Electron localization mechanisms

Perhaps the best guideline to use in designing high Tc materials is to look for electron localization mechanisms, as suggested by Sleight... 

Disorder and correlation are often both present in a system. One then has the more difficult task of ascertaining which is the dominant electron localizing mechanism. As might be expected, the most useful experimental approaches to this problem involve... 

Two mechanisms which contribute to GMR have been identified, a "non-local" mechanism and a "quantum" mechanism. To understand the first or non-local, mechanism it is necessary to understand that on the scale of the electron mean free path (possibly 10 to 20 nanometers at room temperature) electrical conduction is a non-local phenomenon. Electrons may be accelerated by an electric field in one region and contribute to the current in other regions. To a good approximation they may viewed as contributing to the current until they are scattered. 

Redress can be obtained by the electron localization function (ELF). It decomposes the electron density spatially into regions that correspond to the notion of electron pairs, and its results are compatible with the valence shell electron-pair repulsion theory. An electron has a certain electron density p, (x, y, z) at a site x, y, z this can be calculated with quantum mechanics. Take a small, spherical volume element AV around this site. The product nY(x, y, z) = p, (x, y, z)AV corresponds to the number of electrons in this volume element. For a given number of electrons the size of the sphere AV adapts itself to the electron density. For this given number of electrons one can calculate the probability w(x, y, z) of finding a second electron with the same spin within this very volume element. According to the Pauli principle this electron must belong to another electron pair. The electron localization function is defined with the aid of this probability ... 

In a pericyclic reaction, the electron density is spread among the bonds involved in the rearrangement (the reason for aromatic TSs). On the other hand, pseudopericyclic reactions are characterized by electron accumulations and depletions on different atoms. Hence, the electron distributions in the TSs are not uniform for the bonds involved in the rearrangement. Recently some of us [121,122] showed that since the electron localization function (ELF), which measures the excess of kinetic energy density due to the Pauli repulsion, accounts for the electron distribution, we could expect connected (delocalized) pictures of bonds in pericyclic reactions, while pseudopericyclic reactions would give rise to disconnected (localized) pictures. Thus, ELF proves to be a valuable tool to differentiate between both reaction mechanisms. 

The study of chemical reactions requires the definition of simple concepts associated with the properties ofthe system. Topological approaches of bonding, based on the analysis of the gradient field of well-defined local functions, evaluated from any quantum mechanical method are close to chemists intuition and experience and provide method-independent techniques [4-7]. In this work, we have used the concepts developed in the Bonding Evolution Theory [8] (BET, see Appendix B), applied to the Electron Localization Function (ELF, see Appendix A) [9]. This method has been applied successfully to proton transfer mechanism [10,11] as well as isomerization reaction [12]. The latter approach focuses on the evolution of chemical properties by assuming an isomorphism between chemical structures and the molecular graph defined in Appendix C. 

The most noticeable example is that concerning Ru(bipy)32 + ions in acetonitrile solutions at a Pt electrodes with the reaction mechanism formulated as following. In the electrochemical reactions, the parent ions Ru(bipy)32+ undergo70,71 one-electron reduction (with the added electron localized on individual ligand -orbitals) and oxidation (with removal of a metal t2g electron) followed by ion s annihilation with the formation of the excited 3 Ru(bipy)32 + state and subsequent emission of light. 

An X-ray photoelectron spectroscopic study of Ni(DPG)2I showed no evidence of trapped valence or any appreciable change in the charge on the metal upon oxidation.97 The site of partial oxidation and hence the electron transport mechanism is still unclear but one explanation of the relatively low conductivity is that the conduction pathway is metal centred and that the M—M distances are too long for effective orbital overlap. Electron transport could be via a phonon-assisted hopping mechanism or, in the Epstein—Conwell description, involve weakly localized electronic states, a band gap (2A) and an activated carrier concentration.101... 

Tachikawa (1999) also analyzed mobilities of carriers along the silicon chain, and his results should be mentioned separately. As it turned out, the mobility obtained for a positive charge (hole) was several times larger than that for an excess electron. This result suggests that the localization mechanism of a hole and that of an electron are different from each other. Probably, an excess electron is trapped in the defect of the main chain, whereas a hole is not trapped. The defects are mainly structural ones, such as branching points and oxidized sites (Seki et al. 1999). This can lead to a different electron conductivity. Continuation of the polysilane ion radical studies will hopefully result in some important technical applications. 

A theoretical study on the reaction mechanism for the Bergman cyclization from the perspective of the Electron Localization Function and Catastrophe Theory has been reported.175 The authors argue that topological analysis of electron localization function can be used to complement the molecular orbital- or valence bond-based methods. 

A subset of electron-hole radical pairs exhibits features of Spin Correlated Radical Pair (CRRP) electron spin polarization mechanism [101] which can be observed at somewhat longer times via light/field modulated (LFM) EPR measurements. This technique is only sensitive to the light dependent part of the EPR spectrum on the time scale of the light modulation frequency (millisecond regime, insert Fig. 1.15). Using LFM EPR it was observed that both the transitions of the holes localized on the surface modifier and electrons localized on the Ti02... 

Our simulations are based on well-established mixed quantum-classical methods in which the electron is described by a fully quantum-statistical mechanical approach whereas the solvent degrees of freedom are treated classically. Details of the method are described elsewhere [27,28], The extent of the electron localization in different supercritical environments can be conveniently probed by analyzing the behavior of the correlation length R(fih/2) of the electron, represented as polymer of pseudoparticles in the Feynman path integral representation of quantum mechanics. Using the simulation trajectories, R is computed from the mean squared displacement along the polymer path, R2(t - t ) = ( r(f) - r(t )l2), where r(t) represents the electron position at imaginary time t and 1/(3 is Boltzmann constant times the temperature. 

These two products can be explained by an elimination-addition mechanism, called the benzyne mechanism because of the unusual intermediate. Sodium amide (or sodium hydroxide in the Dow process) reacts as a base, abstracting a proton. The product is a carbanion with a negative charge and a nonbonding pair of electrons localized in the sp2 orbital that once formed the C—H bond. 

As described in the previous section, experiments on LEE induced desorption of H-, O- and OH- from physisorbed DNA films, made it possible to demonstrate that the DEA mechanism is involved in the bond breaking process responsible for SB. The abundant H yield was assigned to the dissociation of temporary anions formed by the capture of the incident electron by the deoxyribose and/or the bases, whereas O production arose from temporary electron localization on the phosphate group [47], However, the source of OH- could not be determined unambiguously, and Pan et al. suggested that reactive scattering of O- may be involved in the release of OH [47], To resolve this problem, Pan and Sanche [58] investigated ESD of anions from SAM films of DNA. Their measurements allowed both the mechanism and site of OH- production to be determined. 

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