Quantum mechanical tunneling process

In impure metals, dislocation motion ocures in a stick-slip mode. Between impurities (or other point defects) slip occurs, that is, fast motion limited only by viscous drag. At impurities, which are usually bound internally and to the surrounding matrix by covalent bonds, dislocations get stuck. At low temperatures, they can only become freed by a quantum mechanical tunneling process driven by stress. Thus this part of the process is mechanically, not thermally, driven. The description of the tunneling rate has the form of Equation (4.3). Overall, the motion has two parts the viscous part and the tunneling part. 

In all these calculations it was found that although the activation energy seems to be rather low, which might support the occurrence of classical over barrier reactions, the actual process is, however, a pure quantum mechanical tunneling process. 

This chapter presents some effects symmetry has on the rates and mechanisms of chemical reactions. The reaction kinetics of low mass groups like dihydrogen or dideuterium, in particular at low temperatures, is strongly influenced by quantum mechanical tunneling processes and the Fermi postulate of the symmetry of the... 

When the ion-state concentrations determined by Eigen et al. (1964) are combined with measured static conductivities, the mobility of the positive ion state is found to have the anomalously large value of 0-075 cm s. Such a high mobility can only be the result of some sort of quantum-mechanical tunnelling process, as we shall see later. For such a process i/ o so that, from... 

As the theoretical treatment of reactions involving hydrogen needs to take the quantum mechanical nature of the light hydrogen atom into account, the implications of quantum-mechanical tunneling processes through the activation barrier will be covered first. 

A model which takes into account the spin-rotation interaction has been found to satisfactorily explain the 0 rotation band of PHg. The millimetre-wave spectra of HCP and DCP have been compared with those of HCN and DCN. A method of estimating frequencies of bands in this region due to processes such as pseudorotation has been suggested. This new approach involves calculation of the rovibronic energy levels from the effects of quantum-mechanical tunnelling. ... 

A number of chemical phenomena cannot be explained by any mechanism other than quantum-mechanical tunnelling. The more obvious of these include electrochemical processes that depend on the transfer of electrons across electrode surfaces, and solid-state rearrangements that involve the rotation of bulky moeities in sterically restricted space. Neither of these phenomena has been studied in quantitative detail. 

These predictions can provide an experimental test of the mechanism for quantum-mechanical tunneling effects on electron transfer processes in solution and in glasses over a wide temperature range. 

Our data show that in all hybrids, the thermal electron transfer process (Eq (2)) is remarkably insensitive to temperature, suggesting that ET proceeds by quantum mechanical tunnelling to quite high temperatures. Figure 8 shows the temperature dependence of k, the rate constant for the thermal Fe (CN )P-> (MP) electron transfer for M = Mg and Zn. For [(ZnP), Fe (CN )P], kb decreases by less than a factor of three from 300 K to 100 K ... 

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. 

Electron-transfer proteins have a mechanism that is quite different from the conduction of electrons through a metal electrode or wire. Whereas the metal uses a continuous conduction band for transferring electrons to the centre of catalysis, proteins employ a series of discrete electron-transferring centres, separated by distances of I.0-I.5nm. It has been shown that electrons can transfer rapidly over such distances from one centre to another, within proteins (Page et al. 1999). This is sometimes described as quantum-mechanical tunnelling, a process that depends on the overlap of wave functions for the two centres. Because electrons can tunnel out of proteins over these distances, a fairly thick insulating layer of protein is required, to prevent unwanted reduction of other cellular components. This is apparently the reason that the active sites of the hydrogenases are hidden away from the surface. 

Devault (1984) Quantum Mechanical Tunneling in Biological Processes, 2nd ed., Cambridge University Press, Cambridge. 

A key point that must be made is diat quantum mechanical tunneling through the Marcus-theory barrier when it is non-zero can increase the rate for electron transfer just as is true for any other activated process. Because the electron is so light a particle, tunneling can be a major contributor to die overall rate. Models for electron tunneling will not, however, be presented here. 

Totally deuterated aromatic hydrocarbons yield measured phosphorescence lifetimes greater than their protonated analogs.182 This behavior is ascribed to the closer spacing of vibrational levels in deuterated compounds with a consequent decrease in probability for nonradiative T -> S0 transitions. Quantum mechanical tunnelling may also contribute to the rate of the radiationless process with the normal compounds. 

Duke, CB, Concepts in Quantum Mechanical Tunneling in Systems of Electrochemical Interest, to be published in the proceedings of the Third Symposium on Electrode Processes, Boston, MA, May 1979, The Electrochemical Society, Princeton, NJ. 

This process takes place within the very thin interfacial region at the electrode surface, and involves quantum-mechanical tunneling of electrons between the electrode and the electroactive species. The work required to displace the H20 molecules in the hydration spheres of the ions constitutes part of the activation energy of the process. 

The reaction occurs at the surface of the electrode (Fig ). The electroactive ion diffuses to the electrode surface and adsorbs (attaches) to it by van der Waals and cou-lombic forces. In doing so, the waters of hydration that are normally attached to any ionic species must be displaced. This process is always endothermic, sometimes to such an extent that only a small fraction of the ions be able to contact the surface closely enough to undergo electron transfer, and the reaction will be slow. The actual electron-transfer occurs by quantum-mechanical tunnelling. 

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