By Robert E. Collin, Francis J. Zucker
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58): (58) 51 Nonzero value of the overlap determinant (59) confirms that in contrast to thermal reaction, the photochemical 2s + 2s addition is allowed. 1 * _ 2 Ds+s - 1 1 2 *0 1 2 (59) 2 On the other hand, the alternative 2s + 2a mechanism, characterized by the assignment (60) and consequently by the overlap determinant (61), is forbidden. (60) 1 * 2 D s+a = 1 2 1 2 =0 1 (61) 2 In a completely analogous way it would now be possible to analyze any other photopericyclic reaction. The typical feature of all these reactions is the speCific "closed shell" form of the excited wave function
The field of the rational design of compounds with desired biological properties, and also in the chemical theory. (68) Because of normalization, the values of this index are bounded by the inequality (69). e. when A = B, and with increasing deviations between the structures its value monotonously decreases. Within the framework of the topological approximation  allowing to eliminate some problems with the invariance of this index to the distance and the mutual orientation of the molecules, the above general definition (68) can be rewritten in the form (70), where 0A and Os are topological density matrices of the structures A and B respectively.
33a) (33b) 1 0 5 +5 = 21 2 1 2 =0 1 (34) -2 In keeping with the expectation of the Woodward-Hoffmann rules, its zero value confirms the forbiddeness of the process. The alternative supra-antara mechanism characterized by the assignment (35) then analogously gives the overlap determinant (36), the nonzero value of which confirms the expected allowedness of the process. (35) 41 1 1 2 1 :;t: 0 (36) 2 2 3/ + The same procedure can be now used to the analysis of any other peri cyclic reaction. A number of such examples involving also more delicate reactions where the classical technique of correlation diagrams encounters some difficulties, can be found in the original literature.