Resonance tunneling, electron transfer

When the gap is large, the sketch in Fig. 9 shows that a second channel will open when there is a vibrational resonance - that is, when eV = ho, with o one of the vibrational frequencies of the molecule. This is vibronic resonance, and energy will transfer from the momentum of the tunneling electrons into the vibrations of the molecule. The interaction is quite weak (because the tunneling time is so short) ... 

Fig. 2 (a) Schematic representation of the energy levels diagrams for a DBA system and a MBM junction in which the electron transfer process is dominated (b) by superexchange or non-resonant tunnelling, (c) by resonant tunnelling or (d) by hopping ... 

Chi Q, Farver O, Ulstrup J (2005) Long-range protein electron transfer observed at the singlemolecule level in situ mapping of redox-gated tunneling resonance. Proc Natl Acad Sci USA 102 16203-16208... 

Fig. 1. The Marcus parabolic free energy surfaces corresponding to the reactant electronic state of the system (DA) and to the product electronic state of the system (D A ) cross (become resonant) at the transition state. The curves which cross are computed with zero electronic tunneling interaction and are known as the diabatic curves, and include the Born-Oppenheimer potential energy of the molecular system plus the environmental polarization free energy as a function of the reaction coordinate. Due to the finite electronic coupling between the reactant and charge separated states, a fraction k l of the molecular systems passing through the transition state region will cross over onto the product surface this electronically controlled fraction k l thus enters directly as a factor into the electron transfer rate constant...

This is called a chemical, radical or stepwise mechanism. Or was it (ii) by the action of the bridging group to increase the probability of electron transfer by tunneling, termed resonance transfer 56,9i... 

A lively subsection in applications of quantum theory to transitions at electrodes concerns the tunneling of electrons through oxide films. This work has been led by Schmickler (1980, 1996), who has used a quantum mechanical approach known as resonance tunneling to explain the unexpected curvature of Tafel lines for electron transfer through oxide-covered electrodes (Fig. 9.21). 

The basic idea of resonance tunneling relies on the reasonable assumption that there are impurity states in the oxide film (regarded as a semiconductor), the energy of which is in resonance with that of electrons in the metal on which the film has been formed. One considers the situation in terms of two coordinated tunnel transfers, one from the metal to the impurity state and then from the impurity state to an ion adsotbed at the oxide/solution interface. 

Cai Z, Sevilla MD (2000) Electron spin resonance study of electron transfer in DNA inter-double-strand tunneling processes. J PhysChem B 104 6942-6949 Cai Z, Sevilla MD (2003) Electron and hole transfer from DNA base radicals to oxidized products of guanine in DNA. Radiat Res 159 411-419... 

If the Fermi level approaches the energy of the orbitals of the molecular bridge, resonant electron transfer may take place—either by hopping or resonant tunneling. In this case the conduction of electrons will occur through the molecular orbitals. 

Messer A, Carpenter K, Forzley K, Buchanan J, Yang S, Razskazovkii Y, Cai Z, Sevilla MD. (2000) Electron spin resonance study of electron transfer rates in DNA Determination of the tunneling constant beta for single-step excess electron transfer. J Phys Chem B 104 1128-1136. 

In thermally activated ET we are interested in the electronic states at the transition state (TS). When the system is at equilibrium in either the initial or final state (where D and A are well out of resonance), the diabatic states, xj/j and i/y, can be taken to be essentially the same as their adiabatic counterparts, xj/ and xj/2. When the system with weakly coupled D and A is suddenly carried into the TS by a fluctuation, we adopt the picture that the system remains in the (now nonstationary) xf/ state until (with some finite probability) it dynamically tunnels (see below) to i/y and irreversibly relaxes to the equilibrium product. The required resonance of D and A is a statement of the Franck-Condon control of thermally activated electron transfer [6, 8, 60] that is, at the TS,... 

Figure 1.24 Schematic representation of electron transfer reaction to the conduction band for direct (1) and resonance tunneling (2).

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