Chiral: axis centre

In 2004, Walsh s group developed L-proline-catalysed aldol reactions of atropisomeric amides sueh as benzamides and naphthamides. " The DKR process simultaneously established the stereoehemistry of the atropisomeric amide chiral axis and a stereogenic centre, providing high enantioselectivities, as shown in Scheme 2.101. 

Chirality is a property of the entire molecule and there are molecules that are chiral but do not contain a chiral centre. For example, 1,3-dimethylallene is a chiral molecule since it has no plane of symmetry, and it can exist as a pair of mirror images (Figure 20.73). The molecule has a chiral axis rather than a chiral centre. The presence of two rigid 7t bonds prevents free rotation around the three central carbon atoms. 

We have seen in Section 4.1.4 that = n and that S2 = i, so we can immediately exclude from chirality any molecule having a plane of symmetry or a centre of inversion. The condition that a chiral molecule may not have a plane of symmetry or a centre of inversion is sufficient in nearly all cases to decide whether a molecule is chiral. We have to go to a rather unusual molecule, such as the tetrafluorospiropentane, shown in Figure 4.8, to find a case where there is no a or i element of symmetry but there is a higher-fold S element. In this molecule the two three-membered carbon rings are mutually perpendicular, and the pairs of fluorine atoms on each end of the molecule are trans to each other. There is an 54 axis, as shown in Figure 4.8, but no a or i element, and therefore the molecule is not chiral. 

Here, ry is the separation between the molecules resolved along the helix axis and is the angle between an appropriate molecular axis in the two chiral molecules. For this system the C axis closest to the symmetry axes of the constituent Gay-Berne molecules is used. In the chiral nematic phase G2(r ) is periodic with a periodicity equal to half the pitch of the helix. For this system, like that with a point chiral centre, the pitch of the helix is approximately twice the dimensions of the simulation box. This clearly shows the influence of the periodic boundary conditions on the structure of the phase formed [74]. As we would expect simulations using the atropisomer with the opposite helicity simply reverses the sense of the helix. 

The interconversion of enantiomers can be viewed in general as requiring inversion at a particular atom or twisting about an axis of the molecule. Provided these processes are inhibited to some degree, the chirality of a molecule will be detectable so that any chiral species may be said to contain centres and/or axes and/or planes of chirality.115,116,117,118 The precise meanings and utility of these concepts are, however, a matter of some debate,115,116 129 and they have not been extensively applied to coordination compounds. 

The structure must build up a tilted phase, commonly a smectic C phase. The molecules contain at least one chiral centre and the symmetry cannot be assumed as C2h symmetry, but only as C2V symmetry. This is consistent with a polar twofold axis perpendicular to the long molecular axis. 

One simple practical method of assessing the possibility of the existence of non-superimposable mirror images, particularly with complex structures, is to construct models of the two molecules. The property of chirality may alternatively be described in terms of the symmetry elements of the molecule. If there is a lack of all elements of symmetry (i.e. a simple axis, a centre, a plane, or an n-fold alternating axis) the chiral molecule is asymmetric, and will possess two non-superimposable mirror image structures (e.g. 2a and 2b). If, however, the molecule possesses a simple axis of symmetry (usually a C2 axis) but no other symmetry elements, the chiral molecule is dissymmetric. Thus 4a and 4b are dissymmetric and the simple C2 axis of symmetry, of for example 4a, is shown below. If the molecule possesses a centre of symmetry (C.) or a plane of symmetry (alternating axis of symmetry (S ), the mirror images of the molecule are superimposable and the molecule is optically inactive. These latter three symmetry elements are illustrated in the case of the molecule 4c. 

The stack of BEDT is of the so-called a-phase. The sulphur-sulphur contacts between the stacks (S- S distances s= 3.47 A, shorter than the sum of the van der Waals radii of 3.6 A) and within the stack (S S distances w4.l-4.2A) give the layers a decidedly two-dimensional character. The BEDT donors are related by a two-fold screw axis, and therefore have no real chiral nature (the molecules have pseudo-centre symmetry). There are several hydrogen bonds between the hydrogen atoms of the ethylene groups of BEDT and the carboxylate groups of the counter-ion. The material is a semiconductor, where the conductivity falls as the temperature is lowered, from about 1 S cm 1 at room temperature. 

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. 

This structure has two chiral centres, so how will we know which diastereoisomer we have The answer was simple the stereochemistry has to be tram because Feist s acid is chiral it can be resolved (see later in this chapter) into two enantiomers, Now, the cis diacid would have a plane of symmetry, and so would be achiral—it would be a meso compound, The trans acid on the other hand is chiral— it has only an axis of symmetry. If you do not see this, try superimposing it on its mirror image. You will find that you cannot. 

The phenonium ion is nonetheless still chiral, since it has an axis (and not a plane or centre) of symmetry, so if we use an enantiomerically pure starting material we get an enantiomerically pure product. 

This may not be obvious in the normal drawing (which has a centre of symmetry), but rotation around the central C-C bond clearly shows the plane of symmetry. Neither plane nor centre of symmetry may be present in a chiral molecule, but a C2 axis is allowed (Chapter 16). 

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