Grid Coordinates and Molecular ID Numbers

Cartesian coordinates of the six carbon atoms in chair-cyclohexane are obtained from the grid coordinates (a-d) along with, and oriented according to, the unit vectors by the geometrical relationships  

Analogously, the grid coordinates for two staggered rotamers of n-butane (the gauche rotamer is chiral) are presented in Table 2 the origin, as before, is at carbon 

The derived molecular numbers (MID) are 7.722 for the gauche rotamer and 7.680 for the anti rotamer. If a methyl group is attached to carbon atom 1 in chair-cyclohexane, the grid coordinates for the methyl carbon atom are 0,0,0,1 for the axial conformer (resulting in MID = 16.599) and 0,1,0,0 for the equatorial conformer (resulting in MID = 16.530), and thus differentiating these geometrical diastereomers. 

The MID values for hydrogen-depleted staggered rotamers of -alkanes are about twice as large as the corresponding number of carbon atoms. Among staggered rotamers of the same linear alkane, the maximum MID corresponds to the most coiled rotamer, and the minimum MID to the most extended (all-a fi) rotamer.  

Another approach for a stereochemical index Q encoding information on cis-trans isomerism in alkenes was described by Estrada on including a corrected electron charge density calculated with the MOP AC version 6.0, the following 

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