Similarity Indices and the Least Motion Principle

A number of previous examples has demonstrated that the applicability of similarity indices in the theory of pericyclic reactions is indeed very broad. The basis of this exploitation is the intuitively expected relation of the similarity indices to the extent of electron reorganization and the so-called least motion principle. Since in all previous applications this relation has remained only at the level of the intuitively expected parallel it is desirable to analyze the above relation in more details. 

The simplest situation is in the case of the index Ppp, the physical meaning of which can be best demonstrated by transforming the density matrices, Qp, in terms of 

The coefficients C converting the matrix into the diagonal form are then used also for the transformation of the matrix Qp (79). 

Although this transformation does not simplify the form of the matrix flp (it still contains both diagonal and nondiagonal terms), the advantage of the transition to the molecular basis is nonetheless quite clear. Because of the special diagonal form of 

Whereas the index r characterizes the electron reorganization by one value expressing the total difference of electron configurations of the reactant and the product, the index J expresses the same difference not by the total but by the mean value along the concerted reaction path. 

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