Bond-State Models

Barzoukas and Blanchard-Desce proposed an approach of molecular engineering using multivalence-bond state models [55]. Push-pull polyenes were shown also to present an enhancement of the TPA response and a loss of transparency of molecules, as a function of the increase of the polyenic chain length [56,57]. Trends observed in these polyenic systems are supported by the large third-order optical nonlinearities measured in asymmetric carotenoids, in which the role of the large value of dipole moment difference A/z was shown [58]. 

FIG. 9 Typical ground states for a simple glass forming bond fluctuation model [42,47],... 

The transition-state model is generally somewhat more accurate than the collision model (at least with p = 1). Another advantage is that it explains why the activation energy is ordinarily much smaller than the bond enthalpies in the reactant molecules. Consider, for example, the reaction... 

The Coleman-Fox two state model describes the situation where there is restricted rotation about the bond to the preceding unit (Scheme 4.3). If this is slow with respect to the rate of addition, then at least two conformations of the propagating radical need to be considered each of which may react independently with monomer. The rale constants associated with the conformational equilibrium and two values of Pirn) are required to characterize the process. 

Interestingly, 8-aminoxy acids which are homologs of y-amino acids have also been found to promote the formation of turns and helices. In apolar solvent and in the solid state, model diamides consisting of /9 -aminoxy add residues adopt a novel N-O turn stabilized by both a nine-membered H-bonded ring between C=0 and NHj+2, and a six-membered ring formed between N-O and NH +1. The X-ray crystal structure of a corresponding triamide revealed two consecutive C9 N-O turns suggesting a novel 1.79-helical fold [279]. 

In this section, the state of the art of the lattice description of real polymers in terms of the bond fluctuation model augmented with bond length and bond angle potentials has been discussed. It has been shown that the approach has both merits and weaknesses. 

The X-ray structure of the dibromine complex with toluene (measured at 123 K) is more complicated, and shows multiple crystallographically independent donor/acceptor moieties [68]. Most important, however, is the fact that in all cases the acceptor shows an over-the-rim location that is similar to that in the benzene complex. In both systems, the acceptor is shifted by 1.4 A from the main symmetry axis, the shortest Br C distances of 3.1 A being significantly less than the sum of the van der Waals radii of 3.55 A [20]. Furthermore, the calculated hapticity in the benzene/Br2 complex (x] = 1.52) is midway between the over-atom (rj = 1.0) and over-bond (rj = 2.0) coordination. In the toluene complex, the latter varies from rj = 1.70 to 1.86 (in four non-equivalent coordination modes) and thus lies closer to the over-bond coordination model. Moreover, the over-bond bromine is remarkably shifted toward the ortho- and para-carbons that correspond to the positions of highest electron density (and lead to the transition states for electrophilic aromatic bromination [12]). Such an experimental location of bromine is in good agreement with the results of high level theoretical... 

V. S. Urusov, I. P. Orlov, State-of-the-art and perspectives of the bond-valence model in inorganic chemistry. Crystallogr. Rep. 44 (1999) 686. 

Typical Ni—L bond lengths have been extracted from the Cambridge Structure Database (CSD) and listed in tabular form.321 Also, Ni11—L bond lengths from the CSD have been analyzed by the BDBO technique, which is related to the bond valence model (BVM) where the total bond order is equal to the oxidation state of any atom.322 Selected mean Ni—L distances from the CSD source are collected in Table 2. 

Fig. 17 Plot of the calculated secondary deuterium KIE versus the extent of O—H bond formation for the model elimination reaction at 45°C Models 1 and 2 have different imaginary frequencies and no coupling of the Ca—D bending vibrational motion with the C0—H stretching motion in the transition state. Models 3,4 and 5 have increasing extents of coupling between the Ca—D bending and C —H stretching motion in the transition state. Reproduced, with permission, from Saunders (1997).

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