Topologic distortion

The basic perovskite structure ABX3 forms the prototype for a wide range of other structures related to it by combinations of topological distortions, substitution of the A, B and X ions, and intergrowth with other structure types. These compounds exhibit a range of magnetic, electrical, optical, and catalytic properties of potential application in solid state physics, chemistry, and materials science. 

The response of a topological distortion to experimental study would be of the dual wave-particle kind. It generates a local wave field in its immediate environment and this field constitutes the wave that appears to guide... 

The topological distortion across these polymer films can be described by modern percolation theory, and used to define the maximum in the sodium transport versus caustic concentration curve as an optimum restricted pore volume. 

One of the interesting predictions of the Su-Schrieffer-Heeger model [158, 159] is that the electronic excitations are closely related to the topological distortions of the conjugated polyene chain. It is predicted that solitons are the elementary excitations both for optical... 

Figure 5. (a) A wedge cut construction [39] to illustrate the topological nature of the distortion... 

Figure 8.21 shows functions of the distorted topologies that are not pointed at the origin, and j (0) < 1. The reason is that the presented model is not an ideal two-phase system, because it considers smooth transitions of the electron density between the crystalline and the amorphous layers. 

The Sn6P6 cluster 19c crystallizes in the triclinic space group PI. It forms a distorted hexagonal Sn6P6 prism with three-coordinated Sn and four-coordinated P atoms (Fig. 20) (39), that is, the structure is topologically identical with that of solvent-free 17 (see Fig. 18). 

To achieve non-zero 7ta—7tb conjugation, the pi NBOs of 18 may polarize in opposite directions, leading to a wavefunction of lower symmetry than the nuclear framework. Alternatively, the nuclear framework may distort to diamond-like D2h geometry. However, each such distortion destabilizes what is already a highly unfavorable Lewis-structure wavefunction, so cyclobutadiene is expected to remain highly destabilized relative to other possible polyene topologies. 

One way of getting rid of distortions and basis set dependence could be that one switches to the formalism developed by Bader [12] according to which the three-dimensional physical space can be partitioned into domains belonging to individual atoms (called atomic basins). In the definition of bond order and valence indices according to this scheme, the summation over atomic orbitals will be replaced by integration over atomic domains [13]. This topological scheme can be called physical space analysis. Table 22.3 shows some examples of bond order indices obtained with this method. Experience shows that the bond order indices obtained via Hilbert space and physical space analysis are reasonably close, and also that the basis set dependence is not removed by the physical space analysis. 

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