Pseudoscalar Properties and Chiral Zeroes

Chirality in the world of observables is characterized by pseudoscalar properties—properties that remain invariant under proper rotation but change sign under improper rotation. Enantiomers and, in general, enan-tiomorphous molecules, have identical scalar properties, such as melting points or dipole moments, and pseudoscalar properties that are identical in 

FIGURE 12 Conversion of (+)- into (- )-isopropylmalonamic acid. The step at which the configuration changes from S to i is boxed. 

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- 

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.  

FIGURE 13 Enantiomorphs of topologically chiral constructions. Top Trefoil knot. Center Four-crossing two-component link. Bottom Oriented two-crossing link. 

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