Basic Electron Tunneling Theory

A strict quantum mechanical calculation of a tunneling system the size of a protein quickly becomes intractably complex. Fortunately, relatively simple theory has been successful at organizing and predicting electron tunneling rates in proteins. When the donor and acceptor redox centers are well separated, non-adiabatic electron transfer theory applies Fermiis Golden Rule, in which the rate of electron transfer is proportional to two terms, one electronic. Hah, and the other nuclear, FC (Devault, 1980). 

The electronic coupling Hah between the reactant with the donor reduced, and the product with the acceptor reduced, depends on the ability of the electron wavefunction to penetrate the classical forbidden insulating barrier between the donor and acceptor. 

For any given barrier height V, the rate of tunneling of an electron with mass m will fall off exponentially with distance R through the barrier. 

The higher the barrier, the larger the exponential coefficient p and the more dramatically the electron transfer rate decays with distance. By a fortunate coincidence of units, the P in is approximated by the square root of the barrier height in eV. Thus for typical biological redox centers that must overcome a barrier of about 8eV to be ionized in a vacuum, we can estimate the P for exponential decay of electron transfer in vacuum to be about 2.8 Much less of a barrier is presented by a surrounding organic 

---

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). 

So, the description of the theory of electron tunneling transfer is logically accomplished in this chapter - it describes the methods of calculation of the electron matrix element, whereas the methods of calculation and the form of the vibration part of the transition probability was represented in Chapter 2. Besides, in Chapter 3 the procedure of the calculation of the rate constant of tunneling transfer in the conditions of the violation of Born-Oppenheimer s approach is examined. The basic results of this chapter may be formulated as follows. 

The basical theories, equipments, measurement practices, analysis procedures and many results obtained by gas adsorption have been reviewed in different publications. For macropores, mercury porosimetry has been frequently applied. Identification of intrinsic pores, the interlayer space between hexagonal carbon layers in the case of carbon materials, can be carried out by X-ray dififaction (XRD). Recently, direct observation of extrinsic pores on the surface of carbon materials has been reported using microscopy techniques coupled with image processing techniques, namely scarming tunneling microscopy (STM) and atomic force microscopy (AFM) and transmission electron microscopy (TEM) for micropores and mesopores, and scanning electron microscopy (SEM) and optical microscopy for macropores [1-3],... 

What is scanning tunneling microscopy How does it work 2. Summarize the history of the atomic idea. How was Dalton able to convince others to accept an idea that had been controversial for 2000 years 3. State and explain the law of conservation of mass. 4. State and explain the law of definite proportions. 5. State and explain the law of multiple proportions. How is the law of multiple proportions different from the law of definite proportions 6. What are the main ideas in Dalton s atomic theory How do they help explain the laws of conservation of mass, of constant composition, and of definite proportions 7. How and by whom was the electron discovered What basic properties of the electron were reported with its discovery 8. Explain MUlikan s oil drop experiment and how it led to the measurement of the electron s charge. Why is the magnitude of the charge of the electron so important 9. Describe the plum-pudding model of the atom. 

---