Orientation Averages of the Discrimination

The treatment of these averages [Craig, Power and Thirunamachandran (1971)] is simplified by a decomposition of the magnetic moment into components parallel and perpendicular to the electric moment fi according to mb = mj) -f- m. If b is replaced by its enantiomer we must specify the conditions of the replacement the enantiomer being generated by inversion in the origin, the new moments are 

Two corresponding auxiliary expressions derived from the optical-rotatory tensor R, are the following  

As already remarked the imaginary part of the pseudo-scalar i determines the optical rotatory power. X m is a polar vector perpendicular to the electric dipole direction and 2 - - its (scalar) magnitude. In both the averages to be discussed the contribution by R- averages to zero. Where the molecules are locked with electric dipole directions fixed, but are each free to rotate independently about these axes, the averaged discriminating term is given by expression (III. 15) 

This average depends only on the contracted R tensor /i m, apart from the angle parameters specifying the directions of the electric moments and /t relative to the separation R as polar direction. 6a. 4 a, a polar angles of and Y is the angle between /i and fi, according to (III.16), 

The parallel arrangement is formed when molecule b is related by a translation to molecule a, and then allowed rotational freedom about R. The antiparallel arrangement involves translation and a rotation by n of molecule b about an axis perpendicular to R, so that the electric dipole sense is reversed from that of a. In the first (parallel) arrangement 6a = 6b=y=0 and the interaction between molecules of the same chirality is 

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