Chirality of the constituent molecules

In this chapter, we have surveyed a wide range of chiral molecules that self-assemble into helical structures. The molecules include aldonamides, cere-brosides, amino acid amphiphiles, peptides, phospholipids, gemini surfactants, and biological and synthetic biles. In all of these systems, researchers observe helical ribbons and tubules, often with helical markings. In certain cases, researchers also observe twisted ribbons, which are variations on helical ribbons with Gaussian rather than cylindrical curvature. These structures have a large-scale helicity which manifests the chirality of the constituent molecules. 

In thermotropic liquid crystals, the cholesteric sense is determined by the chirality of the constituent molecule the cholesteric sense of the liquid crystals of an optical isomer must be opposite to that of its mirror image isomer. When equal moles of both isomers are mixed (racemic mixture), the twisting power falls to zero and the... 

J, G and K, H ) which could generate form chirality as a direct result of the molecular chirality of the constituent molecules. 

When the mesogenic compounds are chiral (or when chiral molecules are added as dopants) chiral mesophases can be produced, characterized by helical ordering of the constituent molecules in the mesophase. The chiral nematic phase is also called cholesteric, taken from its first observation in a cholesteryl derivative more than one century ago. These chiral structures have reduced symmetry, which can lead to a variety of interesting physical properties such as thermocromism, ferroelectricity, and so on. 

We illustrated in Section II why conventional X-ray diffraction cannot distinguish between enantiomorphous crystal structures. It has not been generally appreciated that, in contrast to the situation for chiral crystals, the orientations of the constituent molecules in centrosymmetric crystals may be unambiguously assigned with respect to the crystal axes. Thus, in principle, absolute configuration can be assigned to chiral molecules in centrosymmetric crystals. The problem, however, is how to use this information which is lost once the crystal is dissolved. 

Note 2 The () in SmC and analogous notations indicate, as in 3.1.5.1.2 (Note 6), that the macroscopic structure of the mesophase is chiral. However, it is also used simply to indicate that some of the constituent molecules are chiral even though the microscopic structure may not be. 

Since there is only a small energy difference between the different conformational states depending upon the presence or absence of a Pro, Gly or N-alkylated amino acid residue, and upon the chirality of the constituent amino acid residues and also to a lesser extent upon the side-chain functionalities, it is not possible to unambiguously predict the conformation of a cyclic pentapeptide. These molecules have often been studied in different solvents and solvent effects were neglected, and/or the methodology to handle such conformational equilibrium was not available. It is only recently that modem NMR techniques and computational procedures have become available to treat this complex problem of fast exchanging conformational equilibria. 36,269,270 ... 

Two characteristics determine the shape of molecular aggregates. The first is the shape of the constituent molecules, which sets the curvature of the aggregate. The second is coupled to the chirality of the molecules, which also determines the curvature of the aggregate, via the geodesic torsion. The bulk of this chapter is devoted to an exploration of the effect of molecular shape on aggregation geometry. An account of the theory of self-assembly of chiral molecules is briefly discussed at the end of this chapter. 

As with the nematic phase, a chiral version of the smectic C phase has been observed and is denoted SmC. In this phase, the director rotates arotmd the cone generated by the tilt angle [9.32]. This phase is helielectric, i.e. the spontaneous polarization induced by dipolar ordering (transverse to the molecular long axis) rotates aroimd a helix. However, if the helix is unwotmd by external forces such as surface interactions, or electric fields or by compensating the pitch in a mixture, so that it becomes infinite, the phase becomes ferroelectric. This is the basis of ferroelectric liquid crystal displays (section C2.2.4.4). If there is an alternation in polarization direction between layers the phase can be ferrielectric or antiferroelectric. A smectic A phase formed by chiral molecules is sometimes denoted SmA, although, due to the untilted symmetry of the phase, it is not itself chiral. This notation is strictly incorrect because the asterisk should be used to indicate the chirality of the phase and not that of the constituent molecules. 

Since the discovery of the first liquid crystalline material in 1888, helicity has proven to be one of the most fascinating topics in this field."" Several liquid crystalline phases with helical structure were reported, such as chlolesteric phase, blue phase, ferroelectric and antiferro-electric smectic phases, and helical smectic A phase. In most of these helical phases, at least a fraction of the constituent molecules have an asymmetric carbon, and it was long believed that chirality at a molecular level is a prerequisite to construct chiral architectures at the mesoscopic level. However, Watanabe et al. reported the first example of spontaneous helix formation in liquid crys-... 

Cholesteric liquid crystals are similar to nematic phases except that the molecular orientation between one layer and the next shows a progressive helical order. This helical structure arises from the chiral properties of the constituent molecules. Chiral molecules differ from their mirror image and have a left- or right-hand sense and are called enantiomorphic. The director is not fixed in space and rotates throughout the sample as shown in Figure 3.3. 

