Angular distortion

In order to study lattice relaxation effect by ASR we assume a simple model. As a first step we consider the terminal point approximation. Here the distortion of the lattice taken into account is the stretching or the contraction and angular distortion of the bond connecting two sites in a lattice and the effect of neighbouring site is neglected. As a result of such distortion the structure matrix takes the form ... 

Pure computational results indicate that it should be possible to observe bond fixation in angularly distorted benzenes. Structural studies, either experimental or high-level computational, show that simple cyclic annelations are ineffective at inducing such bond fixation. Computational investigations of arenes with bicyclic annelations predict that these systems will show the desired bond fixation, trisbi-cyclo[2.1.1]hexabenzene, is the favored structure. 

Effects other than angular distortions can lead to bond fixation. A simple model based on Hiickel aromatic theory accounts for a large number of such cases (e.g., starphenylene and triphenylene). Ideas that electronegative groups in the annelation are responsible for the bond fixation are shown to be inconsistent when tested against a significant sample of data. 

In the halides bridging anions lead to distorted CrXe octahedra sharing corners in which there are four short approximately equal Cr—X bonds and two long trans Cr—X bonds. There is also angular distortion of the octahedra. The fluoride has the tetragonal (distorted) rutile structure and the other halides chain-type structures. The mixed crystal (Mn, Cr)I2 is isotypic with monoclinic Crl2 (Table 34). 

As well as departure from octahedral symmetry of the tetragonal type discussed above, angular distortions in which M—L bond lengths are preserved unchanged present a fairly obvious case for the application of the AOM. An octahedron squashed or elongated in the C3 axis is an example. In the resultant D3d symmetry the -orbitals are split into three sets, one of symmetry alg and two of symmetry eg. In fact, the expressions for and (p = alg or eg) in terms of the angle of distortion are not simple and the existence of two sets of the same symmetry label creates complications. However, it is readily shown that it is a two-parameter problem in the AOM, eG and en, the same level as for LFT (see equation 9). In principle, the two energy separations available should allow the evaluation of both parameters. 

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