The Journal of
Physical Chemistry
0 Copyright, 1990, by the American Chemical Society V O L U M E 94, N U M B E R
5 M A R C H 8,1990
LETTERS Importance of “Fast” Solvent Relaxatlon Components to Electron-Transfer Rates: Comparisons between Barrier-Crossing Frequencies and Subpicosecond Time-Resolved Solvation Dynamics Michael J. Weaver,* George E. McManis, Department of Chemistry, Purdue University, West Lafayette, Indiana 47907
Wlodzimiez Jarzeba, and Paul F. Barbara* Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455 (Received: September 29, 1989)
The solvent-dependent barrier-crossing dynamics for outer-sphere electron transfer as derived from metallocene rate and optical barrier data are compared with subpicosecond timeresolved solvation dynamics obtained from timedependent fluorescence Stokes shifts with coumarin probes. In the majority of cases, especially for propylene carbonate and methanol, the “fast” (51 ps) relaxation components identified in the latter measurements appear to provide an important contribution to the barrier-crossing dynamics, although exceptions are also observed. Possible limitations to the influence of additional “fast” solvent relaxation components upon electron-transfer dynamics are briefly discussed.
Progress in our understanding of the manner in which solvent dynamical properties influence the rates of electron transfer and other condensed-phase chemical processes is occurring rapidly at the present time (refs 1-3 are recent overview articles). These are being fueled by continuing theoretical developments, emphasizing increasingly molecular rather than continuum solvent descriptions (e.g., refs 4-8), along with an impressive array of new (1) Maroncelli, M.; Maclnnis, J.; Fleming, G. R.Science 1989,243, 1674. (2) Bagchi, G. Annu. Rev. Phys. Chem. 1989,40, 115. (3) Barbara, P. F.; Jarzeba, W. Adv. Photochem., in press. (4) Wolynes, P. G. J. Chem. Phys. 1987, 86, 5133. (5) Rips, I.; Klafter, J.; Jortner, J. J . Chem. Phys. 1988,88, 3246; 1988, 89, 4288. (6) Nichols, A. L.; Calef, D. F. J . Chem. Phys. 1988, 89, 3783.
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experimental information. Broadly speaking, the latter are of three types.l” The first involves the measurement of time-dependent fluorescence Stokes shifts (TDFS) for chromophores forming suitable charge-transfer excited state^.'-^*^ Such measurements enable the dynamics of polar solvation around a newly formed dipole to be followed, most recently on time scales down to ca. 0.1 PS.~,’O In addition to this direct dynamical information, measurements of electron-transfer (ET) rates from either photoexcited or ground states enable the role of solvation dynamics (7) Bagchi, B.; Chandra, A. J. Chem. Phys. 1989, 90, 7338. (8) Madden, P.; Kivelson, D. Adv. Chem. Phys. 1984, 56, 467. (9) Simon, J. D. Acc. Chem. Res. 1988, 21, 128. (10) Kahlow, M. A.; Jarzeba, W. T.; Kang, T. J.; Barbara, P. F. J . Chem. Phys. 1989, 90, 15 1.
0 1990 American Chemical Society
1716 The Journal of Physical Chemistry, Vol, 94, No. 5, 1990
on the ET barrier-crossing frequency to be assessed. So far, most photoexcited ET reactions examined in this context yield reaction times comparable to the solvation times, 7,, extracted from TDFS measurements, consistent with the presence of small ( 5 k B n barriers3*’’(kB is the Boltzmann constant). In contrast, thermal (ground-state) electron-exchange reactions typically exhibit markedly larger barriers (>5kB7‘) even in the absence of inner-shell (reactant bond distortional) components, reflecting the intrinsic outer-shell (solvent reorganization) barrier AG*,. Under these circumstances, the reaction times are much , that “steady-state” conditions apply12where the longer than T ~so electron-exchange rate constant can be written simply in the familiar form
Letters Given the direct dynamical information provided by the former measurements, it is of interest to ascertain to what extent the “faster” versus “slower” solvent relaxation components thus identified influence the activated barrier-crossing dynamics as reflected in the latter results. This objective is pursued in the present Letter, particularly in relation to the widely considered p r e d i c t i ~ n , ~discussed ~,~~,~~ previously in this c ~ n t e x t , l ’ *that ~ ~ faster overdamped components of the dielectric relaxation can exert important accelerating influences upon u,. The analysis herein employs previously unreported TDFS data in water, acetone, dimethyl sulfoxide (DMSO), and benzonitrile as well as recently published results for methanol, acetonitrile, propionitrile, and propylene carbonate.I0
Results and Discussion Self-Exchange Kinetics. A complication in extracting solvent The preexponential factor can conveniently be expressed for acdynamical information from electron-exchange rate constants for tivation-controlled intermolecular ET asI3-l4 comparison with relaxation time data obtained from TDFS measurements is that the reaction rates need to be corrected for A = Kp~el~n (2) the solvent-dependent barriers, AG*,.18-20 A further intricacy, highlighted recently,20 is that k,, will only respond to solvent where K pis a precursor preequilibrium constant, K,] is the electronic dynamics to the extent that significant reaction adiabaticity is transmission coefficient, and un is the nuclear frequency factor maintained. For markedly nonadiabatic processes (Le., K , ~
