Enantiomorphs , defined

The derivation of phases for noncentrosymmetric structures is more difficult, because the values are not restricted to 0° or 180°. In addition to the origin-defining phases, an enantiomorph-defining phase must be selected. Usually phases are derived by the tangent formula ... 

Phases are assigned to a limited number of selected reflections. These are the starting set and include those that define the location of the origin [origin-defining phases) and those that define which enantiomorph of the crystal structure, if any. is chosen enantiomorph-defining phases). 

These results allowed the proposal, at the beginning of the 1980s, of a different molecular model for cholesteric induction 65,66 This model is sketched in Figure 7.15 in the case when both nematic host and chiral guest have a biaryl structure. Nematic molecules exist in chiral enantiomorphic conformations of opposite helicity in fast interconversion. The chiral dopant has a well-defined helicity (M in Figure 7.15) and stabilizes the homochiral conformation of the solvent In this way, the M chirality is transferred from the dopant to the near molecule of the solvent and from this to the next near one and so on. This... 

Prelog and Helmchen (5) defined pseudoasymmetry as the duality resulting from the two ways with which one can combine two enantiomorphic ligands with two enantiotopic spaces (Fig. 4). This represents an innovation because it limits pseudoasymmetry to achiral compounds (35). This follows from the fact that enantiotopic spaces can exist only if the molecule possesses an element of... 

It has been recognized147 that chirality measures can be subdivided into two types those that gauge the extent to which a chiroid differs from an achiral reference object (measures of the first kind) and those that gauge the extent to which two enantiomorphs differ from one another (measures of the second kind). In chirality measures of the first kind, the question to be answered is How dissimilar are the chiroid and its achiral reference object In chirality measures of the second kind, the question is How dissimilar are the two enantiomorphs of a chiroid In both cases the underlying concept is that of a distance, measured either between a chiral and an achiral object or between two enantiomorphous chiroids. That is, the degree of chirality of a chiroid X is defined in relation to another, chiral or achiral, reference object Xref The less these two objects match, the more chiral is X. 

Certain types of knots and links exist as topologically chiral enan-tiomorphs. Such enantiomorphs cannot be interconverted by continuous deformation ( ambient isotopy ). Homochirality classes can therefore be defined for this type of mathematical object. ... 

The Hausdorff chirality measure is a chirality measure of the second class [Buda and Mislow, 1992]. Let Q and Q denote two enantiomorphous, nonempty, and bounded sets of points defined in the geometrical space (x,y,z). Let d(q,q ) denotes the distance between two points G Q and qi G Q. Then, the Hausdorff distance h between sets Q and Q is defined as... 

The additional symmetry elements which are necessary for the 230 space groups to define the symmetry of all crystals (i.e. enantiomorphic and non-enantiomorphic) are glide planes (i.e. mirror reflection + translation) and improper rotation axes (rotation axis + inversion). 

We define a molecule as a recognizable chemical unit connected within itself by bonds, these being much shorter than any distance to atoms of surrounding units, which are often identical or enantiomorphic, i.e. symmetry-related to the reference... 

The first method is the classical technique of Pasteur, which entails the mechanical separation of enantiomorphic crystals formed simultaneously while the mother liquor remains racemic. Enantiomer separation by this particular method is extremely time-consuming and is really impossible unless the crystals form with well-defined hemihedral faces. Nevertheless, it is often the method of choice to obtain the seed crystals required for other direct crystallization procedures. When a particular system has been shown to be a conglomerate, and the crys-... 

The isospecificity of a catalyst is defined by the statistical parameter b, which represents the probability of a correct monomer insertion in the enantiomorphic site, at a given polymerization temperature. Assuming epimerization to be negligible in liquid monomer (hobs = h). the Arrhenius plot of In-[h/(l — h)] versus 1/Tp yields straight lines of slope AAi /R, from which the values of enantioface selectivity AAi enant = I AE jj — AE rel is estimated (Scheme 32). 

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