Quantum reactive scattering via the log derivative version of the Kohn variational principle: General theory for bimolecular chemical reactions

The log derivative version of the Kohn variational principle is reviewed in the context of a general bimolecular chemical reaction. The basis of this review, namely, the Wigner and Eisenbud general formulation of rearrangement scattering, has been well known for many years. Therefore, so as to avoid any unnecessary confusion, the relationship between their equally famous ℛ matrix theory and Kohn’s variational derivation is carefully described. The log derivative matrix is then eliminated from a basis set representation of Kohn’s principle to leave a unitary and symmetric variational expression for the scattering matrix S. This new expression is expected to find its most fruitful application in the iterative solution of very large quantum scattering problems for which transitions from only a few initial states are required.