The dimensionality and choice of effective Hamiltonians for molecular collisions

The flexibility in choice of effective Hamiltonians is illustrated by considering various different dimensionality reducing procedures. Only a few members of the entire family of effective Hamiltonians have thus far been employed in actual computations. All the effective Hamiltonians are presented for two colliding molecules, and the reduced atom-molecule situation is also considered. The two-molecule case in body-fixed coordinates is treated in more detail since it has not been extensively examined before. Exactly analogous space-fixed and body-fixed dimensionality reductions are shown to be possible by appropriate selection and coupling of states. The available ranges of computing expense are discussed and the various methods related in these terms. Computing time and accuracy requirements are examined in regard to choosing an effective Hamiltonian. Further avenues of pursuit and calculations are suggested by these considerations.