Superexchange electron tunneling mediated by solvent molecules: Pulsed electron paramagnetic resonance study on electronic coupling in solvent-separated radical ion pairs

Nanosecond pulsed electron paramagnetic resonance spectroscopy is applied to characterize exponential decay onstants (β) of the squared electronic coupling matrix element (V _DA ²) in transient, solvent-separated radical ion pairs (RIP) composed of quinone anions and several cation radicals in aprotic liquid solutions of N,N-dimethylformamide, DMSO, and benzonitrile. The distance dependence of singlet-triplet energy splitting (2J) is shown to be described by β in V _DA for charge-recombination processes. We show that the radical pair mechanism (RPM) electron spin polarization (PRPM) is quite sensitive to β. The β value is characterized by using the stochastic Liouville equation to fit the experimental PRPM values. The β values (from 0.8 to 1.0 Å ^-1) manifest that V _DA is governed by the superexchange mechanism mediated by the intervening solvent molecules from a result that the β increases with increasing the tunneling energy gap (ΔG _eff) for solvent oxidation or reduction in several intermolecular electron-transfer systems. We propose a simple three-dimensional model of V _DA, in which the through-solvent tunneling pathways are exponentially increased with the increase in the intermolecular distance in bulk, condensed media. This model explains the ΔG _eff dependence of β, including the data previously reported on the charge-transfer reactions both in liquid and frozen (77 K) solutions. Effective solvent-solvent coupling is estimated to be V _B ≈ 850 cm ^-1 at a mean nearest-neighbor distance of 5.7 Å. This relatively large magnitude of v _B may agree with dynamical amplifications of the effective coupling by low-frequency motions of the mediators as reported in charge-transfer reactions in biological systems. (Balabin, I. A.; Onuchic, J. Science 2000, 290, 114 and Troisi, A.; Orlandi, G. J. Phys. Chem. B 2002, 106, 2093.).