Pathway chiral

Figure 36. Conversion of an asymmetric square pyramid (top left) into its mirror image (top right) along a chiral pathway. Four spheres with different but variable diameters are centered at the vertices of the square base. The spheres labeled a and b shrink and expand, respectively, until their diameters are switched. This is followed by a similar switch in the diameters of spheres c and d.

FIGURE 3 Conversion of an unlabeled asymmetric tetrahedron (top left) into its mirror image (top right) by continuous deformation (small arrows) of the geometric figure along a chiral pathway. 

The existence of chiral pathways in this molecule is made possible by the existence of the two independent degrees of freedom that govern internal motion, rotation, and inversion. As molecular complexity increases, the number of degrees of freedom also increases and, unless an achiral pathway is energetically much preferred, it becomes more and more likely that enantiomerization proceeds by a chiral pathway. For example, it is extremely improbable that reversal of helicity in a polymeric chain involves an achiral intermediate or transition state. There is a strong resemblance here to the stochastic achirality of ensembles of achiral molecules discussed previously. 

A formal limit is reached when, due to structural constraints, all achiral pathways along the enantiomerization trajectory become energetically inaccessible under normal laboratory conditions. Chiral pathways then remain the only alternative. In 1954 it was pointed out that a compound of the type 4-[( )-5ec-butyl]-4 -[(S)- ec-butyl]-2,2, 6,6 -tetra-methylbiphenyl consists entirely of asymmetric molecules that undergo rapid enantiomerization, and that conformational racemization, in the... 

Because enantiomers have oppositely signed pseudoscalar properties, chiral zeroes are unavoidable at some stage in the conversion of a molecule into its enantiomer along a chiral pathway. This is true of chirally connected enantiomeric conformations in chemically achiral molecules, such as (lf )-menthyl (15)-menthyl 2,2, 6,6 -tetranitro-4,4 -diphenate, and of chirally connected enantiomers, such as ( + )- and (- )-isopro-pylmalonamic acids. More generally, as previously noted, any chiral molecule composed of five or more atoms is in principle always capable of conversion into its enantiomer by chiral as well as by achiral pathways, provided that this is energetically feasible. Hence, unless it can be demon-... 

A chiral Lewis acid can be used to bind to substrate or radical species and determine the approach of the other reacting component while accelerating the chiral pathway relative to the background reaction. 

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