Sequential or superexchange mechanism in bridged electron transfer distinguished by dynamics at a bridging molecule

Two kinds of mechanisms are well known for electron transfer (ET) in the system DMA where a donor D and an acceptor A are fixed in a close distance by a bridging molecule M. When the free energy Delta G(m) of the intermediate state vertical bar m > of DM(-)A is much higher than the thermal energy k(B)T above the initial state of D(-)MA, the ET occurs unistep from D to A by the superexchange (SX) mechanism, passing vertical bar m > as a quantum-mechanical virtual state. However, when Delta G(m) becomes not much higher than k(B)T, the ordinary sequential (OS) ET may manifest itself, where the second ET from vertical bar m > to the final state of DMA(-) takes place after thermalization of phonons in vertical bar m >. Recently, much interest has been aroused in how the SX mechanism switches to the OS one as Delta G(m) is lowered. This subject has often been described conventionally by summation of the rate constant for the SX mechanism and that for the OS one. However, such convention cannot be justified, since these mechanisms are realized in mutually opposite limits concerned with dynamics in mediation of ET by a bridging molecule, hence they cannot both be realized simultaneously in a single system. An observation of such a bridged ET by Paulson, Miller, Gan and Closs (J. Am. Chem. Soc. 2005, 127, 4860) provides a good example of this feature. Describing their observation in a unified framework for the ET, it is shown that the switch occurs at Delta G(m) congruent to -0.5 eV, which is much lower than 0.3 eV reported by them, where the hot-sequential ET reveals itself, taking place during thermalization of phonons in vertical bar m >.