Achirality homochirality classes

The absence of an achiral boundary along the conformational enantiomerization trajectory of chemically achiral compounds, such as the ones discussed above, precludes partitioning of conformations along the path into homochirality classes. As noted above, under such circumstances it becomes meaningless to speak of these conformations as right-handed or left-handed because no point can be defined, other than arbitrarily, where right switches to left and vice versa. 

L spaces of Fig. 1 constitute homochirality classes because enantiomor-phous triangles cannot be chirally connected passage between the two spaces is impossible without crossing an achiral boundary. 

Fig. 12 represent particular stationary points on the multidimensional potential energy surface and are chirally connected through a continuous reaction pathway that involves no achiral intermediates this is evidently the case because the product of the reaction sequence is not racemic. Hence, they cannot be partitioned into R and L homochirality classes. 

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. 

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