Bond Distortion

We began this section with an inquiry into how to define the size of a polymer molecule. In addition to the molecular weight or the degree of polymerization, some linear dimension which characterizes the molecule could also be used for this purpose. For purposes of orientation, let us again consider a hydrocarbon molecule stretched out to its full length but without any bond distortion. There are several features to note about this situation ... 

Table 1 Hsts some of the physical properties of duoroboric acid. It is a strong acid in water, equal to most mineral acids in strength and has a p p o of —4.9 as compared to —4.3 for nitric acid (9). The duoroborate ion contains a neady tetrahedral boron atom with almost equidistant B—F bonds in the sohd state. Although lattice effects and hydrogen bonding distort the ion, the average B—F distance is 0.138 nm the F—B—F angles are neady the theoretical 109° (10,11). Raman spectra on molten, ie, Hquid NaBF agree with the symmetrical tetrahedral stmcture (12).

Fig. 17. Bond distortion energy of silicate structure in the absence and presence of water...

The anomalously reduced stabilities of certain nonalternant hydrocarbons and higher members of [4n+2] annulenes arise from their seemingly peculiar geometrical structures in which a strong bond distortion often accompanied by a molecular-symmetry reduction occurs. 

Remembering that the polarizabilities are expressed in units of it follows that the largest positive eigenvalue corresponds to the energetically most favorable second-order bond distortion, and the type... 

The second-order bond distortions predicted on the basis of the Huckel values are not in good agreement with those predicted using... 

The symmetries of the lowest excited states listed in Table 1 are nothing but the symmetries to which the most soft second-order bond distortions belong. It is seen that the types of symmetry reduction predicted using the symmetry rule are in complete agreement with those obtained on the basis of the dynamic theory. 

Table 1. The second-order bond distortion in the ground states of nonalternant hydrocarbons...

Using the same method as described in II.B, Binsch and Heil-bronner have examined the second-order bond distortion in the lowest excited states of nonalternant hydrocarbons (I, IV—VII, X, XI, XIII — XV and XVII), and have shown that, of the molecules examined, only VI and XVII suffer a molecular-symmetry reduction in the lowest... 

As the starting geometries for iterative calculation, we take all the possible structures in which bond lengths are distorted so that the set of displacement vectors may form a basis of an irreducible representation of the full symmetry group of a molecule. For example, with pentalene (I), there are 3, 2, 2 and 2 distinct bond distortions belonging respectively to a, b2 and representations of point group D21,. 

It is concluded that the magnetic susceptibility of a conjugated molecule is a very sensitive indicator of bond distortion and, in the... 

The results of our calculations based on both the static and dynamic theories show that most of the nonbenzenoid cyclic conjugated systems examined exhibit in a greater or lesser degree a marked double-bond fixation. The static theory indicates that even in benzene there exists a hidden tendency to distort into a skewed structure and that such a tendency is actually realized in [4n-f-2] annulenes larger than a certain critical size. In nonalternant hydrocarbons bond distortion is a rather common phenomenon. Fulvenes, fulvalenes and certain peri-condensed nonalternant hydrocarbons undergo a first-order bond distortion, and... 

The type of the most favorable second-order bond distortion is given by the eigenvector corresponding to the largest eigenvalue. 

The bond distortions that are required to transform the bound ground state substrate to its transition state structure and then to the product state structure(s) are commonly facilitated by introducing strain into the substrate molecule, through confor-... 

Figure 4.24 also shows that multiple bonds distort the bond angles in the same way as a lone... 

In order to make things a bit more concrete at this point we display in Figure 1 a sterically favorable configuration for a reactive ion pair (Tl). Only the 3d atomic orbitals most directly involved in the electron exchange are shown. The theoretical model developed here is based on a so-called "outer-sphere" mechanism, in which the inner-sphere reactants preserve their integrity in the course of the exchange reaction (aside from bond distortions associated with the activation step). The... 

The activated complexes have no bond distortion in either the olefin or the catalyst molecule provided that the catalyst is able to furnish the hydrogen and accept another at a distance of approximately... 

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