Delocalized states

A major discrepancy that remains unresolved in the excited-state properties of the [Fe384]° cluster in D. gigas Fdll concerns the existence of a low-lying, fully valence-delocalized state that becomes populated at temperatures above 25 K. 8uch a state is clearly apparent in the temperature-dependent Mossbauer studies of reduced D. gigas Fdll (29) and P. furiosus 3Fe Fd (198) and is represented by one quad-rupole doublet with AEq 0.9 mm/s and S = 0.45 mm/s. 8uch a... 

Solid mixed ionic-electronic conductors (MIECs) exhibit both ionic and electronic (electron-hole) conductivity. Naturally, in any material there are in principle nonzero electronic and ionic conductivities (a i, a,). It is customary to limit the use of the term MIEC to those materials in which a, and 0, 1 do not differ by more than two orders of magnitude. It is also customary to use the term MIEC if a, and Ogi are not too low (o, a i 10 S/cm). Obviously, there are no strict rules. There are processes where the minority carriers play an important role despite the fact that 0,70 1 exceeds those limits and a, aj,i< 10 S/cm. In MIECs, ion transport normally occurs via interstitial sites or by hopping into a vacant site or a more complex combination based on interstitial and vacant sites, and electronic (electron/hole) conductivity occurs via delocalized states in the conduction/valence band or via localized states by a thermally assisted hopping mechanism. With respect to their properties, MIECs have found wide applications in solid oxide fuel cells, batteries, smart windows, selective membranes, sensors, catalysis, and so on. 

In electron transfer reactions one studies the conversion of an electron state localized on A to one localized on B. One can also consider the relaxation of a charge localized state to the adiabatic delocalized state [366],... 

Returning to (1.26), with f3a 0(rj / 0), we see that it has at least (N — 1) real roots, whose corresponding wave functions are delocalized and have reduced energies in the bulk band (1.18) of width AXk = 2. The remaining two roots may both be real, so that they too lie in the band, and the system supports only delocalized states. If, however, one or both of the remaining roots have 14-values of the form (1.31), then a new situation arises, which requires further analysis. Inserting (1.31) in (1.18) gives... 

In (2.43), p must be small, because a cyclic crystal supports only delocalized states, so the poles at X / X° are located close to the unit-circle contour. This observation is connected with the notion of complex energy ( 3.2), since, for p small, (2.43) in (1.18) ... 

A major technological innovation that opens up the possibility of novel experiments is the availability of reliable solid state (e.g., TiSapphire) lasers which provide ultra short pulses over much of the spectral range which is of chemical interest. [6] This brings about the practical possibility of exciting molecules in a time interval which is short compared to a vibrational period. The result is the creation of an electronically excited molecule where the nuclei are confined to the, typically quite localized, Franck-Condon region. Such a state is non-stationary and will evolve in time. This is unlike the more familiar continuous-wave (cw) excitation, which creates a stationary but delocalized state. The time evolution of a state prepared by ultra fast excitation can be experimentally demonstrated, [5,7,16] and Fig. 12.2 shows the prin-... 

These two types of exciton are schematically illustrated in Figure 4.13. The Mott-Wannier excitons have a large radius in comparison to the interatomic distances (Figure 4.13(a)) and so they correspond to delocalized states. These excitons can move freely throughout the crystal. On the other hand, the Frenkel excitons are localized in the vicinity of an atomic site, and have a much smaller radius than the Mott-Wannier excitons. We will now describe the main characteristics of these two types of exciton separately. 

One striking result [64] involves making a small change in regularity when one GC pair in a strand is simply inverted to CG, the local defect CG pair drops 0.6 eV below its previous position—that drop is 15 times the calculated bandwidth. This electrostatic stabilization means that the defect level is far from the conducting delocalized states, and corresponds to Anderson-type localization. With Anderson locahzation of this depth, the conductance is expected to decay exponentially. Indeed, exponential decay of conductance has been discussed in a number of measurements both on A-DNA and on poly(GC) sequences [65-67]. 

All the above-considered photoelectrochemical phenomena are based on the transition of light-excited electrons into a localized state in the solution, namely at the energy levels associated with individual ions or molecules. However, the phototransition is also possible when the electrons pass into a qualitatively different delocalized state in the solution it is this type of phototransition that represents photoemission (Barker et al, 1966). The emitted delocalized electron in the solution is then thermalized and localized to form a solvated (hydrated in aqueous solution) electron. The energy level, which corresponds to the solvated electron, lies below the bottom of the band of permitted delocalized states in the solution. Finally, the electron may pass from the solvated state to an even lower local energy level associated with an electron acceptor in the solution (see Fig. 30). 

Fig. 30. Diagram of transitions related to photoemission into solution 1—photoexcitation of an electron and photoemission, 2—thermalization of the photoemitted electron in the solution, 3—solvation of the thermalized electron, and 4—trapping of the solvated electron by acceptor A in the solution. de)oc is the lower edge of the band of delocalized states in the solution, solv is the energy level of the solvated electron, and EA is the acceptor energy level.

In chelate and macrocyclic complexes, electronic states may exist which are of a delocalized nature they pertain to the system of metal and ligands. Such states are not simply derived from metal d—d states or from free ligand states and transitions involving delocalized states are often quite intense. 

Other noteworthy achievements of solid-state 13C CP/MAS NMR in the context of carbonium ions are that (1) the sec-butylcarbonium ion can be identified at low temperatures in a sec-butyl chloride/antimony pentafluoride matrix in the temperature range 80-190 K (2) the norbornyl carbonium ion has been characterized (356,396) at temperatures down to 5 K, there being a strong (but not yet incontrovertible) indication that the controversial non-classical ion (398) exists and (3) the homotropylium ion is best represented (399) by the completely delocalized (homoaromatic) seven-membered state (a below) rather than the incompletely delocalized state (b). 

What are the conditions which lead to the localization of an excess electron in a liquid The nature of the transition between localized and delocalized states—i.e., the dependence on the fluid density, temperature, and pressure—in a system where the interactions between excess electrons are negligible is of obvious interest. 

What is the nature of the transition to the metallic state in a liquid containing a high density of excess electrons When the concentration of excess electrons in a liquid is gradually increased, a transition from behavior characteristic of a localized state to that characteristic of a delocalized state is observed—e.g., in concentrated metal-ammonia solutions and in metal-molten salt mixtures. 

The study of electron-solvent interactions in nonpolar monoatomic liquids (e.g., liquid rare gases) provides valuable information concerning the short range interactions between an excess electron and the solvent molecules. These studies provide an interesting model for electron localization arising from short range repulsions, as for liquid helium, and lead to a deeper understanding of the transition between the localized and delocalized states of an excess electron in simple fluids. 

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