Quantifying the degree of molecular shape distortion. a chirality measure

We suggest that the "black or white" attitude towards chirality (either chiral or non-chiral) overlooks fine details of the shape of molecules. We argue that a measure is in order to quantitate the intuitive feeling that, say, 2-deuteriobutane is "less chiral" than 2-iodobutane. Such a measure, X, which is based on relative molecular shape distortions, is proposed and its properties demonstrated for a series of chiral monohalogenated n-alkanes. For instance, the X values for 2-F-, 2-Cl-, 2-Br-, and 2-I-butane (anti conformation) are 0.17, 6.67, 15.46 and 29.76, respectively, emphasizing that inducing chirality in butane by substitution with F causes only a minor shape distortion, while distortion due to iodine is considerable. The gradual change in chirality of rotamers is manifested by a continuous gradual change in the X value of the rotamers of 2-halogenobutanes. The application of the χ scale to two-dimensional chirality is demonstrated for monosubstituted naphthalenes. An outlook for applications of the shape-distortive scale to issues other than chirality is given.