Versus Delocalized States

The high electrical conductivity of metals as well as the high electron (and hole) mobility of inorganic covalently boimd semiconductors have both been clarified by the band theory [19], which states that the discrete energy levels of individual atoms widen in the solid state into alternatively allowed and forbidden bands. 

The highest energy occupied allowed band of a metal, or conduction band, is only partially filled with electrons, up to the so-called Fermi level. Hence, electrons located close to this Fermi energy are easily excited to the unoccupied level of the band, where they behave as free electrons. In a semiconductor (like in an insulator), the highest occupied allowed band is totally filled, and called valence band (VB), whereas the conduction band (CB) corresponds to the lowest unoccupied allowed band, which is completely empty. The injection of electrons in the CB occurs either thermally (in an intrinsic semiconductor) or through doping (extrinsic semiconductor). Electrons in the conduction band of metals or semiconductors move in delocalized states, and their wave function can be approximated to that of a free electron, that is, a progressive plane wave 

In delocalized bands, the charge transport is limited by the scattering of the carriers by lattice vibrations (phonons). Therefore, an increase in the temperature, which induces an increase in the density of phonons, leads to a decrease in the mobility. 

In disordered materials such as amorphous silicon, the mobility is so low that it would correspond to a mean free path lower than the distance between atomic sites, which is not physically pertinent. In a classical paper, Anderson [20] has shown that disorder in a solid may result in a localization of the states, in which case the one-electron wave frmction takes an exponential form 

---

Voss, T., C. Bekeny, J. Gutowski et al. 2009. Localized versus delocalized states Photoluminescence from electrochemically synthesized ZnO nanowires. J. Appl. Phys. 106 054304. 

Stockman, M. I., Faleev, S. V., and Bergman, D. J. (2001). Localization versus delocalization of surface plasmons in nanosystems can one state have both characteristics Physical Review Letters 87 167401-167404. 

Lindenberg and Ratner have discussed the question of localized versus delocalized valency states by using a four-site model. In the simplest case, this is the system H2 H2, in which the two H-H distances can be varied to provide different values of the coupling parameter. The criteria for valence trapping, and rates of intramolecular electron transfer are discussed in terms of the model. ... 

DR. ALBERT HAIM (State University of New York at Stony Brook) Dr. Meyer considered plots of optical transition energy versus 1/D(optical) minus 1/D(static) for various types of systems, some of which were binuclear and clearly delocalized. If instead, one considers a ruthenium(II) pentaamine bound to N-methyl-4,4,-bipyridinium, is this in any way different from the bridging situation In some instances there was a similar dependence for both the mononuclear systems and the binuclear systems. But some of these mononuclear systems did not seem to behave similarly. Is there any connection between whether that simple linear relationship works or not and whether the system is localized or delocalized ... 

Transition state imbalance in the deprotonation of substituted 2-tetralones by hydroxide ions has been described. A Brpnsted plot of logA versus substrate pAfa is linear, with slope —a) of —0.60 0.01 but the negative deviation of the point for the 6-nitro derivative suggests that delocalization of charge lags behind proton transfer. ... 

For the ANI radical cation, an acidity constant pKa = 6.4 was obtained182 however, no experimental BDE of this ion has been reported. A linear correlation of the oxidation potentials of anilines versus the acidities of the corresponding radical cations was observed. Recent ab initio calculations198 derived a value of BDE(N+—H) = 418 10 kl mol-1 for the aniline radical cation, relative to the Ph—N—H+ cation in its singlet ground state. Removal of an electron reinforces the strength of the N—H bond, due to the electron delocalization. 

---