Chirality point groups

The examples 6a and 6b are added as a test of spatial vision one is achiral (point group. S ), one is chiral (point group D2). This problem is best solved (6a ), 6b S4) by projecting the models on a plane through the spiro-carbon and perpendicularly arranged to the obvious two-fold axis. 

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. 

In addition to the most abundant fullerene, namely [60]fullerene, a number of higher fullerenes have also been isolated and characterized, including [70] (point group D . ), chiral [76] (point group Dj), the D and Cj isomers... 

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. 

All have pyramidal molecules (Cj point group for OSX2), and OSFCl is chiral though stereochemically labile. Dimensions are in Table 15.14 the short O-S distance is notable. The unstable compound OSI2 was mentioned on p. 692. 

What are the point groups of the complexes shown in Fig. 9.8 and why are they chiral ... 

Molecules that belong to Cn or Dn point groups are also chiral. For instance, tra i-2,5-dimethylpyrrolidine (Fig. 1-9), containing a twofold rotation axis, belongs to the point group C2 and is chiral.5 7... 

An introduction to point groups containing chiral molecules can be found in any of the leading text books. For example, in Eliel, E. L Wilen, S. H. Mander, L. N. Stereochemistry of Organic Compounds, John Wiley Sons, Inc., New York, 1994. 

From the chemical point of view, in diasteieoselective syntheses, several kinds of reactions like hydrogenation [273,277-286], hydrogenolysis [287-293], isomerization [294], and epoxidation [295-300] are involved. Hydrogenation is the most important application of heterogeneous catalysis because of its potential to produce a wide variety of chiral functional groups. 

It is evident that methods analogous to the ones developed here could be applied to molecular properties which, instead of being pseudoscalar, belong to some other representation of the skeleton point group (vector, tensor, etc. properties). To treat such properties, one needs only to induce from a different representation of than the chiral one. 

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,... 

In the orthorhombic point group mm2 there is an ambiguity in the sense of the polar axis c. Conventional X-ray diffraction does not allow one to differentiate, with respect to a chosen coordinate system, between the mm2 structures of Schemes 15a and b (these two structures are, in fact, related by a rotation of 180° about the a or c axis) and therefore to fix the orientation and chirality of the enantiomers with respect to the crystal faces. Nevertheless, by determining which polar end of a given crystal (e.g., face hkl or hkl) is affected by an appropriate additive, it is possible to fix the absolute sense of the polar c axis and so the absolute structure with respect to this axis. Subsequently, the absolute configuration of a chiral resolved additive may be assigned depending on which faces of the enantiotopic pair [e.g., (hkl) and (hkl) or (hkl) and (hkl)] are affected. 

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... 

The Td point group behaves as expected and offers no special problems. Of course, % - 0 for CH4, CH3C1, and CH2ClBr. For an asymmetric center (point group Cj), % is a quantitative measure of how chiral is the distribution of the property in question, taken to be simply atomic mass in all these examples. Thus, % is -0.0052 for (Rj-CHDCIBr, +0.0052 for (5>CHDClBr, +0.041 for (Rj-CHFCIBr, and -0.041 for (5j-CHFClBr. In terms of other chirality... 

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