Scalar triple-product functions

During the optimisation of the structure against the distance constraints it is usual to incorporate chiral consiraints. These are used to ensure that the final conformation is the desired stereoisomer. Chiral constraints are necessary because the interatomic distances in two enantiomeric conformations are identical and as a consequence the wrong isomer may quite legitimately be generated. Chiral constraints are usually incorporated into the error function as a chiral volume, calculated as a scalar triple product. For example, to maintain the correct stereochemistry about the tetrahedral atom number 4 in Figure 9,16, the following scalar triple product must be positive ... 

For such a transformation, the scalar function is given as the simple triple product... 

In other words, S contains all the functions with the single exchanged spin-orbital. Similarly, D would be the combination of the functions with double exchanges, T with triple exchanges, and so forth. With such a notation, the function F can be treated as the scalar product of the basis vectors Yo, S, D,... and the coefficient vector... 

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