Crystal localized

We now investigate how the occurrence of localized states is governed by the values of the parameters z, z, and r/ which define the interaction between the foreign atom and the crystal. Localized states exist if either one or both of Equations (13) and (15) have real roots Real roots exist for given ri in regions of the zz -plane defined by the two hyperbolas... 

In Sects. 2.1 and 2.2 we have shown that the vibronic coupling produces a displacement of the nuclei into equivalent potential wells. Indeed this is quite exact for isolated molecules or for an isotropic environment (gas, solution), while in crystals local forces may stabilize one of various distortions. On the other hand a fully static picture is true... 

Apart from concentration dependance, sorption is strongly exothermic and desorption endothermic, so that sorption heats and desorption cools the crystals locally. Since Da = Do exp — E/RT, Da for sorption could exceed Da for desorption. 

Another example is a cubic crystal (local symmetry group Oh) with a twofold degenerate ground state, an Eg or E term, as in octahedral [Cu06] with Cu " at the center (Fig. 3). Its highest occupied orbital is Cg with components 6 = 3z — r ) and 8 = — y ) populated with three electrons or, in other terms, one hole. 

These molecule interaction schemes that exclude the intramolecular interactions have, however, to be distinguished from the atom interaction or relay-type models that originally were aimed at determining the molecular polarizabilities from the dipolar interactions between effective atomic polarizabilities and that require additional terms to account for the overlap between the atomic densities and for charge transfer effects [82]. Nevertheless, this approach was recently extended to describe both intra- and intermolecular interactions and, consequently, the corresponding atomic parameters could be used to evaluate the crystal local held factors [83],... 

CRYSTAL Local All-electron www.crystal.unito. it/index.php... 

In a crystal of identical chromophores, for example, a naphthalene crystal, local excitations may be transferred to other sites, just like electrons or holes. Excitation energy transfer (EET) is also called electron-hole pair transfer because the excited electron and remaining hole are transferred simultaneously to the other atom or molecule. Degeneracy appears in a finite system with two identical chromophores. In a repetitive system, the excitations may be delocalized, but this is not always the case. Devices for solar light harvesting, and natural antenna systems are examples of such repetitive systems. It is important to understand their properties. 

FIGURE 1.30 Shapes of liquid crystals (local molecular orientation [LMO]) with digitized contours model of series II kerogens (sporopollenin) (a) 002 dark-field image. Inset is a sketch of a LMO. (b) The same in 11 dark field. (From M. VUley. Simulation ther-mique de revolution des kerog nes. These d Etat Orleans 1979. With permission.)... 

Table 9.17. Centroids positions xu, X2i, isi), in a.u., and polarization fractions pi for functions Wi(r) in the SrZrOs crystal localized according to the Waimier-Boys mixed scheme [63]...

The use of localized orbitals for the cluster calculation is an efficient approach for defective crystals. To connect the perfect crystal localized orbitals and molecular cluster one-electron states the molecular cluster having the shape of a superceU was considered [699]. Such a cluster differs from the cyclic cluster by the absence of PBC introduction for the one-electron states. Evidently, the molecular cluster chosen is neutral and stoichiometric but its point symmetry can be lower than that of the cyclic cluster. Let the locaUzed orthogonal crystalline orbitals (Wannier functions) be defined for the infinite crystal composed of snpercells. The corresponding BZ is L-times reduced (the snpercell is supposed to consist of L primitive unit cells). The Wannier functions W r — Ai) are now introdnced for the supercells with the translation vectors and satisfy the following equation ... 

If information is converted to x,y coordinates and transmitted by scanning to a picture screen of cholesteric liquid crystals, localized heating can be obtained on the screen corresponding to the electronic information. When the points of localized heating have different heat content, a colored picture is formed. 

Evaporation-induced MOF growth combined with a precise control of the MOF precursor solution volume in a precise location offers a powerful tool to master single crystal localization with high spatial accuracy. This approach also offers the possibility of controlling MOF crystal formation by tuning the volume of the precm or solution. In the papers by Bellido et aP and Carbonell et al. examples of how to chemically functionalize the... 

Bittl, R., Zech, S.G., Fromme, R, Witt, H.T., and Lubitz, W., Rulsed ERR structure analysis of photosystem I single crystals localization of the phylloquinone acceptor. Biochemistry, 36, 9774, 1997. 

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