Elsevier

Chemical Physics Letters

Volume 294, Issues 1–3, 11 September 1998, Pages 19-25
Chemical Physics Letters

Blocking of bridge-mediated electron transfer by an external magnetic field

https://doi.org/10.1016/S0009-2614(98)00843-4Get rights and content

Abstract

The rate expression for the low-temperature bridge-mediated electron transfer (ET) in a donor–acceptor complex is derived including the influence of an externally applied magnetic field. A blocking of the ET is demonstrated for a bridge with two paramagnetic ions having incompletely filled 3d-shells. The blocking can appear (i) if each of the paramagnetic ions has a “frozen” angular momentum in its ground-state multiplet, and (ii) if the ion (which has to stay in its electronic ground-state) reduces its spin from S to S−1/2 during the formation of the virtual bound state with the transferred electron. To observe the blocking the spin projection of the transferred electron has to be m=−1/2, and the spin projection of each paramagnetic ion should be its minimal value M=−S.

Introduction

Electron transfer (ET) mediated by bridging groups is one of the basic reaction events in chemistry and biology 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. The insight into ET gained by the experimental and theoretical work done over decades led to the dream of molecular electronics 12, 13, 14, 15, 16, 17, 18. Of particular interest are those ET reactions in which the electronic levels of the bridge (B), responsible for the ET process, are shifted far from the donor (D) and acceptor (A) levels. In such a case the ET reaction proceeds as D−–B–A → D–B–A−, and the intermediate states D–B−–A are practically not populated by the transferred electron. They only result in the creation of an effective electronic coupling TDA between the D and A.

The same situation can be met for a molecular wire connecting two micro-electrodes. Here, the magnitude of the interelectrode current is governed by an effective coupling which is determined by the parameters of the molecular wire 17, 18.

In changing the relaxation characteristics of the D–B–A system or those parameters which determine the effective electronic coupling TDA one can increase or decrease the ET rate by orders of magnitude. Recently, such a control scheme has been proposed by changing the D and A energy levels as well as the coupling TDA via regular and stochastic electric fields (see 19, 20, 21, 22, 23).

Of special interest would be the magnetic field control of ET reactions in D–A complexes containing paramagnetic ions. Such control schemes have been studied less intensively. Ferraudi 24, 25, 26 has dealt with such problems. He could demonstrate a magnetic field dependence of the quantum yield as well as the bimolecular rate for the ET from Cl−2 and Br−2 to Co2+ or Mn2+ complexes. In particular, he showed that the isotopic hyperfine coupling induced multiplet transitions and the Δg mechanism gave a significant contribution to the magnetic field effect on ET.

It is the purpose of the present Letter to present a magnetic field-control scheme which differs significantly from that of Ferraudi. Instead of acting as electron donors or acceptors, the paramagnetic ions are embedded in the bridge structure of the D–B–A complex where they form quantum mediators. In this way, the wavefunctions of the paramagnetic ions only provide a spin-dependent overlap with the wavefunctions of the remaining units of the ET chain, leading to an effective coupling between the donor and the acceptor. At low temperatures the population of different spin states of the bridging paramagnetic ions may depend strongly on the applied magnetic field strength. Hence, the switching among different ET channels depends on the magnetic field as well.

Before discussing the magnetic field influence on bridge-mediated ET reactions we note the paper of Bittl and Schulten 27, 28. These authors were apparently the first who studied theoretically the strong correlation between a “through space” electron exchange interaction in photogenerated zwitterionic biradicals (in D–B–A type systems) and the magnetic field dependent yield of the triplet state population. Their results demonstrated the influence of the exchange coupling on the ET efficiency in the charge recombination reaction within a biradical pair.

Additionally, we mention here earlier quasi–classical calculations on ET reactions mediated by an antiferromagnetically ordered bridge. It was shown in Ref. [18] that one has to expect a strong dependence of the ET rate k on the applied magnetic field h, and on the exchange interaction (within the bridge).

Section snippets

Model and theory

In the following, we analyze low-temperature ET reactions of the type D−–B–A → D–B–A−, which are mediated by bridging states D–B−–A. We concentrate on the case of two paramagnetic ions per bridge coupled one to another by the exchange interaction. They are assumed to be incorporated into neighboring units of an N-unit bridge chain. In molecular systems like those discussed in [29] each paramagnetic ion is surrounded by nonmagnetic ions (ligands) which create a “crystal field”. The combined

Results

As already mentioned we restrict ourselves to a special kind of paramagnetic ion with “frozen” angular momentum in their electronic ground-states. Since the coupling of an additional electron to a paramagnetic ion reduces the ground state spin of such an ion from S to S−1/2, one expects special spin limitations of the ET reaction in the presence of a magnetic field. These limitations are contained in the matrix elements given by Eq. (8)which describe an electron jump from a nonmagnetic unit to

Conditions for observation

In this Letter the magnetic-field control of bridge-assisted ET reactions has been considered. The forbidden transfer of a spin-down electron which forms the basis for the ET control relies on two conditions. The transfer should be mediated by special paramagnetic ions with “frozen” angular momentum, and each paramagnetic ion has to reduce its spin from S to S−1/2 during the creation of a bound state between the transferred electron and the ion.

In the following we discuss in somewhat more

Acknowledgements

We gratefully acknowledge the support of this work by the Volkswagen-Stiftung, Germany, and by the Fund of Fundamental Researches of the Ukrainian Ministry for Science and Technology, Project No 2.4/625 (EGP and IST).

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