Electron tunneling theories

The activation energy of most of the eh reactions, 3.5+0.5 Kcal/mole, is much less than the hydration energy of the electron, -40 Kcal/mole. There are other barriers against reaction, such as repulsion by electrons in molecules. This can only be an accident in the classical mechanism, but not in electron tunneling theory as long as the reaction is exothermic overall. 

An appreciation of the basic parameters of electron tunneling theory and a survey of the values of these parameters in natural systems allows us to grasp the natural engineering of electron transfer proteins, what elements of their design are important for function and which are not, and how they fail under the influence of disease and mutation. Furthermore, this understanding also provides us with blueprint for the design of novel electron transfer proteins to exploit natural redox chemistry in desirable, simplified de novo synthetic proteins (Robertson et al., 1994). 

This has grown to form a considerable area of chemistryIt includes such varied topics as the ab initio calculation of electronic matrix elements/ the effect of bridging groups,electron tunneling theories,selection rules for electron transfer, and the distance dependence of electron transfer rates/ ... 

Non-adiabatic multiphonon electron tunnelling theory has been used to interpret kinetic data on a number of redox reactions of cytochrome c and yields a self-exchange rate constant for the protein of 1.7 x 10 s (ATT =4.9 kcal... 

A Kuki, PG Wolynes. Electron tunneling paths in proteins. Science 236 1647-1652, 1987. T Ziegler. Approximate density functional theory as a practical tool m molecular energetics and dynamics. Chem Rev 91 651-667, 1991. 

Figure 12-5. Kcprcscmauun of Uie calculated injcciiou curretu on a 111 j vs scale. Tlic dashed line indicates tile slopes predicted by Fowler Nordheiin tunneling theory lor A=0.8eV assuming that the effective mass equals the free electron mass.

When the current in molecular junctions is dominated by electron tunnelling (Fig. 2b), it can be described as a first approximation by Simmons s theory [40,41]. In this model, the current depends on (1) the height O of the potential barrier, which is determined by the interactions of the electron with the medium and (2) the thickness d of the barrier (Fig. 3). 

Kirtley J, Soven P (1979) Multiple-scattering theory of intensities in inelastic-electron-tunneling spectroscopy. Phys Rev B 19 1812-1817... 

Knockenmuss R, Hipps KW (1982) Some proposed modifications in the theory of inelastic electron tunneling spectroscopy and the source of parameters utilized. J Phys Chem 86 4477-4480... 

It is beyond the scope of this text to continue the discussion of Marcus theory. Qualitatively, the student should understand that electrons must find a path through the protein from the donor species to the acceptor. This may take place through bonds as outlined above or through electron tunneling events in which electrons travel through space between orbitals of the donor species to the acceptor species. Chapter 6 of reference 13 presents a clear explanation for further reading. 

As we have discussed in Chapter 2, a direct consequence of the Bardeen tunneling theory (or the extension of it) is the reciprocity principle If the electronic state of the tip and the sample state under observation are interchanged, the image should be the same. An alternative wording of the same... 

Feuchtwang, T. E. (1979). Tunneling theory without the transfer Hamiltonian formalism V. A theory of inelastic electron tunneling spectroscopy. Phy.s. Rev. B 20, 430-455, and references therein. 

If the localized electron tunnels out through the barrier (state 1 in Fig. 12 b) a certain amount of f-f overlapping is present. States like 1 in Fig. 12 b are called sometimes resonant states or "virtually bound" states. In contrast with case 2 in Fig. 12b, which we may call of full localization , the wave function of a resonant state does not die out rapidly, but keeps a finite amplitude in the crystal, even far away from the core. For this reason, overlapping may take place with adjacent atoms and a band may be built as in ii. (If the band formed is a very narrow band, sometimes the names of localized state or of resonance band are employed, too. Attention is drawn, however, that in this case one refers to a many-electron, many-atoms wave function of itinerant character in the sense of band theory whereas in the case of resonant states one refers to a one-electron state, bound to the central potential of the core (see Chap. F)). 

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