Electron transfer reactions tunnelling

Zimmt, M. B. and D. H. Waldeck (2003). Exposing the solvent s role in electron transfer reactions tunneling pathways and solvation. J. Phys. Chem. 107, 3580. 

Daizadeh I, Guo J-X and Stuchebrukhov A 1999 Vortex structure of the tunneling flow in long-range electron transfer reactions J. Chem. Phys. 110 8865-8... 

In this section, we switch gears slightly to address another contemporary topic, solvation dynamics coupled into the ESPT reaction. One relevant, important issue of current interest is the ESPT coupled excited-state charge transfer (ESCT) reaction. Seminal theoretical approaches applied by Hynes and coworkers revealed the key features, with descriptions of dynamics and electronic structures of non-adiabatic [119, 120] and adiabatic [121-123] proton transfer reactions. The most recent theoretical advancement has incorporated both solvent reorganization and proton tunneling and made the framework similar to electron transfer reaction, [119-126] such that the proton transfer rate kpt can be categorized into two regimes (a) For nonadiabatic limit [120] ... 

Cytochrome c is responsible for accepting an electron from cytochrome Ci and transferring it to cytochrome c oxidase. The electron transfer reaction may occur via the exposed portion of the ring or by tunnelling through the protein (and involving an outer-sphere mechanism). The details of this process have not been fully elucidated and have remained the focus of much research. 

Nitzan A, Jortner J, Wilkie J, Burin AL, Ratner MA (2000) Tunneling time for electron transfer reactions. J Phys Chem B 104(24) 5661-5665... 

Stuchebrukhov AA (1996) Tunneling currents in electron transfer reactions in proteins. J Chem Phys 104(21) 8424-8432... 

Schmickler W, Tao N (1997) Measuring the inverted region of an electron transfer reaction with a scanning tunneling microscope. Electrochim Acta 42 2809-2815... 

Another type of electrochemical reaction, an electron-transfer reaction, is indicated near the bottom of Fig. 1.1. In the example shown an oxidized species is reduced by taking up an electron from the metal. Since electrons are very light particles, they can tunnel over a distance of 10 A or more, and the reacting species need not be in contact with... 

For my first volume as Editor, I have invited Professor Colin D. Hubbard (University of Erlangen-Niirnberg, Erlangen, Germany and University of New Hampshire, Durham, NH, USA) as co-editor. Professor Hubbard studied chemistry at the University of Sheffield, and obtained his PhD with Ralph G. Wilkins. Following post-doctoral work at MIT, Cornell University and University of California in Berkeley, he joined the academic staff of the University of New Hampshire, Durham, where he became Professor of Chemistry in 1979. His interests cover the areas of high-pressure chemistry, electron transfer reactions, proton tunnelling and enzyme catalysis. 

Does T differ significantly from unity in typical electron transfer reactions It is difficult to get direct evidence for nuclear tunnelling from rate measurements except at very low temperatures in certain systems. Nuclear tunnelling is a consequence of the quantum nature of oscillators involved in the process. For the corresponding optical transfer, it is easy to see this property when one measures the temperature dependence of the intervalence band profile in a dynamically-trapped mixed-valence system. The second moment of the band,... 

An improved and direct correlation between the experimental rate constant and [obtained using Eq. (49)] is observed if v = /zd is used instead of v = 1/Tt, the solvent-dependent tunneling factor is utilized, and only AG (het) of Eq. (8) is used in Eq. (49) (see triangles in Fig. 18). Furthermore, the inverse of the longitudinal solvent relaxation time Xi is not necessarily the relevant one to use as the frequency factor v (see empty circles in Fig. 18). Similar conclusions were reached by Barbara and Jerzeba for the electron transfer reaction in homogeneous solutions. Barbara and Jerzeba measured the electron transfer time... 

Fig. 8-16. Electron state density in a semiconductor electrode and in hjrdrated redox partides, rate constant of electron tunneling, and exchange redox current in equilibrium with a redox electron transfer reaction for which the Fermi level is close to the conduction band edge eF(sc) = Fermi level of intrinsic semiconductor at the flat band potential 1. 0 (tp.o) = exchange reaction current of electrons (holes) (hvp)) - tunneling rate constant of electrons (holes).

Fig. 8-41. Electron transfer reaction of hydrated redox particles in equilibrium on a metal electrode covered with a thick film (F, solid curve) and with a thin film (F, dashed curve) >cs = electron transfer current via the conduction band >scl = tunneling electron current through a depletion layer in the conduction band >vb = hole transfer current via the valence band.

In Chapter 7 general kinetics of electrode reactions is presented with kinetic parameters such as stoichiometric number, reaction order, and activation energy. In most cases the affinity of reactions is distributed in multiple steps rather than in a single particular rate step. Chapter 8 discusses the kinetics of electron transfer reactions across the electrode interfaces. Electron transfer proceeds through a quantum mechanical tunneling from an occupied electron level to a vacant electron level. Complexation and adsorption of redox particles influence the rate of electron transfer by shifting the electron level of redox particles. Chapter 9 discusses the kinetics of ion transfer reactions which are based upon activation processes of Boltzmann particles. 

Specific conditions of the electron transfer reactions on Hg surfaces covered with sulfur compounds have been intensively investigated by Majda, Bilewicz, Slowihski, and coworkers [122-129]. The studies on electron tunneling involving Hg—Hg junction and mono- or bilayers of alka-nethiolate trapped between small mercury... 

A typical example of a special state is as follows. Electron transfer reactions at an atom are aided by vibrations that equilibrate the interatomic distances that differ for the two oxidation states. Thus a low-energy, high-amplitude vibration is desirable. The vibration could have the further function that it provided a time-dependent fluctuation of the redox potential. As I and Goldanskii in this volume have pointed out, this allows a precise matching of the redox potential of one redox couple with another leading to tunneling of electrons. 

The kinetics of electron transfer reactions at electrodes can be explained either by surmounting an activation barrier due to the chemical reorganization of the reactants or by tunnelling through the potential barrier across the electrode—solution interface. 

In the electron transfer literature it has become common to describe electron transfer reactions that occur through vibrational distributions below the intersection as having occurred by nuclear tunneling and the actual electron hopping event as electron tunneling . 

In electrode kinetics, interface reactions have been extensively modeled by electrochemists [K.J. Vetter (1967)]. Adsorption, chemisorption, dissociation, electron transfer, and tunneling may all be rate determining steps. At crystal/crystal interfaces, one expects the kinetic parameters of these steps to depend on the energy levels of the electrons (Fig. 7-4) and the particular conformation of the interface, and thus on the crystal s relative orientation. It follows then that a polycrystalline, that is, a (structurally) inhomogeneous thin film, cannot be characterized by a single rate law. 

The present chapter comprises a review of tunneling phenomena in nuclear, atomic, and solid-state physics, tunneling effects during the transfer of atoms in chemical reactions in gases, liquids, and solids, as well as of tunneling phenomena in electron transfer reactions in gases. 

There are also certain data on electron tunneling in electron transfer reactions in liquids. The ideas about electron tunneling have been used by Anbar and Hart [75] to interpret the anomalously large rate constants for the diffusion controlled reactions of hydrated electrons with some inorganic anions in aqueous solution. Table 5 represents the data on the largest values of the rate constants, ke, observed for the reactions of eaq with various inorganic anions and cations. Theoretical diffusion rate constants, kA, for... 

In this chapter, a general quantum mechanical description of electron tunneling in condensed media is given. Let us consider the electron transfer reaction... 

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