A generalized scaling of a chiral index for molecules

We propose a scaling of an intrinsic molecular chirality index calculated from atomic positions. Its application to the design of chiral molecules through a consideration of atomic or group chiral indices is discussed for a range of molecules from small molecules to liquid crystal molecules. It is found to indicate the trend in change of chirality of a molecule caused by an atom or group substitution. Comparison is made between the method of scaling and an analytic calculation of the index for an orthogonal tetrahedron. We investigate the effect of substitution of atoms and groups in real liquid crystal molecules by application of the generalized chiral index