The influence of symmetry

The influence of symmetry. It can be predicted that no C=C stretching vibration will appear in the infra-red from compounds with a trans double bond at a centre of symmetry. This arises from the fact that infra-red absorption takes place only when there is a change of dipole moment, and there is no appreciable change involved in the C=C stretching vibration of a trans symmetrical molecule. On the other hand, some change will occur in the dipole moment in the case of compounds with cis double bonds, whilst both types will be active in Raman spectra [47, 55]. The intensity of the C=C double bond in the infrarred would therefore be expected to diminish when it is moved from the end of a chain towards the centre and the molecule becomes more symmetrical. This affords a 

Numerous examples of this effect are known. Thus, ethylene and trans-dichloroethylene are both inactive in the infra-red in this 

Intensity studies on the C=C linkage will therefore yield some indication of the nature of the double bond involved, and in cases where this is known they can be used for the study of cis—trans isomerism. A typical example of the latter use is that of Bernstein and Fowling [15] in studies on cis- and trans-1 2-dichloro-l-propene and their deutero-derivatives. After separation of the two isomers they could be readily identified by the relatively high intensity of the C=C absorption at 1606 cm (D) and 1614 cm (H) in the c/s-compound, against the low intensity of the bands at 

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An illustrative example of the influence of symmetry on the number of vibrations is provided by the homologous series of cyclic sulfur allotropes S (n = 6-12). The IR absorptions for these ring systems are weak owing to the low polarity of S-S bonds. However, sulfur is a good Raman scatterer because S-S bonds are readily polarised. The various sulfur allotropes have different symmetries in addition to a different number of sulfur atoms and, consequently, each allotrope exhibits a characteristic Raman spectrum (Figure 3.8). ... 

Naphthazarin, Fig. 12 (I), and its mono-methyl and di-methyl derivatives, Fig. 12 (II), (III), (IV), are /3-dicarbonyls that have been used to study the influence of symmetry on tunnelling138). They have no option but to exist in the cis enol configurations. A great deal of work has been done on the naphthazarins because of their structural relationship to certain anti-cancer antibiotics139). Debate has turned on the nature of the hydrogen bonds - are they centred or non-centred ... 

Recently, interesting symmetry effects have been discovered in connection with the quantum kicked rotor (see, e.g., Dittrich and Smilansky (1991a,b), Bliimel and Smilansky (1992), Thaha et al. (1993), Thaha and Bliimel (1994)). The issue concerns the influence of symmetries and their destruction on the localization length of the quantum kicked rotor. Can these symmetry effects be observed in atomic and molecular physics We think that this issue is important and propose the search for the influence of symmetry on the localization length of dynamically localizing systems as an interesting and important topic for future research. Therefore, the purpose of this section is to sketch briefly the essence of these recent discoveries as an incentive for their application in atomic and molecular physics. 

The Influence of Symmetry on the Electronic Structure of the Photosynthetic Pigment-Protein Complexes from Purple Bacteria... 

The influence of symmetry is seen in the terephthalic 3 and isophthalic 4 series. The unsymmetrical ring placement in 4(i) and 4(ii) lowers by 25 K and 77 K compared with their counterparts 3(i) and 3(ii), respectively. 

Archer AJ (2005) Dynamical density fimctional theory phase separation in a cavity and the influence of symmetry. J Phys Condens Matter 17 3253-3258... 

These theorems on the influence of symmetry on general properties of potential energy hypersurfaces can be viewed as constraints inherent in the nuclear configuration space M, affecting all energy functions defined over M. In fact, M has more stmcture than a simple metric space, and M should never be considered without this additional structure. 

We shall briefly come back to the problem of the influence of symmetry effects in Ch. XVIII. 

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