Configuration Spaces for Molecules with Several Symmetrical Reference Structures

5 Configuration Spaces for Molecules with Several Symmetrical Reference Structures 

So far, we have been assuming that the choice of a suitable reference structure is obvious. There is no problem as long as the distortions from some symmetrical struc- 

It is not obvious how to define a configuration space with the required symmetry properties. One possibility is to start from symmetry adapted linear combinations of the three distance coordinates  

With distance coordinates we can define the size and shape of a triangle but not its sense of chirality. To achieve this, vectors are needed. We define vectors d 2, d, d x, from atoms 1 to 2, 2 to 3, and 3 to 1, respectively, whose lengths correspond to any permutation of the distances 0, b, c. Next we replace by a coordinate S l which includes chirality by evaluation of the vector product di2 xd23 (or 23X4/3, or 4/3, xdx2, since all three vector products are equal by virtue of = 0). 

These products are each in magnitude twice the area F of the triangle, but their sign s is different for a clockwise and an anti-clockwise arrangement of the three vectors. Thus, we can choose 

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