Delocalized electron states

The SHG/SFG technique is not restricted to interface spectroscopy of the delocalized electronic states of solids. It is also a powerful tool for spectroscopy of electronic transitions in molecules. Figure Bl.5.13 presents such an example for a monolayer of the R-enantiomer of the molecule 2,2 -dihydroxyl-l,l -binaphthyl, (R)-BN, at the air/water interface [ ]. The spectra reveal two-photon resonance features near wavelengths of 332 and 340 mu that are assigned to the two lowest exciton-split transitions in the naphtli-2-ol... 

The low BE region of XPS spectra (<20 — 30 eV) represents delocalized electronic states involved in bonding interactions [7]. Although UV radiation interacts more strongly (greater cross-section because of the similarity of its energy with the ionization threshold) with these states to produce photoelectrons, the valence band spectra measured by ultraviolet photoelectron spectroscopy (UPS) can be complicated to interpret [1], Moreover, there has always been the concern that valence band spectra obtained from UPS are not representative of the bulk solid because it is believed that low KE photoelectrons have a short IMFP compared to high KE photoelectrons and are therefore more surface-sensitive [1], Despite their weaker intensities, valence band spectra are often obtained by XPS instead of UPS because they provide... 

Figure 2-41 compares the electron level diagram of intrinsic semiconductors with that of hydrated redox particles at the standard concentration. The two diagrams resemble each other in that the Fermi level is located midway between the occupied level and the vacant level. It is, however, obvious that the occupied and vacant bands for semiconductors are the bands of delocalized electron states, whereas they are the fluctuation bands of localized electron states for hydrated redox particles. 

Over the past 10-15 years, several model systems that maintain the copper ion mixed-valence, delocalized electronic state with short Cu-Cu bond distances as in the CcO enzyme—Cu -Cu Cu -Cu =Cu Cu - —have been... 

The bonding combination of the Kekule structures is a delocalized electronic state and can be described by the resonating linear combination of the two structures, eq 1. 

The coexistence of the different types of minima can be a key to understand the nature of the transient X in the photocatalytic reaction. We can suppose that by initial photoexcitation the electron is transferred to a one-site localized electronic state. After some time the electron can relax to another minimum corresponding to more delocalized electronic state which may be considered as the transient X. Although the energy of delocalized minima is slightly higher, this transition can take place at room temperature. A more delocalized electronic distribution can increase the probability for decatungstate to go into reaction with a substrate. 

A. Kohler, D.A. dos Santos, D. Beljonne, Z. Shuai, J.L. Bredas, A.B. Holmes, A. Kraus, K. Mullen, and R.H. Friend, Charge separation in localized and delocalized electronic states in polymeric semiconductors. Nature, 392, 903-906 (1998). 

FIGURE 12. The two paths an electron can take in transferring between two localized sites A and B in a protein structure. Route 1 is achieved by tunneling through the intermediate medium, while route 2 involves activation into extended and delocalized electronic states of the protein structure. 

The packing density of the constituent atoms in the interior regions of protein molecules is, on average, equivalent to that of most organic compounds in the crystalline state. As such, it is possible to consider that membrane proteins may exhibit some of the solid-state electronic properties which have been extensively studied in elemental amorphous materials and organic polymers. Such properties include electronic conduction via localized and delocalized electronic states. When localized states are... 

The high electronic conductivity of the 7c-conjugated polymers (e.g. polypyrrole, polyacetylene) determined by the presence of delocalized electronic states, puts those polymers into the category of synthetic metals. The lower electronic conductivity of the redox and ion-exchange polymers, compared with the 7r-conjugated polymers, is due to the presence of localized electronic states. The redox polymers, which contain redox electroactive centres, conduct current by electron self-exchange... 

The conditions for validity of the NFE model break down for conductivity values near the loffe-Regel limit, that is, o-(O) 07. As discussed in Sec. 2.3.2, electronic transport in this situation is best described as diffusion of electrons from atom to atom, even though the system is stiD metallic with delocalized electron states. In this connection, it is interesting that near the range where cr(0) 07, the temperature coefiScient d n.(r(Q)/d nT)y is clearly positive (Freyland, 1981 Freyland et al., 1974). 

Electroabsorption and electroreflectance have provided a sensitive and selective tool to study delocalized electron states in semiconductors (1). Singularities of the band structure, like band extrema respond particularly sensitive to electric fields and the corresponding optical transitions are clearly resolved even in case of low oscillator strength. In case of localized states, however, the external fields in the range of 10 kV/cm cannot compete with the much larger local fields and the field induced perturbation of optical transitions becomes unresolvable. This limitation qualifies electromodu-lated spectroscopy as a selective tool to study delocalized states in organic crystals. 

On the contrary, the optical spectra for the metallic regime indicate delocalized electronic states near Ef, as already explained in the previous section. Thus, on the metallic side of the M-I transition, PPy-PFg is a disordered metal and can be described well by the LMD model [1162], while, on the insulating side, PPy-PF5 is characterized as a Fermi glass, which is attributed to disorder in the context of Anderson IcKaliza-tion. 

The optical spectra of structurally improved materials are compared with those obtained from conventionally prepared materials. While the structurally improved materials show distinct metallic signatures indicative of delocalized electronic states at the Fermi level, the optical spectra of the conventional samples indicate that the states near the Fermi level are localized due to severe disorder in the context of Anderson localization. Thus, conventional samples can be characterized as a Fermi glass. In this case, the two categories of samples show different charge dynamics in the far-infrared consistent with theoretical predictions. 

The outer-shell electrons of transition metals are separated into two bands. The filling of the narrow d-band corresponds to the occupation of the t/-shell, whereas a broad 5j 7-band is produced by the valence electrons of the free atom, rf-states are comparatively non-dispersive, the electrons being rather localized, whereas 5/ -states are more free-electron like. In real space this means that whereas rf-electrons to a large proportion reside around a certain atomic core or within a certain Wigner-Seitz cell sp-electrons penetrate the entire bulk [5]. Hence a comprehensive theoretical model of a metal surface has to account for delocalized electron states as well as for the discrete atomic character of the adsorbent. 

In a metal the conductivity remains finite as the temperature approaches 0. This is due to the fact that there are delocalized electronic states at the Fermi... 

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