Localized pair

In a similar vein the in-phase combination of the 7r ,f3 localized pairs, which is CH antibonding but CC bonding, is possibly the lowest unoccupied orbital it lies very close to the [Pg.19]

Figure 4.3 The most probable arrangement of the electrons in the valence shell of fluorine in the HF molecule. Only one localized pair is formed with the other electrons equally distributed in a ring behind the... 

It is quite small for metals where the bonding is spread out over large numbers of atoms and it has intermediate values for ionic crystals where the overall bonding is delocalized, but local pairs of ions interact strongly. These relationships are discussed in some detail in later chapters. 

Heterocyclic ligands such as pyridine (py), V-methylimidazole (Meim), benzotriazole (btaH) and related molecules are good ligands due to the presence of at least one nitrogen ring atom with a localized pair of electrons. When this nitrogen bears a substituent, such as in pyrrole, the coordinating possibilities are reduced or absent. 

Figure 8. Pressure-Y diagram at 250 K for nonlocalized pair CHt-P and localized pair Kr-Q at a total pressure of 1000 torr. Component A is the first specie named.

In summary, in operation of adsorption systems involving a localized and non-localized pair, selection of best separability is dependent both on the Henry constant and on the type of site interaction. Higher Henry constant combined with a localized site favours the employment of high pressure systems conversely, higher Henry constant combined with a non-localized site favours low pressure systems. The choice of appropriate temperatures depends on whether the Henry constants diverge or converge as the temperature is altered. 

So, the localized pairs display themselves at the stage when they become decoupled and contribute to the conductance. The negative magnetoresistance serves as an indirect manifestation of the specific insulating state destroyed by the field. However, as the theory [9, 10] relates only to the vicinity of the SIT, the negative magnetoresistance happens beyond the range of its action. 

We have seen in this chapter how the total energy of a liquidlike ensemble of molecules can be calculated starting from COSMO calculations and taking into account deviations from the simple conductor-like electrostatic interactions as well as hydrogen bonding and vdW interactions as local pair-wise interactions of molecular surfaces. This is a very different way of quantifying the total energy than the ways usually used in all kinds of... 

Rather than deriving the general formulas related to Coleman s extreme configuration [107], we will derive the statistical coherent dissipative ensemble in a much more simple way, see also Ref. [95] for more details. To exemplify the generality of our formulation, we will thus consider M = N/2 bosons (or N fermions) described by set of n > N/2 localized pair functions or geminals h =. .. 1%, obtained from appropriate pairing of one-particle... 

By construction, Equation 6.65 is a global property built from local (pair-wise) contributions according to Equation 6.64. 

But octahedral if1 cations never form localized pairs, since the other empty ds orbitals are too close energetically. The cations are, therefore, only slightly displaced from the centre of the anion octahedra, and the cations in the central row obtain four close cation neighbours while the other cations only have two cation neighbours (see Fig. 9). The de levels of the cations, therefore, will form an incompletely filled band and give rise to... 

Further comparative calculations by both VB and MO methods on BeEfe have been reported, using a minimal STO basis, with exponents optimized for various r zsz With choice of particular VB configurations, it is shown that a model based on the resonance valence state, including ionic configurations, is particularly useful. Both methods show a localized-pair bond description to be useful. 

The connection between SC and an MIT (where the insulating state is due to localization) in the cuprates, as well as in other systems with a similar phase diagram, has been pointed out by Osofsky et al. [49], The conclusion from the present approach is that if a pairing interaction exists, and the insulating state is characterized by the existence of localized pairs at low temperatures, then an SC phase, based on the same pairing interaction, ought to exist around the MIT regime. 

To connect with the previous section, we start by employing a set of n localized pair functions h = (hi, h2,. ..hn) also called geminals, here obtained from appropriate pairings of the particle-antiparticle basis spin functions in Eq. (18). For future use, we incorporate the subsequent transformations... 

Exciton — A bound and thus localized pair of an - electron in the conduction band and a hole in the valence band. An exciton is an elementary excitation and quasiparticle in solids. See also Frenkel, defects in solids. Ref [i] Eliott SR (1998) The physics and chemistry of solids. Wiley, Chichester... 

In any case the spin-Peierls transition is driven by one-dimensional pre-transitional structural fluctuations [46]. Such fluctuations start to develop at some temperature TF above TsP. The effect of these critical fluctuations is to induce a local pairing of the spins which leads to an observable deviation of the magnetic susceptibility x below TF from the general Bon-... 

Properties of When Surplus Segments are Locally Paired... 

It is shown in this chapter that, while the Lewis model of the electron pair does not correspond to the existence of spatially localized pairs of electrons, it does find a more abstract but no less real physical expression in the topological properties of the Laplacian of the charge density, the quantity V p(r) as defined in eqn (2.3) (Bader and Ess6n 1984 Bader et al. 1984). The... 

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