17. Problem Decomposition Techniques in Quantum Mechanical Reactive Scattering

In this chapter we discuss strategies for efficiently solving quantum mechanical reactive and inelastic scattering problems using algebraic variational methods. First we review the outgoing wave variational principle. Then we review three aspects of its implementation where problem decomposition techniques are used to make the calculations efficient. The first of these involves partitioning the Hamiltonian into a distortion part that is solved numerically and a coupling part that is treated by expanding the difference of the full outgoing wave and the distortion-potential-induced part of the outgoing wave in a basis. The second involves problem decomposition in channel space or physical space in order to obtain efficient basis functions for the fully coupled problem. In this section we also propose a new pre-diagonalization technique that may be used as the basis of a divide-and-conquer approach. Finally, we consider schemes for partitioning basis functions into Hilbert subspaces as direct analogs of domain decomposition in physical subspaces.