Electron fluctuations

Among the recently published works, the one which showed that the cyclic structures of water clusters open up to form a linear structure above a certain threshold electric field value a was a systematic ab initio study on the effect of electric field on structure, energetics, and transition states of trimer, tetramer, and pentamer water clusters (both cyclic and acyclic) [36], Considering c/.v-butadiene as a model system, the strength and the direction of a static electric field has been used to examine the delocalization energy, the probabilities of some local electronic structures, the behavior of electron pairs, and the electronic fluctuations [37]. Another recent work performed by Rai et al. focused on the studies using the DFT and its time-dependent counterpart of effects of uniform static electric field on aromatic and aliphatic hydrocarbons [38],... 

FIGURE 28.4 (See color insert following page 302.) Scheme of TS structures together with relative electron fluctuation magnitudes and ELF = 0.60 pictures for reactions A-D. 

While the T — 0 limit has been taken formally, it should be noted that the electronic fluctuation correlations at room temperature are essentially equivalent to those at T = 0 for normal, nondegenerate systems. (Thermal photons at room temperature are generally unable to excite electronic transitions )... 

In the related work of Kim and Hynes [50], Equations (3.107) and (3.112) have been designated, respectively, by the labels SC (self-consistent or mean field) and BO (where Born-Oppenheimer here refers to timescale separation of solvent and solute electrons). More general timescale analysis has also been reported [50,51], Equation (3.112) is similar in spirit to the so-called direct RF method (DRF) [54-56], The difference between the BO and SC results has been related to electronic fluctuations associated with dispersion interactions [55], Approximate means of separating the full solute electronic densities into an ET-active subspace and the remainder, treated, respectively, at the BO and SC levels, have also been explored [52],... 

Table 1. Hierarchy of coupled cluster methods for response calculations. The table summarizes to which order in the electron fluctuation potential ground state and single excitation energies and response functions are obtained correctly at a given level of the correlation treatment. The analysis is based on a Mpller-Plesset like partitioning of the Hamiltonian as H(t, e) = F+ U + V t, e), where U is the electron fluctuation potential [58, 59]...

Electrochemical dissolution of electrons (fluctuation of solvent is a source of traps)... 

The final property of methods which we will consider here is the limit of reliable measurement. This is the quantitative aspect of the common limit of detection—the smallest amount or concentration of a substance which provides a measurable response by a specified method. Although the limit of detection is a widely used term, particularly by advertisers of scientific instruments, it and related terms are not well defined, accepted, or understood. In fact, this characteristic, although intuitively simple, may not be a stable attribute of analytical methods, but more a function of external influences such as laboratory environment or electronic fluctuations. 

A considerable number of lanthanides show valence instabilities. Among them Sm, Eu, Tm and Yb are able to fluctuate between the trivalent and divalent electronic configurations, depending on the environmental conditions. On the tetravalent side, although Pr and Tb are suspected to have some hybridization of localized-conduction states, only Ce clearly shows such an effect. Some of its compounds are unique for the study of the electronic fluctuation between the trivalent and tetravalent configurations. The 4f electron hybridization is the origin of the Ce demagnetization, volume reduction, anomalous temperature dependence of the transport properties, and a number of other abnormal behaviours. 

If the ion is specifically adsorbed, the clear distinction between reduced and oxidized states is no longer possible as a consequence of the formation of bonding orbitals and the fast electron fluctuation between the metal surface and the adsorbed ion. The solvation shell cannot achieve a stable configuration for oxidized and reduced states of the adsorbed ion. Instead, an intermediate solvent distribution develops for a mean residence probability of an electron on the adsorbed ion. 

Fig. 48. Comparison of the different experimental methods probing the time-scale of phononic as well as electronic fluctuations (see text).

Another popular electronic measure of aromaticity is the fluctuation index (FLU) (2005JCP014109). It measures electron fluctuation differences with respect to an aromatic reference system by comparing the contiguous electron delocalization indices (1999JPCA304) along cychc structure. The FLU index is close to 0 in aromatic species and departs from this value in nonaromatic ones. The drawback in this case is similar to that for geometry-based indices, namely the dependence on the reference systems. 

Donatti and VoUet s group reported a complete structural evolution of their light sono-aerogels as a functirai of the heat treatment up to 1,100°C (Figure 20.19) [68]. These aerogels exhibit pronounced structural differences with those formerly described. They present a slope lailmass fractal, having neat pore-solid boundaries due to weak electronic fluctuations. 

The observation that silica facilitates reduction, while on aliunina reduction of Cr is more difficult, supports the idea of a support controlled redox behavior. Thus, the supports take actively part in the redox chemistry of Cr. This can be explained with the hardness-softness concepts, first introduced by Pearson the higher the Al-content of the support, the harder the support, the less polarizable or susceptible for electron fluctuations, tbe more difficult reduction [13,14]. 

This is a remarkable result. Whereas it has been suspected by many authors (see Grimely [62]) that a relation between bondstrength and local density of states at the Fermi level should exist, Eq. (25) states this relation with the modification that the grouporbital local of states should be used. Others [63] have derived related expressions, but ignored the (Ep) term. Falicov and Somorjai [64] propose to correlate catalytic activity with low-energy local electronic fluctuations in transition metals. 

---