Electron tunnelling relation

Consider a linear analogue of Fig. 9.9. This figure is a simplification23 of the potential energy-distance relations when there is a vibrational stretching of theH+-0 bond in the system M(e) + H+-OH2 or the M-H bond in the system M-H + H20. It is concerned with proton stretching as a precondition for electron tunneling. It is obvious (Fig. 9.28) that... 

To conclude, we shall estimate the characteristic distance r2, at which the electron tunnels during the ionization of the atoms in the external field. This estimation can be conducted with the help of the relation r2 cs I/F. Substituting into this formula, for instance, the energy of He ion ionization, 1 0.076 eV and F = 200kV cm-1, we find r2 = 40 A. According to eqn. (8), the probability of ionization by means of electron tunneling at a distance r2 at such values of I and F is equal to 5 x 109s. ... 

This volume is concerned with providing a modern and comprehensive account of theories and experiments relating to electron-tunneling reactions in chemistry. The authors view of the detailed objectives and scope of the book are summarised in Chapter 1. 

Let us note that the quantum phonon assistance of the electron tunneling (/3-term in equations (1) and (2)) constitutes the difference of the model from the related dimer and exciton quantum models where instead of /3 Y.n (h2n + 2n)° n °f equation (1) there stands Acrxn, where A is the distance between the levels [4,5],... 

In parallel, the related activity was in the field of single-electron shuttles and quantum shuttles [143-153]. Finally, based on the Bardeen s tunneling Hamiltonian method [154-158] and Tersoff-Hamann approach [159,160], the theory of inelastic electron tunneling spectroscopy (IETS) was developed [113-116,161-163],... 

The K parameter, the electronic transmission coefficient, is related to the extent of overlap between the donor and acceptor orbitals. When this overlap is very small, electron tunneling frequency determines the pre-exponential factor, the reaction is nonadiabatic and k <1. Such overlap may be diminished if the electrode-reactant distance, in the course of the charge transfer, is increased due, for instance, to the presence of a blocking film on the electrode. On the other hand, when the overlap is relatively large, k is close to 1. Only when the reactant is near the electrode surface does significant overlap of donor and acceptor orbitals occur. 

In Fig. 20 we portray the results of model calculations for the time dependence of /(f), based on Eqs. (86), (92) and (93), for superfluid ( He)jy clusters with Af = 1.88 X 10 at r = 0.4 K. These calculations were performed for d = 39 A, which falls well in the physically acceptable region of d. This /(f) versus f curve exhibits a near exponential decay with time, with the characteristic lifetime Ttun for electron tunneling. Using the simple relation /(T-ruN)/f(0) = we obtained from Fig. 20 that ttun — 8 x lO s for Ai= 1.88 x 10, which is included in Table VII. 

Krische MJ, Lehn JM (2000) The Utilization of Persistent H-Bonding Motifs in the Self-Assembly of Supramolecular Architectures. 96 3-30 Krumholz P (1971) Iron(II) Diimine and Related Complexes. 9 139-174 Kuhn FE, Herrmann WA (2000) Rhenium-Oxo and Rhenium-Peroxo Complexes in Catalytic Oxidations. 97 213-236 Kubas GJ, see Ryan RR (1981) 46 47-100 Kuki A (1991) Electronic Tunneling Paths in Proteins. 75 49-84... 

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