Molecular symmetry chirality

Several groups have studied the structure of chiral phases illustrated in Fig. IV-15 [167,168]. These shapes can be understood in terms of an anisotropic line tension arising from the molecular symmetry. The addition of small amounts of cholesterol reduces X and produces thinner domains. Several studies have sought an understanding of the influence of cholesterol on lipid domain shapes [168,196]. 

Remarkable chiral patterns, such as those in Figs. IV-15 and XV-8, are found in mixtures of cholesterol and 5-dipalmitoyl PC (DPPC) on compression to the plateau region (as in Fig. XV-6). As discussed in Section IV-4F, this behavior has been modeled in terms of an anisotropic line tension arising from molecular symmetry [46-49]. 

In Chapter 4, on molecular symmetry, 1 have added two new sections. One of these concerns the relationship between symmetry and chirality, which is of great importance in synthetic organic chemistry. The other relates to the connection between the symmetry of a molecule and whether it has a permanent dipole moment. 

From these examples, it becomes clear that molecular symmetry can spontaneously break into chiral domains in the absence of any external force or seed. However, in every known case, the net symmetry remains intact, and the overall chirality sums to zero in the environment. Nevertheless, the spontaneous formation of macroscopic chiral regions in systems of associating achiral molecules is of interest to those who contemplate induction of molecular chirality in the context of prebiotic reaction chemistry. 

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

In catalysts obtained from chiral stereorigid metallocenes of class III with C2 molecular symmetry (helical), such as racemic isomers of ansa-metallocenes, e.g. rac.-(IndCH2)2MtX2 (Table 3.1) and rac.-(ThindCH2)2MtX2, the two coordination positions available for the incoming monomer and the growing... 

It is known from experience that only chiral molecules have the ability to rotate the plane of polarization. This observation suggests that molecular chirality is a manifestation of residual orbital angular momentum, and vice versa. When an achiral molecule is placed in a magnetic field the molecular magnetic vectors are aligned in the diection of the field and not along the local molecular symmetry directions. The molecule therefore acquires a... 

There are two types of molecular symmetry that cause chemical-shift equivalence. Nuclei or groups of nuclei that are interchangeable by a symmetry operation involving a simple n-fold axis of symmetry (Cn) have been termed equivalent, and are isochronous in chiral and... 

The elusive relationship between molecular chirality and optical activity, as well as the Faraday effect, likewise reduce to the minimization of orbital angular momentum as a function of molecular symmetry. 

There is considerable scope for further work on the topic of molecular chirality. There is a clear definition of how to relate optical rotation to degree of chirality in terms of molecular symmetry. The ultimate aim is a theoretical framework for the quantitative interpretation of optical rotary dispersion and circular dichroism of chiral materials. The importance of this pursuit is almost self-evident. 

The molecular structure of (+)-25 in the crystal of the trihydrate is depicted in Fig. 10. The coordination polyhedra surrounding the silicon atoms Si and Si are distorted trigonal bipyramids (Berry distortions [8] 7.7 % and 10.6 %, respectively), in which each of the axial positions are occupied by carboxylate oxygen atoms. The molecular symmetry of the pentacyclic molecular framework of (+)-25 may be described as approximately >2 if the two ammoniomethyl groups are ignored. Thus, the absolute configurations of the two chiral silicate moieties are identical. 

The C4-chiral thiazolidine-2-thiones and oxazolidine-2-thiones developed by us proved to be efficient for chiral induction. They should be applicable to practical syntheses of drugs. Novel chiral designs using these functional and chiral heterocycles seem likely in the future, especially when used in combination with organometallic reagents and/or molecular symmetry. Creative investigations employing such chiral heterocycles and related compounds will be extensively pursued. 

Chiroptical spectroscopies are based on the concept of chirality, the signals are exactly zero for non-chiral samples. In terms of molecular symmetry, this means that the studied system must not contain a rotation-reflection axis of symmetry. This lapidary definition implies that the more known symmetry elements (symmetry plane - equivalent to the one-fold rotation-reflection axis and the center of symmetry - equivalent to the two fold rotation-reflection axis) must also be absent and that the system must be able to exist at least formally in two mirror image-like forms. At first glance this limitation seems to be a disadvantage, however, this direct relation to molecular geometry gives chiroptical properties their enormous sensitivity to even minor and detailed changes in the three-dimensional structure. 

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