Transition localization—delocalization

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... 

The conclusions reached by Costentin and SavOant are in fact quite consistent with our own. The main difference is that, according to these authors, the notion of an imbalanced transition state should be placed within the context of charge localization-delocalization heavy-atom intramolecular reorganization rather than of synchronization (or lack thereof) between charge delocalization and proton transfer. ... 

Peak I (parallel polarized) originates from 7T-7T transitions between delocalized (d) levels. Its transition energy is blueshifted with respect to the experimental data due to solid state effects and geometric relaxation, neglected in the theoretical calculations discussed here [32,69]. Peak III originates from l —> d /d —> l (l localized) transitions and has a dominant polarization perpendicular to the chain axis, while peak IV results from l —> l excitations and is polarized parallel to the chain axis. 

Lindgren et al. studied the excited state and phosphorescence of platinum(II) acetylides (5.9) with the DFT/B3LYP method [103], The calculated UV/Vis absorption spectra revealed that the orientation of the phenyl rings relative to the P-Pt-P axis has a strong correlation with the intensity of the absorption band. The broken symmetry phenomenon was also confirmed in the lowest triplet excited state, which leads to a OC-Ph bond on one side and a C=C=C bond on the opposing side. Quadratic response calculations of spin-orbit coupling showed that the intensity of the phosphorescence of these complexes arises mainly from the a—>n type T- l) transitions localized at the OC-Pt-P fragment, but not from the delocalized 7t—type transitions. The quadratic response calculations also reproduced an increase of xR from PEj to PE2 (5.9), which was also determined experimentally. 

In this paper, we studied the glass transition and the localization-delocalization transition in a disparate-size hard-sphere mixture from a dynamical viewpoint. For Cl = 0.5, the existence of the delocalized phase of the small particles is confirmed by investigating the frequency-dependent diffusion constant. Near the glass transition, we found an additional quasi-elastic structure in " q,uj) and Di(u>) at small o), which suggests that the diffusion mechanism of the small particles would change from the liquid-like diffusion to a slow diffusion in a random potential. 

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]. 

Like in molecular quantum chemistry, the localized-delocalized antagonism is omnipresent in the theoretical literature on itinerant magnetism. On the one hand, the Hubbard model [292] and related theories for strongly correlated systems have been employed to study rare-earth and also transition metals. Since the latter do not have flat bands, extensions to the Hubbard theory are required [293-295] also, to make the model Hamiltonians (almost) exactly solvable, simplifications are introduced. On the other hand, density-functional theory is able to extract Stoner s parameters [296,297] for a self-consistent description of itinerant magnetism [298]. As has been illustrated before, the theoretical limits of the LDA became apparent from Fe phase stability problems (see Section 2.12.1) and were solved by using gradient corrections. The present status of DFT in the treatment of cooperative magnetism has also been reviewed [299]. 

The degeneration of multiplicities does not apply regarding the spin, but at the fact that there are two types of electromagnetic polarization (g = 2), given that the transition from the discrete statistics to the continuous one is done through the small space of the phases, quantum normalized in the sense of Heisenberg localization/ delocalization through the analytical transformation... 

Figure 15 (a) Phase diagram of a binary polymer blend N= 32) as obtained from Monte Carlo simulations of the bond fluctuation model. The upper curve shows the binodais in the infinite system the middle one corresponds to a thin film of thickness D=2.8/ e and symmetric boundary fields [wall = 0.16, both of which prefer species A (capillary condensation). The lower curve corresponds to a thin film with antisymmetric surfaces (interface localization/delocalization). The arrow marks the location of the wetting transition. Full circles mark critical points open circles/dashed line denotes the triple point, (b) Coexistence curves in the (T, A/y)-plane. Circles mark critical points, and the diamond indicates the location of the wetting transition temperature. It is indistinguishable from the temperature of the triple point. Adapted from Muller, M. Binder, K. Phys. Rev. 2001, 63, 021602. ... 

Figure 18 (a) Binodals of a symmetric, binary polymer blend confined into a film of thickness D= 2.6/ e as obtained by self-consistent field calculations. The strength of preference at one surface is kept constant. The surface interactions at the opposite surface vary, and the ratio of the surface interactions is indicated in the key. +1.0 corresponds to a strictly symmetric film, and -1.0 marks the interface localization-delocalization transition that occurs in an antisymmetric film. The dashed curve shows the location of the critical points. Filled circles mark critical points and open circles/dashed horizontal lines denote the three-phase coexistence (triple point) for - 0.735 and -1.0. The inset presents part of the phase boundary for antisymmetric boundaries, (b) Schematic temperature dependence for antisymmetric boundaries. The three profiles correspond to the situations (u), (m), and (I) in the inset of (a), (c) Coexistence curves in the// /-A/y plane. The ratio of surface interactions varies according to the key. The analogs of the prewetting lines for A//pw< 0 and ratios of the surface interactions, -0.735 and -1.0, are indistinguishable, because they are associated with the prewetting behavior of the surface with interaction, which attracts the A-component. Reproduced from Muller, M. Binder, K. Albano, E. V. Europhys. Lett. 2000, 50, 724-730, with authorization of http //epljournal.edpsciences.org/... 

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 volumetric and calorimetric results of Regnier et al. [46], giving the structure and density of the sohdified monolayers of Xe on exfoliated graphite at temperatures from 102.1 to IlOK, did not permit one to distinguish a localization-delocalization phase transition. Other interesting aspects are found by studying the melting curve to temperatures above 120 K [15]. 

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. 

For samples F and G, there is a strong peak at 1.5 eV, more pronounced in the lowest o-dc sample, G. When the peak at 1.5 eV is strong, the reflectance in the far-infrared is diminished. This indicates that there is a second localization-delocalization" transition from isolated polarons localized to one or two C6H4N repeat... 

Therefore, the entropy representation of the reaction mechanism reveals the whole complexity of this transformation, while the associated Minimum Energy Path (MEP) profile only localizes the transition state on PES, missing the crucial transitory localization/delocalization and relaxational phenomena involved in this two-step process. 

According to Mott s conception [47] the transition from delocalization to localization (e.g. metal-insulator transition, transition from isolated states within the band gap to impurity bands) occurs when the mean distance exceeds a certain critical value (oc ci/ ) — the distance of the effective Bohr s radius (more precisely 4 x Bohr s radius). The critical behaviour exhibits similarities to that treated in Section 5.7.2. 

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