Electron localized-delocalized transition

For the elements highlighted by the diagonal strip there is an indication that the / and d electrons may be balanced between being localized and itinerant. According to Smith and Kmetko (1983), materials close to this localization-delocalization transition can have their properties modified appreciably by small... 

If the Fermi level is at an energy such that the electronic states are extended, then finite conductivity at zero temperature is expected. This model assumes that the substantial disorder is homogeneous through the isotropic three-dimensional sample. Other external parameters such as magnetic field or pressure can affect the localization/delocalization transition and the localization lengths. This model has received much experimental attention for doped and ion implanted polymers [2,49], although more recent studies of ion-implanted rigid rod and ladder polymers reveals a three-dimensional semimetallic conductor with weak localization effects [50]. 

The transition to the type I structure in NpAs is almost certainly an electronic one. On cooling into this phase the resistivity increases (Aldred et al. 1974) by a factor of almost 100. Further work is needed to determine whether it are the 5f electrons that are partially localizing at To, and thus causing a reduction in the resistivity. Certainly the materials with the 3k structure exhibit properties resembling localized systems. One of the normal criteria for a localized-delocalized transition is a volume change however, magnetoelastic effects often prevent a clear identification of a purely electronic transition. 

The results of the calculations include total energies, zero-pressure properties, pair distribution functions, electron densities, localization-delocalization transitions, and the metal-insulator transition. Table 6 compares a few of the results with those from other calculations and from experiments.These calculations clearly demonstrate the feasibility of QMC treatments for solid material for a range of densities. 

In a similar fashion the bonding in H2 might be formally regarded as a complementary pair of one-electron donor-acceptor interactions, one in the ot (spin up ) and the other in the 3 (spin down ) spin set.8 In the long-range diradical or spin-polarized portion of the potential-energy curve, the electrons of ot and (3 spin are localized on opposite atoms (say, at on HA and 3 on HB), in accordance with the asymptotic dissociation into neutral atoms. However as R diminishes, the ot electron begins to delocalize into the vacant lsB(a) spin-orbital on HB, while (3 simultaneously delocalizes into Isa on HA, until the ot and (3 occupancies on each atom become equalized near R = 1.4 A, as shown in Fig. 3.3. These one-electron delocalizations are formally very similar to the two-electron ( dative ) delocalizations discussed in Chapter 2, and they culminate as before (cf. Fig. 2.9) in an ionic-covalent transition to a completely delocalized two-center spin distribution at... 

Throughout we make use of the pseudogap model outlined in Chapter 1, Section 16- A valence and conduction band overlap, forming a pseudogap (Fig. 10.1). States in the gap can be Anderson-localized. A transition of pure Anderson type to a metallic state (i.e. without interaction terms) can occur when electron states become delocalized at EF. If the bands are of Hubbard type, the transition can be discontinuous (a Mott transition). 

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. 

The existence of polarizability thus renders impossible any unique scale of electrophilic reactivity. The two most common theoretical measures, namely ir-electron densities and localization energies, correspond to transition states approximating the ground state and the Wheland intermediate, respectively, whereas the transition state (the precise structure of which is unknown), lies somewhere in between, it Densities, which relate to a situation where inductive effects are dominant, will tend to predict a relatively low 2- 3-rate ratio since all of the heteroatoms are inductive acceptors (-/). By contrast, since it electrons are delocalized from the heteroatoms more to the 2- than to the 3-position, localization energies will predict a high 2- 3-rate ratio. The importance of these factors becomes particularly evident in consideration of the substitution of benzo derivatives of these molecules (Chapter 8). 

Analysis of the electron localization function for geometries of the same reaction path provides an alternative, but compatible, perspective on the evolution of electronic structure. The novel asynaptic basin of the DRA, which represents a pair of electrons that is delocalized over the periphery of the ammonium cation core, is transformed into a conventional, monosynaptic basin that is associated with the departing hydrogen at the geometries near the transition state. After the transition state, the NH system may be described as a hydride-ammonia complex. 

A proper description of electronic defects in terms of simple point defect chemistry is even more complicated as the d electrons of the transition metals and their compounds are intermediate between localized and delocalized behaviour. Recent analysis of the redox thermodynamics of Lao.8Sro,2Co03. based upon data from coulometric titration measurements supports itinerant behaviour of the electronic charge carriers in this compound [172]. The analysis was based on the partial molar enthalpy and entropy of the oxygen incorporation reaction, which can be evaluated from changes in emf with temperature at different oxygen (non-)stoichiometries. The experimental value of the partial molar entropy (free formation entropy) of oxygen incorporation, Asq, could be... 

Then, the 5/electrons in actinides appear less localized than the 4/electrons in rare earths. Moreover, their behaviour is different from that of d electrons in the transition metals. The 5/ electrons therefore constitute an intermediate group of electrons in order to understand their behaviour, it is thus necessary to take into account properties involving localized or delocalized electrons. 

The physicochemical properties of actinide metals confirm the presence of band-like 5f electrons up to Pu. The participation of these 5f electrons in the metallic bond is assumed to begin with Pa. In the first half of the actinide series, 5f electrons are similar to d electrons in typical transition metals the 5f electron orbitals are more extended than 4f orbitals for the light actinides, 5f electrons are "delocalized" and hybridized in a rather large band with 6d and/or 7s electrons. Starting with Am, the 5f electrons are localized again, like 4f electrons in the lanthanides. 

F. Fenske. We demonstrate for transition metal complexes that the non-empirical Fenske-Hall (FH) approach provides qualitative results that are quite similar to the more rigorous treatment given by density functional theory (DFT) and are quite different from Hartree-Fock-Roothaan (HFR) calculations which have no electron correlation. For example, the highest occupied molecular orbital of ferrocene is metal based for both DFT and FH while it is ligand (cyclopentadienyl) based for HFR. In the doublet (S = 1/2) cluster, Cp2Ni2(pi-S)2(MnCO)3, the unpaired electron is delocalized over the complex in agreement with the DFT and FH results, but localized on Mn in the HFR calculation. A brief description of the theory of FH calculations is used to rationalize the origin of its similarity to DFT. 

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