Quantum reactive scattering for A + BCD→AB + CD reactions: Coupled channel distorted wave theory

This paper presents a general theoretical formalism for describing quantum reactive scattering in four atom reactions of the type A + BCD→AB + CD based on the coupled channel distorted wave method (CCDW). In this formalism, we have derived expressions for the Schrödinger equation in body-fixed axis (bfa) coordinate systems associated with the A + BCD and AB + CD arrangement channels, and we have reduced the CCDW scattering matrix to a six dimensional internal coordinate quadrature in terms of the bfa wave functions. Explicit expressions for the nonreactive (coupled channel) centrifugal and potential coupling matrices are derived for both A + BCD and AB + CD using the bfa frame isomorphic Hamiltonian. The interconnection between A + BCD and AB + CD coordinate systems is explored in detail, and it is found that the resulting CCDW scattering matrix is similar in form to that derived earlier for atom-diatom collisions, with the main conceptual difference associated with use of an Eckart frame to define the vibrational wave functions for BCD. The relation between the Eckart and scattering frames is discussed in depth. Also, the imposition of parity decoupling in the CCDW calculation is developed for both the CC Hamiltonian matrices and the distorted wave overlap.