Global equilibrium conditions for hybridization tetrahedra

The matrix elements of SA can be evaluated using a fundamental fact concerning quaternions the rotation of the vector part of an HO according to eqs. (3.92), (3.93), and (3.94) in the quaternion representation can be written as  

performing the necessary algebra, we arrive at a pair of 4 x 4 matrices  

In their terms the sought symmetric matrix EA acquires the form  

This comprises the global equilibrium condition for hybridization tetrahedra in the FAFO model. Their direct relation with the molecular shape which enters in an invariant manner through the bond vectors eRmL . is remarkable. As previously, the above 

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