Chiral pairs

The theory of the separation of geometric isomers on stationary phases that have a number of sterogenic centers has not been developed to the point where a particular stationary phase together with an appropriate mobile phase can be deduced for the separation of a specific pair of isomers. A number of theories have been put forward to explain the resolution of geometric isomers (some of which have been quite "imaginative" and "colorful") yet a reliable theory to help in phase selection for a hitherto unresolved chiral pair is still lacking. Unfortunately, the analyst is left with only two alternatives. The first is to search the literature for a model separation similar to the problem in hand and start with that phase system or, alternatively, resort to the technique of the early days of LC, namely, find the best phase system by a trial-and-error routine. 

Mixtures of N-(a-methylbenzyl) stearamides with both stearoyltyrosine and stearoyltryptophan methyl esters show no discrimination in their pressure-area relationships at 35°C, regardless of the surface pressure to which the films are compressed (Fig. 34). The Yl/A curves for homo- and hetero-chiral pairs are exactly coincident. 

A structurally unusual 3-blocker that uses a second molecule of itself as the substituent on nitrogen is included here in spite of the ubiquity of this class of compounds. Exhaustive hydrogenation of the chromone (13-1) leads to a reduction of both the double bond and the carbonyl group, as in the case of (11-2). The car-boxyhc acid is then reduced to an aldehyde (13-2) by means of diisobutylaluminum hydride. Reaction of that intermediate with the ylide from trimethylsulfonium iodide gives the oxirane (13-3) via the addition-displacement process discussed earlier (see Chapters 3 and 8). Treatment of an excess of that epoxide with benzylamine leads to the addition of two equivalents of that compound with each basic nitrogen (13-4). The product is then debenzylated by catalytic reduction over palladium to afford nebivolol (13-5) [16]. The presence of four chiral centers in the product predicts the existence of 16 chiral pairs. 

An additional chiral reference system based on chiral pairs of oriented lines has recently been proposed.140... 

The presence of a chiral center is a sufficient, but not a necessary condition, for the existence of chirality in a molecule. Tor example, numerous biphenyl derivatives may exist in chiral pairs... 

Figure 2-36. Illustrations of chiral pairs, (a) Decorations (in Bern, Switzerland, photograph by the authors) whose motifs of fourfold rotational symmetry are each other s mirror images (b) Quartz crystals (c) J. S. Bach, Die Kunst der Fuge, Contrapunctus XVIII, detail (d) Legs (detail of Kay Worden s sculpture, Wave, in Newport, Rhode Island), (photograph by the authors) (e) A molecule and its mirror image in which a carbon atom is surrounded by four different atoms, for example, CHFClBr.

Once all the trans arrangements are listed, drawn, and checked for chirality, we can check for duplicates in this case, A3 and B2 are identical. Overall, there are four nonchiral isomers and one chiral pair, for a total of six. 

The mirror image is different, so there is a chiral pair. 

The mirror images are identical, so there is only one isomer. There are two chiral pairs and one individual isomer, for a total of five isomers. 

The number of chiral pairs, for a given decoration pattern, the number of times the deter-minantally antisymmetric character" appears in the decoration character. From this result the number of achiral structures is obtained as the difference between the total number of decoration isomers possible and the number of chiral pairs. The total number of isomers is the... 

Four other polyhedra based on 24-vertex cages exhibiting cubic symmetry can be formed from the regular orbit structure of the previous section. Two of these are chiral pairs, the dextro snub cube and its chiral partner, the laevo snub cube the third is the regular orbit of Td point symmetry, while the fourth is the regular orbit of Th symmetry. 

There are three crystal modifications of racemic crystals, depending on the difference in strength of the intermolecular interactions between the enantiomeri-cally hetero- and homo-chiral pairs of the racemate the modifications are racemic compound, conglomerate, and racemic sohd solution (Fig. 5.2). Preferential crystallization can only be applied to a conglomerate. However, most racemic crystals are racemic compounds, and conglomerates are very rare (a few percent of racemic crystals in our experience). This means that we have to transform a racemic compound into a conglomerate in order to carry out the enantioseparation of the racemate by preferential crystallization. 

With two consecutive digits as the basis for the comparison of the codes we doubled the number of distinct chiral classes. The most chiral pair is now ( C, C ) at the distance 11. Table 32 gives the history of inaeased differentiation among chiral enantiomers as the length of the window of comparison is gradually increased. Entries in Table 32 can be used to rank chiral benzenoids. In the case of the... 

The Goldberg numbers characterize a set of fullerenes of increasing size in which all 12 pentagons are equivalent and (beyond C20) isolated from one another. They have particular electronic properties as we will see later. Isomerism is possible, in that distinct (a, b) pairs may yield the same value of n. The smallest such case is = 980 with an isomeric trio of (a, b) = (7,0)(7ft) and the chiral pair (5,3)(7) the smallest case with three distinct integer pairs is the set (23, 4), (21, 7), and (17, 12) which all give = 12,740. 

Figure 2-45. Illustrations of chiral pairs (a) Decorations whose motifs (of fourfold rotational...

Despite the range of species that have been Investigated, the variety of techniques used and the presence of some species differences in response (see, for example, O, there is considerable agreement between workers on the factors that govern neural response,irrespective of whether activity is recorded at a peripheral or higher level (16-19,6). For example, -amino acids elicit the maximum responses, and the most effective member of a chiral pair is the L-lsomer. (Of these, L-glutamlne or L-alanlne are the most powerful stimuli for the majority of species so far tested, but not for all). 

The mirror Image Is different, so there Is a chiral pair. These mirror Images have no Improper axes of rotation, Including neither an Inversion center nor mirror planes. 

Chiral separations are a technical challenge because the enantiomers are chemically and physically very similar, and most chiral pairs show... 

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