Chirality continuous measures

One example of a quantitative measure of molecular chirality is the continuous chirality measure (CCM) [39, 40]. It was developed in the broader context of continuous symmetry measures. A chital object can be defined as an object that lacks improper elements of symmetry (mirror plane, center of inversion, or improper rotation axes). The farther it is from a situation in which it would have an improper element of symmetry, the higher its continuous chirality measure. 

Continuous chirality measure is then defined as follows given a configuration of points P = I, its chirality content is determined by finding the nearest configuration of points Pi - 2 which has an improper element of symmetry, and by calculating the distance between the two sets using Eq. (26). 

Two general classes of chirality measures have been recognized in the first, the degree of chirality expresses the extent to which a chiral object differs from an achiral reference object, while in the second it expresses the extent to which two enantio-morphs differ from each other [Buda et al., 1992]. The continuous chirality measure (CCM) recently proposed [Zabrodsky and Avnir, 1995] is an example of chirality measure belonging to the first class and is based on the general definition of continuous symmetry measure defined as ... 

Keinan et al. found that the quantitative degree of chirality of substrates correlates with their efficiency of reaction with active sites [7]. The degree of chirality, a global shape descriptor, was determined by the use of the continuous chirality measure (CCM) methodology developed previously, which treats chirahty as a continuous structural property and not as a binary quality (chiral/not chiral) [8]. 

The continuous chirality measure is an example of first class chirality measure based on the general definition of continuous symmetry measure it is defined as [Zabrodsky and Avnir, 1995]... 

Continuous Chirality Measure chirality descriptors continuous wavelet transforms spectra descriptors contour length size descriptors ( Kuhn length) contour profiles molecular profiles conventional bond order bond order indices conventional bond order ID number ID numbers core count ETA indices... 

The quantitative study of the transformation of achiral to chiral structures has led to the concept of continuous chirality measures in transition metal chemistry developed by Alvarez and Avnir. ° ... 

CCM = continuous chirality measure CSM = continuous symmetry measure. 

The Measurement of Achirality The Continuous Chirality Measure (CCM) Approach... 

The S(Gj ) thus obtained is the minimal chirality measure of the given configuration, on a continuous scale of 0 S 100. 

Oin search for a discontinuous physical property of a single molecide is discomaged, or at least diverted, by the development of the concept of continuous symmetry measures [127]. Some time ago, Zabrodsky et al. advocated that it was more natural to analyse symmetry properties in terms of a continuous scale rather than in terms of yes and no . In order to justify their view they invoked examples such as symmetry distortions due to vibrations, changes in the aUowedness of electronic transitions due to deviations from an ideal symmetry and so forth. In a similar vein and around the same time Buda et aL [128] defined a degree of chirality as a continuous function that is zero if, and only if, the object is achiral Kanis et al. [129] were motivated to use continuous symmetry measures in their study of the hyperpolarisabihty of non-Unear optic materials in order to provide correlations between structure and physical or chemical properties. Their continuous symmetry metric provided a quantitative characterisation of the extent to which the inversion centre is present for a particular geometry. It then allowed the comparison of computed hyperpolarisabUities with the extent to which the inversion centre remains. 

Zabrodsky H and Avnir D (1995) Continuous symmetry measures. 4. Chirality./owrwu/ of the American Chemical Society 117 462-473. 

L and the D/L ratio approaches zero. After the death of the living organism, proteins start to spontaneously break down. An inter-conversion of the amino acids occurs from one chiral form (L) to a mixture of D- and L- forms following protein degradation this process is called amino acid racemisation. The extent of racemisation is measured by the ratio of D/L isomers and increases as a function of time and temperature. The longer the racemisation process continues the closer to 1 the ratio between the D- and L-forms becomes. If the D/L ratio is <1 it may be possible to use it to estimate age. The D/L ratio of aspartic acid and isoleucine are the most widely used for this dating technique [104]. Dates have been obtained as old as 200 000 years. However, it has been used mainly to date samples in the 5000 100 000 year range. Recent studies [ 105] mention an estimation of the method accuracy to be around 20%. 

---