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Starting from chemical structural theory, in particular the principle of valency conservation, chemical reactions can be analyzed by discrete mathematical methods. Employing graph-theoretical and lattice-theoretical approaches, one obtains reaction lattices which comprise all relevant structures of the chemical process under consideration. The dynamic aspect of the reaction is represented by the dynamic sublattice containing all dynamic graphs. The continuous character of a process involving two sets of reaction partners can be described by the variation of a reaction parameter r. This treatment leads to simple eigenvalue problems, the solutions of which are correlation diagrams for the respective dynamic transition. This formalism is extended by including permanent influences on the dynamic transition. Two classes of such influences are discussed: (a) perturbation by an additional constant dynamic graph Ds, which is linearly superimposed upon the dynamic transition, and (b) modification of the space which underlies the dynamic system by the ‘reaction skeleton’, i.e., the invariant structure of the reaction represented by the static graph S. In the latter case, the algebraic treatment leads to generalized eigenvalue problems. After a general presentation of the mathematical procedure and a short introduction to the computational method, the formalism is applied to electrocyclic reactions involving four carbon centers with special emphasis on the ring closure reaction of butadiene to cyclobutene. The correlation diagrams calculated by the reaction skeleton approach indicate an overall destabilization of the whole system as compared to the ‘pure’ dynamic transition which is in agreement with quantum chemical result. In addition, an internal stabilization effect is observed for these systems leading to a partial allowance of Huckel type electrocyclic four center reactions. In order to understand the thermodynamical preference of butadiene over cyclobutene, conformational aspects are taken into account by including ‘through-space interactions’ into the reaction skeleton. Based upon the resulting diagrams, reaction paths involving geometrical changes are discussed. |
