On the quantification of asymmetry in nature

Abstract

A new concept of quantitative measure of the amount of structural asymmetry is introduced and defined by maximal overlap between two enantiomers of the same chiral body. This concept is to be called chiral coefficient, and it can readily be extended to physical properties such as mass or electronic wave-function distributions over chiral objects such as molecules or unit cells in crystals. The mathematical aspects of these coefficients are discussed. There exist two cases of maximal overlaps, symmetric and asymmetric, where for the asymmetric case there exist two positions of maximal overlap. It is also shown that there always exists a natural directionz for every asymmetric body for any physical property treated. The possibility of quantizing structural asymmetry is discussed, and, if it exists, it may be associated with the naturalz axis of the chiral system. Possible applications of asymmetry quantification are discussed.