Delocalized model

Equation (2.44) indicates that for the delocalized model, the transition dipole intensity ratio is related to 0 Bm. To obtain ()Bi Bm at various temperatures, we utilize Breton s data regarding the angles between the electronic transition moments of the four BChls and the normal axis of the membrane. The calculated %BlBm are listed in Table IV. 

By using Eq. (2.44) and applying QBib2 (Table IV) and the wave function coefficients of the delocalized model at various temperatures to calculate the... 

We calculate three models (1) the dimer model presented in this work (2) the dimer model employed by Scherer et al. and (3) the delocalized model. Table V lists the calculated results as a function of temperature. The anisotropy values for r(ei,e2) at 295 K are found to be quite different between the dimer and delocalized models. The difference is about 53%. Meanwhile, the differences at other temperatures are within about 13-14%. For r(e2,23), the differences are within 24-28%. Table Valso lists the angle between B and B2 in the special pair of R26.Phe-a RCs as a function of temperature. 

At least two possibilities for the structure of the MLCT state exist. It may be formulated as Ru(III)(bpy) (bpyr) +, which has maximum symmetry of C2, or the heretofore commonly presumed Ru(III) (bpy l ) which may have D3 symmetry. We shall refer to the former structure as the "localized" model of the excited state, and the latter as the "delocalized" model. The experimental details of this study are presented elsewhere (19). 

The electrostatically favored cation (Li) and anion (RE) arrangement implies the presence of two different E-, Si- and Li sorts, which has been established by solution and solid-state NMR spectroscopy. The electronic structures of the mixed-valent pnictides 10 and 11 have been simply described as electron-deficient clusters with delocalized framework electrons. Formally the latter consist of two low-valent anediyl moieties RE and eight andiides (RE)2- (E = P, As). The relatively large E-E distances of >4 A exclude the occurrence of localized E-E bonds. However, delocalization of the cluster valence electrons is achieved without Li-Li bonds via Li-mediated multiple bonding. Evidence for this has been seen in the NMR spectra (31P, 7Li, 29Si), which are in accordance with the electron delocalization model (see later discussion). 

The electron distribution in these molecules is best considered in terms of a delocalized model, but it is also convenient to consider the... 

Up to this time there has been no report of the experimental determination of the structure of the parent homotropenylium ion. The three simplest systems that have been studied are 18, 19 and the iron complex 20. Cations 18 and 19 each have an oxygen-containing electron-donor substituent and, as such, appear to have smaller induced ring currents than the parent ion. In fact 18 and 19 have almost identical chemical shift differences (A<5 = 3.10 ppm) between the two C(8) protons. In the case of 20, A<5 is very small and it was considered to be a non-cyclically delocalized model for the bicyclo[5.l.OJheptadienyl cation69. 

An obvious question is, when does one need symmetry correct orbitals The HaO example illustrates that the symmetry correct orbitals will usually extend over a larger region of the molecule than did the symmetry incorrect orbitals from which they were made. The symmetry correct model corresponds to a more highly delocalized picture of electron distribution. We believe that electrons are actually able to move over the whole molecule, and in this sense the delocalized symmetry correct pictures are probably more accurate than their localized counterparts. Nevertheless, for most purposes we are able to use the more easily obtained localized model. The reason the localized model works is illustrated in Figure 10.6. The interaction that produced the delocalized symmetry correct orbitals made one electron pair go down in energy and another go up by an approximately equal amount. Thus the total energy of all the electrons in the molecule is predicted to be about the same by the localized and by the more correct delocalized model. 

Fig. 4. The phosphazene ring (a) island delocalization model predicting nodes in TT-density at the phosphorus atoms (b) dynamic deformation density (at 0.1 eA 3) in the plane of the ring (c) theoretical deformation density (at 0.05 eA-3) of cyclic phosphazene was used as a model (reproduced with permission from Cameron et al. [43]).

Electrochemically, C70 behaves very similarly to C o- Six reduction waves are observed in toluene/acetonitrile, but unlike 50, all six waves can be detected at room temperature (see Fig. 3) [7]. Reduction potentials for C70 obtained under various conditions of solvent and temperature are presented in Table 3. In comparing the corresponding values shown in Tables 1 and 3 for the first and second reduction potentials of Cgo and C70 in acetonitrile/ toluene, one observes that they are nearly identical. However, from the trianion up to and including the hexanion, C70 becomes increasingly easier to reduce than Cgo- A charge separation delocalization model has been evoked to explain this phenomenon [10c]. A noteworthy observation is the fact that the reduction potentials of C70 also appear to be solvent and/or temperature dependent, although no specific studies on the subject have been published. 

The two MO approaches to polyatomic systems, localized and delocalized, are useful in different circumstances. When localized descriptions are possible, they correspond more closely to the simple chemical pictures of electron-pairbonds provided by the Lewis and VSEPR models. Such descriptions are not always possible, and 3c or other delocalized models provide an alternative to the resonance approach (see below and Topic Cl). Delocalized MO theory is also more useful for interpreting electronic spectra of molecules. 

This anomeric (n->CT ) interpretation, employing an electron-delocalization model, is the basis of the phosphorus app lone-pair hypothesis (PAPH). This hypothesis is completed by integration of two observations from the theoretical calculations discussed above (I) bond-weakening effects are calculated to be greater for apical than equatorial P—O bonds and (2) effects on conformational energy and electron distribution are amplified in pentacoordinate transition-state structures. 

The failure of n->o interactions and the electron-delocalization model to rationalize the reverse anomeric effect is argued by Sinnott (1988) to be the major flaw in this model. 

As mentioned in the Introduction (Sect. 1), an approach commonly used in recent years to handle transition metal complexes is the molecular orbital approach. To set the scene for development of a localized model, we will begin our discussion by first giving a general account of this molecular orbital approach (which represents the delocalized model ) based on the octahedral complexes. 

A final example concerns how the locahzed model can be used together with a delocalized model to give rise to the understanding of structures that are much more difficult to analyze. 

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