### Abstract

The effect of dephasing and relaxation on electron transfer in bridged molecular systems is investigated using a simple molecular model. The interaction between the molecular system and the thermal environment is described on the level of the Redfield theory, modified when needed for the description of steady-state situations. Noting that transient as well as steady-state measurements are possible in such system, we discuss the relationship between the rates obtained from these different types of experiments and, in particular, the conditions under which these rates are the same. Also, a formal relation between the steady-state rate for electron transfer across a molecular bridge and the conductance of this bridge when placed between two metal contacts is established. The effect of dephasing and relaxation on the electron transfer is investigated, and new observations are made with regard to the transition from the superexchange to the thermal (hopping through bridge) regime of the transfer process. In particular, the rate is temperature-independent in the superexchange regime, and its dependence on the bridge length (N) is exponential, exp(-βN). The rate behaves like (α_{1} + α_{2}N)^{-1} exp(-ΔE/k_{B}T) beyond a crossover value of N, where ΔE is the energy gap between the donor/acceptor and the bridge levels, and where α_{1} and α_{2} are characteristic times for activation onto the bridge and diffusion in the bridge, respectively. We find that, in typical cases, α_{1} ≫ α_{2}, and therefore, a region of very weak N dependence is expected before the Ohmic behavior, N^{-1}, is established for large enough N. In addition, a relatively weak exponential dependence, exp(-αN), is expected for long bridges if competing processes capture electrons away from the bridge sites. Finally, we consider ways to distinguish experimentally between the thermal and the tunneling routes.

Original language | English |
---|---|

Pages (from-to) | 3817-3829 |

Number of pages | 13 |

Journal | Journal of Physical Chemistry B |

Volume | 104 |

Issue number | 16 |

Publication status | Published - Apr 27 2000 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Engineering(all)

### Cite this

*Journal of Physical Chemistry B*,

*104*(16), 3817-3829.

**Electron transfer rates in bridged molecular systems 2. A steady-state analysis of coherent tunneling and thermal transitions.** / Segal, Dvira; Nitzan, Abraham; Davis, William B.; Wasielewski, Michael R; Ratner, Mark A.

Research output: Contribution to journal › Article

*Journal of Physical Chemistry B*, vol. 104, no. 16, pp. 3817-3829.

}

TY - JOUR

T1 - Electron transfer rates in bridged molecular systems 2. A steady-state analysis of coherent tunneling and thermal transitions

AU - Segal, Dvira

AU - Nitzan, Abraham

AU - Davis, William B.

AU - Wasielewski, Michael R

AU - Ratner, Mark A

PY - 2000/4/27

Y1 - 2000/4/27

N2 - The effect of dephasing and relaxation on electron transfer in bridged molecular systems is investigated using a simple molecular model. The interaction between the molecular system and the thermal environment is described on the level of the Redfield theory, modified when needed for the description of steady-state situations. Noting that transient as well as steady-state measurements are possible in such system, we discuss the relationship between the rates obtained from these different types of experiments and, in particular, the conditions under which these rates are the same. Also, a formal relation between the steady-state rate for electron transfer across a molecular bridge and the conductance of this bridge when placed between two metal contacts is established. The effect of dephasing and relaxation on the electron transfer is investigated, and new observations are made with regard to the transition from the superexchange to the thermal (hopping through bridge) regime of the transfer process. In particular, the rate is temperature-independent in the superexchange regime, and its dependence on the bridge length (N) is exponential, exp(-βN). The rate behaves like (α1 + α2N)-1 exp(-ΔE/kBT) beyond a crossover value of N, where ΔE is the energy gap between the donor/acceptor and the bridge levels, and where α1 and α2 are characteristic times for activation onto the bridge and diffusion in the bridge, respectively. We find that, in typical cases, α1 ≫ α2, and therefore, a region of very weak N dependence is expected before the Ohmic behavior, N-1, is established for large enough N. In addition, a relatively weak exponential dependence, exp(-αN), is expected for long bridges if competing processes capture electrons away from the bridge sites. Finally, we consider ways to distinguish experimentally between the thermal and the tunneling routes.

AB - The effect of dephasing and relaxation on electron transfer in bridged molecular systems is investigated using a simple molecular model. The interaction between the molecular system and the thermal environment is described on the level of the Redfield theory, modified when needed for the description of steady-state situations. Noting that transient as well as steady-state measurements are possible in such system, we discuss the relationship between the rates obtained from these different types of experiments and, in particular, the conditions under which these rates are the same. Also, a formal relation between the steady-state rate for electron transfer across a molecular bridge and the conductance of this bridge when placed between two metal contacts is established. The effect of dephasing and relaxation on the electron transfer is investigated, and new observations are made with regard to the transition from the superexchange to the thermal (hopping through bridge) regime of the transfer process. In particular, the rate is temperature-independent in the superexchange regime, and its dependence on the bridge length (N) is exponential, exp(-βN). The rate behaves like (α1 + α2N)-1 exp(-ΔE/kBT) beyond a crossover value of N, where ΔE is the energy gap between the donor/acceptor and the bridge levels, and where α1 and α2 are characteristic times for activation onto the bridge and diffusion in the bridge, respectively. We find that, in typical cases, α1 ≫ α2, and therefore, a region of very weak N dependence is expected before the Ohmic behavior, N-1, is established for large enough N. In addition, a relatively weak exponential dependence, exp(-αN), is expected for long bridges if competing processes capture electrons away from the bridge sites. Finally, we consider ways to distinguish experimentally between the thermal and the tunneling routes.

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M3 - Article

VL - 104

SP - 3817

EP - 3829

JO - Journal of Physical Chemistry B

JF - Journal of Physical Chemistry B

SN - 1520-6106

IS - 16

ER -