Quantum-Mechanical Transition-Complex Theory of Rearrangement Collisions

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Abstract
The theory of rearrangement collisions is discussed in applications to bimolecular chemical reactions, using the method of stationary-state solutions to the Schrödinger equation to avoid the perplexities associated with the non-orthogonality of initial and final states. The analysis employed is originally due to Gerjuoy [E. Gerjuay Phys. Rev. 109, 1806 (1958); Ann. Phys. (N. Y.) 5, 58 (1958)]. The usual results of the formal theory of scattering, involving the transition matrix element, are derived, and a further explicit development of the theory is given which permits the use of a model Hamiltonian to represent the reacting system. Several alternate expressions are obtained for the transition matrix element, involving the use of the ``transition complex'' eigenfunctions as an approximate basis for expansion of the state vector; and an approximate expansion in ascending orders of ``virtual reactive scatterings'' is introduced as a method for rapidly expanding the state vector.

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