La Coupe du Roi and Its Relevance to Stereochemistry, Combination of Two Homochiral Molecules To Give an Achiral Product

Abstract

The problem of dividing finite geometric objects into isometric segments is examined, including the special case in which an achiral object is bisected into isometric homochiral halves (la coupe du roi). Segmentations that are applicable to molecular systems are shown to be limited to four classes, depending on whether or not the object (molecular model) is achiral, whether or not the combination of the cut and the object (cut-object) is achiral, and whether or not there are mirror elements that pass through the segments. These segmentations have a bearing on previously developed relationships among atoms or groups of atoms in molecules and on chemical fragmentations and combinations of molecules. A chemical analogue for the assembly of two homochiral objects into one achiral object (the reverse of la coupe du roi) is provided by the self-coupling of (+)-4-(bromomethyl)-6-(mercaptomethyl)[2.2]metacyclophane ((+)-15) to give, in a stereospecific manner, the achiral cis dimer 11 (C2ν symmetry). In contradistinction, self-coupling of racemic 15 gives a 1:1 mixture of the above cis dimer and of the trans dimer 12 (C2h): corresponding segments that are homochiral in 11 are heterochiral in 12. © 1983, American Chemical Society. All rights reserved.