Theory of resonances in three-dimensional chemical reactions. I. Feshbach analysis and computational techniques

An analysis of internal excitation resonances in three-dimensional, symmetric atom/diatom chemical reactions is presented. The description is based on the Feshbach projection operator theory and is formulated in terms of ‘‘natural collision coordinates’’ (NCC) and the NCC Hamiltonian appropriate for near-linear intermediates. The resonance theory is reviewed and developed using a computationally oriented matrix notation. Expressions are given for the level operator matrix, formation and decay amplitudes, and S-matrix elements. Computational techniques are emphasized. Symmetry relationships in the theory resulting from reaction symmetry are developed. Finally, resonance effects in cross sections for symmetric reactions are discussed. Numerical applications to a model reaction are presented and analyzed in the following paper.