Symmetry perception

Ouyang, Z., Yuan, S., Brandt, J. and Zheng, C. (1999). An Effective Topological Symmetry Perception and Unique Numbering Algorithm. JChem.Inf.Comput.ScL, 39,299-303. 

The first requirement for development of CSDSymmetry is a robust and automated method for analysing exact and approximate molecular symmetry. The specific methodology that has been employed is a combination of checks for topological equivalence in the 2-D connectivity diagram followed by full 3-D symmetry perception [29]. The first part of the process is based on the fact that atoms related by symmetry within a molecule must have identical chemical environments - that is, symmetry-related atoms... 

Wagemans J. Detection of visual symmetries. In Human symmetry perception and its computational analysis 1996. p. 25—48. 

In addition to macrocycle design, symmetry analysis would also be useful for chain analysis, both to choose chain members and to place zigzags. Symmetry analysis should also be consulted for molecular rotation (see prior section on Making Rings and Chains Horizontal or Symmetrical). Geometrical symmetry perception, though nebulous as described here, probably constitutes the greatest unexploited tool in SDG. 

Quantitative structure-activity relationships are used to model the biological effect of a set of compounds and to propose new structures with optimized biological activity (see Quantitative StructureActivity Relationships in Drug Design). Such a system makes extensive use of structure generation, substructure search, and symmetry perception algorithms. 

The problem of canonical coding, graph isomorphism, and graph automorphism has both mathematical and chemical significance. The mathematical formulation of the problem is briefly set out below, and some cormections with the chemical counterpart are presented. In the subsequent sections, the main algorithms used in chemistry for canonical coding of molecular graphs and constitutional symmetry perception are presented and compared. 

The distance between the two terminal carbon atoms at the TS (central point on the IRC segment) is already 2.291 A, which results in very perceptible changes in the orbital shapes, spin-coupling pattern and overlaps between neighbouring orbitals. Orbital /i (see the central column of orbitals in Fig. 5) becomes less distorted towards the orbital at the other terminal carbon, /g, and this is reflected in a decrease in their overlap (see Fig. 7). Orbitals /2 and /3 (and their symmetry-related counterparts, /5 and /4) attain shapes which are very similar to those of /2 from the TS of the Diels-Alder reaction (see the central column of orbitals in Fig. 1) and of a SC orbital for benzene [8-10]. These changes are accompanied by a tendency towards equalization of the nearest-... 

A Jahn-Teller distortion should also occur for configuration d. However, in this case the occupied orbital is a t g orbital, for example d, this exerts a repulsion on the ligands on the axes x and y which is only slightly larger than the force exerted along the z axis. The distorting force is usually not sufficient to produce a perceptible effect. Ions like TiF or MoClg show no detectable deviation from octahedral symmetry. 

The SMA effect can be traced to properties of two crystalline phases, called martensite and austenite, that undergo facile solid-solid phase transition at temperature Tm (dependent on P and x). The low-temperature martensite form is of body-centered cubic crystalline symmetry, soft and easily deformable, whereas the high-temperature austenite form is of face-centered cubic symmetry, hard and immalleable. Despite their dissimilar mechanical properties, the two crystalline forms are of nearly equal density, so that passage from austenite to a twinned form of martensite occurs without perceptible change of shape or size in the macroscopic object. 

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