Nuclear, Electronic, and Frequency Factors in Electron-Transfer Reactions

Accounts of Chemical Research

Volumn 15, Issue 9, 1982, Pages 275-282

  Sutin, Norman ^a  

^a BROOKHAVEN NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845552919     PISSN: 00014842     EISSN: 15204898     Source Type: Journal    
DOI: 10.1021/ar00081a002     Document Type: Article

References (89)

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24. Equations 1-4 are equivalent to certain equations introduced by Marcus.2
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48. Alternatively, a spin equilibrium may be viewed as a system in which an electronically excited state is thermally populated.
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53. Resonance Raman studies have shown46 that the electron promoted in the MLCT transition in Ru(bpy)32+ is located on a single bipyridine ligand rather than delocalized over all three ligands. Despite this, the MLCT absorption and emission bands show very little solvent dependence. A large solvent dependence in symmetrical systems of this type is not expected if the ligand-to-ligand electron hopping frequency is sufficiently high for the charge distribution in the excited state to be essentially spherically symmetrical on the time scale for solvent polarization. This interpretation is supported by the observation that the electron hopping frequency in Fe(bpy)3+ is >1010 s'1.46
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72. Instead of a very small electronic factor, a small nuclear factor arising from different hydration numbers of the two oxidation states (larger inner-sphere barrier or small Franck-Condon factor) could be primarily responsible for the relatively slow rates of outer-sphere reactions involving the Euaq3+-Euaq2+ couple.
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80. Although the agreement might be improved by mixing in the LF excited state of Ru(bpy)32+, which Ues slightly above the MLCT state, a similar explanation will not hold for Os(bpy)32+, where the LF state lies well above the MLCT state. The shorter lifetime of *Os(bpy)32+ compared to *Ru(bpy)32+ is consistent with the smaller energy gap (and larger spin-orbit coupling) for the former system. In terms of the present model, the relatively long lifetime of the LF excited state of Cr(bpy)33+, for which the Stokes shift is 60 cm'1,70 can be rationalized in terms of the combination of a small electronic factor, resulting from small spin-orbit coupling, and a small nuclear factor, resulting from a small Stokes shift and the absence of an active role for high frequency modes in the metal-centered transition. The absence of a C-H/C-D isotope effect on the lifetime of the Cr(bpy)33+ excited state is consistent with this interpretation.26
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85. When Eout |AE0| and a single internal mode of frequency vin is considered, the following expression for the electron-transfer rate constant at low temperature or low values of E/hv (normal free-energy region, classical solvent) is obtained by using perturbation theory244
86. The agreement may be further improved by the use of expressions in which anharmonicity and frequency changes are explicitly taken into account.
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