem. 1986.90, 3673. (d) Irvine, M. P.;Harrison, R. J.; Beddard, G. S.;Leighton, P.;Sanden, J. K.J. C h e w Phys. 1986, 104, 315. (e) Gould, 1. R.; Ege, D.; Mattas, S. L.;Farid, S.J . Am. Chem. Phys. 1987, 109, 3794. (f) Gould, 1. R.; Morer, J. E.; E 0. D.; Farid, S.J . Am. Chem. Phys. 1988, 110, 1991. ( ) Ohno, R.;Yorhfmura, A.; Shioyama, H.; Mataga, N.J . Phys. Chcm. lS!, 91,4365. (h) Mats a, N.; Asahi, T.;Kanda, Y.;Okada, T.; Kakitani, T. Chem. Phys. 1988, 197, 249. (i) Asahi, T.; Mataga, N. J . Phys. Chem. 1989, 93, 6575.
0 1991 American Chemical Society
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1942 The Journal of Physical Chemistry, Vol. 95, No. 5, 1991
dependence of the E T rate. For nonadiabatic ET, which is also characterized by negligible effects of solvent dynamics, the rate is given by k = (27r/h)pF (1) where Vis the electronic coupling and F is the thermally averaged vibrational overlap nuclear Franck-Condqn factor. Marcus originally considered solely the contribution of low-frequency medium modes to F. In the classical limit, Le., when hw,
