Symmetry chiral point groups

As written, the CIDs (2.3) and (2.5) apply to Rayleigh scattering. The same expression can be used for Raman optical activity if the property tensors are replaced by corresponding vibrational Raman transition tensors. This enables us to deduce the basic symmetry requirements for natural vibrational ROA 15,5) the same components of aap and G p must span the irreducible representation of the particular normal coordinate of vibration. This can only happen in the chiral point groups C , Dn, O, T, I (which lack improper rotation elements) in which polar and axial tensors of the same rank, such as aaP and G (or e, /SAv6, ) have identical transformation properties. Thus, all the Raman-active vibrations in a chiral molecule should show Raman optical activity. 

Asymmetric. Lacking all symmetry elements (point group Ci). All asymmetric molecules are chiral. 

Symmetry operators Symmetry elements Point groups Character tables Vibrational modes in molecules Chiral molecules... 

Several sections of the diffraction space of a chiral SWCNT (40, 5) are reproduced in Fig. 11. In Fig. 11(a) the normal incidence pattern is shown note the 2mm symmetry. The sections = constant exhibit bright circles having radii corresponding to the maxima of the Bessel functions in Eq.(7). The absence of azimuthal dependence of the intensity is consistent with the point group symmetry of diffraction space, which reflects the symmetry of direct space i.e. the infinite chiral tube as well as the corresponding diffraction space exhibit a rotation axis of infinite multiplicity parallel to the tube axis. 

Noncentrosymmetric achiral crystals of monoclinic point symmetry m and of orthorhombic point symmetry mm2 are also appropriate for determination of the absolute configuration of chiral resolved additives. For the point group m, only the left or right halves of Schemes 13a are relevant. In such an arrangement,... 

The monoclinic point symmetry 2 comprises a twofold axis and applies to the commonly observed monoclinic chiral space groups P2X and C2. 

III. Factoring Chirality as Related to Symmetry Elements or Point Groups. 183... 

III. FACTORING CHIRALITY AS RELATED TO SYMMETRY ELEMENTS OR POINT GROUPS... 

Key words Point groups, space groups, molecular symmetry, buckminsterfullerene, Jahn-Teller effect, chirality, dissymmetry, molecular packing, quasicrystals... 

D3)-Trishomocubane (451) is a saturated pentacyclic cage compound who carbon skeleton is made up of fused five-membered rings. The mola ule, which is intrinsically chiral, possesses the rare point group symmetry and is consequently of interest as a test system for chiroptic theories. Whereas racemic 451 has been known for more than a decade the enantiomers have recently b x me available and... 

Draw the formulae of all possible isomers of difluorocyclobutane and determine their symmetry elements and point groups. Assume that the cyclobutane ring is planar. Indicate which isomers are chiral. Use the flow chart in the appendix to assist you. 

Deduce whether enniatin B (a compound with antiretroviral activity) is chiral and determine its symmetry point group. 

There are six isomers of difluorocyclobutane (see below). The vicinal di-substituted isomers B and C (both with a twofold proper axis of symmetry, symmetry point group C2) are chiral and are enantiomers of each other. The cis-configured compound D (with a plane of symmetry, symmetry point group Cs) is achiral and is a meso compound. The compounds A and F (both with two planes of symmetry and on the line of intersection of both planes a twofold axis of symmetry, symmetry point group C2V) and E (with a plane of symmetry, a twofold axis of symmetry perpendicular to it and a centre of symmetry, symmetry point group C21O are all achiral. These results can be verified from the flow chart given in the appendix. 

In order to ascertain which symmetry elements are present in raeso-tartaric acid, it is necessary to look at the various conformations of the molecule. The symmetrical highest energy conformer, i.e. the synperiplanar conformer (sp), has a plane of symmetry in which both enantiomorphic halves of the molecule are reflections of each other. No other symmetry elements are present in this conformation (point group Cs). In the ap conformation of raeso-tartaric acid the only symmetry element present is a centre of symmetry (disregarding the fact that the centre of symmetry is equivalent to any of the infinite number of S2 axes). The symmetry point group is therefore Cj. All other conformations, e.g. the +synclinal conformation (+sc) of raeso-tartaric acid shown below, are chiral and do not possess any symmetry elements and therefore belong to the point group C. ... 

The compound has two chirality centres and three pseudo chirality centres. There is however, only one (achiral) diastereomer of the compound shown in the question. The two isomers can be distinguished from one another solely on the relative position of the chlorine or bromine atoms which lie in a plane which also happens to be the plane of symmetry of the molecule (this is the only symmetry element present, therefore the symmetry point group is Cs). It is possible in this instance to specify the configuration unequivocally using the descriptors E and Z. However, in systematic nomenclature the complete configuration of all the stereogenic centres is specified. Thus the (so-called) Z isomer is (ls,3r,5 ,6r,7S)-l,6-dibromo-3,6-dichloroadamantane and the isomer is (ls,3r,5 ,6s,7S)-l,6-dibromo-3,6-dichloroadamantane, i.e. the two isomers can be distinguished simply by the descriptor used for position 6. 

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