Similarity in the Theory of Pericyclic Reactions

The idea of the quantitative exploitation of molecular similarity for the classification of chemical reactivity is probably due to Polansky [27], who attempted to justify the old Clar s idea of local benzenoid regions in condensed aromatic hydrocarbons [42], For this purpose, Polansky introduced a coefficient rL characterising the similarity of a given local benzenoid fragment L in a 

Because of normalisation by the factor 2Nh (NL is the number of electrons in a fragment L), the values of the coefficient vary between 0-1, measuring thus the degree of similarity. 

More recently the idea of quantitative comparison of electron structure of the molecules was revived by Carbo [28] who proposed for this purpose the similarity index rAB, expressing the desired similarity of two molecules A and B in terms of density matrices (Eq. 2) 

In order to eliminate the problems with the invariance, we proposed some time ago a topological approximation based on the so-called overlap determinant method [43]. This approximation is based on the transformation matrix T that describes the mutual phase relations of atomic orbitals centred on molecules R and P, and thus plays in this approach the same role as the so-called assigning tables in the overlap determinant method (Eq. 4) 

The construction of this matrix is sufficiently described in the original studies [33,43] and therefore it is not necessary to repeat it here. We recall only that the form of the matrix depends on the actual reaction mechanism of the transformation R - P so that it is precisely via this matrix that the possibility of discriminating between various reaction mechanisms enters into play. 

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