Chirality has become arguably the most important topic of research in liquid crystals today. The reduced symmetry in these organized phases leads to a variety of novel phase structures, properties, and applications. Molecular asymmetry imparts form chirality to liquid crystal phases, which is manifested in the formation of helical ordering of the constituent molecules of the phase. Similarly, molecular asymmetry imposes a reduction in the space symmetry, which leads to some phases having unusual nonlinear properties, such as ferroelectric-ity and pyroelectricity. 

The large and anomalous optical rotations observed in the chiral nematic phase are not due to intrinsic spectroscopic properties, i.e., absorption or emission, of the constituent molecules, since they do not persist in the true isotropic phase (i.e., away from pre-... 

The structures of phases such as the chiral nematic, the blue phases and the twist grain boundary phases are known to result from the presence of chiral interactions between the constituent molecules [3]. It should be possible, therefore, to explore the properties of such phases with computer simulations by introducing chirality into the pair potential and this can be achieved in two quite different ways. In one a point chiral interaction is added to the Gay-Berne potential in essentially the same manner as electrostatic interactions have been included (see Sect. 7). In the other, quite different approach a chiral molecule is created by linking together two or more Gay-Berne particles as in the formation of biaxial molecules (see Sect. 10). Here we shall consider the phases formed by chiral Gay-Berne systems produced using both strategies. 

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. 

On the other hand, cellular membranes are composed of chiral molecules such as phospholipids and cholesterol, but the homochirality of these constituents is not obviously manifested in the membrane s structure. However, in certain cases biological membranes exhibit a distinct helical or twisted structure, which is a very conspicuous sign of the chirality of the supramolec-ular aggregate. These chiral supramolecular aggregates are the subject of this chapter. 

The morphological differences between crystals grown in the presence and absence of the additive would then indicate the direction of the substrate molecule W-Y with respect to the polar axis. Consequently, the absolute configuration of the crystal and of the chiral molecular constituents can be derived. The additive need not be chiral, and even if it is, the assignment of the absolute configuration... 

Finally, reference must be made to the important and interesting chiral crystal structures. There are two classes of symmetry elements those, such as inversion centers and mirror planes, that can interrelate. enantiomeric chiral molecules, and those, like rotation axes, that cannot. If the space group of the crystal is one that has only symmetry elements of the latter type, then the structure is a chiral one and all the constituent molecules are homochiral the dissymmetry of the molecules may be difficult to detect but, in principle, it is present. In general, if one enantiomer of a chiral compound is crystallized, it must form a chiral structure. A racemic mixture may crystallize as a racemic compound, or it may spontaneously resolve to give separate crystals of each enantiomer. The chemical consequences of an achiral substance crystallizing in a homochiral molecular assembly are perhaps the most intriguing of the stereochemical aspects of solid-state chemistry. 

As we have seen, one of the main reasons why reactions in crystals lead to high levels of asymmetric induction is that the constituent molecules can be organized in homochiral fixed conformations and intermolecular orientations that are predisposed to formation of a single product enantiomer. With this in mind, it was natural to seek other ways of preorganizing molecules in restricted environments for the purpose of asymmetric synthesis, and one approach that has shown a good deal of promise is the use of chirally modified zeohtes. The great majority of this work has been carried out by Ramamurthy and coworkers at Tulane University [23], and a brief summary is given below. 

A cholesteric, or chiral nematic (N ) phase. This is a positionally disordered fluid in which the constituent molecules align on average their axes along a common direction called the nematic director. Being the DNA helices chiral, the orientational order develops an additional macro-helical superstructure with the twist axis perpendicular to the local director. The phase thus consists of local nematic layers continuously twisted with respect to each other, with periodicity p/2 (where p is the cholesteric pitch see Fig. 8a) [27,28]. For 150-bp helices, the N phase appears at a concentration around 150 mg/mL in 100 mM monovalent salt conditions. This LC phase is easily observed in polarized optical microscopy. Since the N pitch extends to tens of micrometers (that is, across... 

Sometimes the natural products that are needed are immediately obvious from the structure of the target molecule. An apparently trivial example is the artificial sweetener aspartame (marketed as Nutrasweet), which is a dipeptide. Clearly, an asymmetric synthesis of this compound will start with the two members of the chiral pool, the constituent (natural) (S)-amino acids, aspartic acid and phenylalanine. In fact, because phenylalanine is relatively expensive for an amino acid, significant quantities of aspartame derive from synthetic (S)-phenylalanine made by one of the methods discussed later in the chapter. 

R (rectus) and S (sinister) refer to the sequential arrangement of the constituent parts of the molecule around the chiral center. 

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