Classical functional sensitivity analysis of coplanar inelastic scattering for H₂ + H₂ and its isotopic analogues

Energy transfer in the coplanar, rigid-rotor H₂ + H₂ system and its isotopic analogues (H₂ + HD and HD + HD) is studied with the method of classical functional sensitivity analysis. This method allows us to measure the influence of various pieces or regions of the interaction potential on the energy-transfer processes. Five specific conclusions will be demonstrated: (1) Small-magnitude, high-order terms in the potential (as measured by an expansion in a complete set of angular functions) can affect the final energy distribution in important ways. (2) Particular terms in the potential can influence individual observables quite differently. (3) For all of the isotope combinations examined (with the possible exception of HD + HD), rotation-rotation (R ↔ R) and rotation-translation (R ↔ T) energy-transfer processes are approximately separable in the sense that varying a particular term in the potential will affect only energy transfer between a single pair of degrees of freedom. (4) The (R ↔ T) processes are much more sensitive to the potential than are the (R ↔ R) processes. (This result is partially due to the use of classical mechanics.) A consequence of the R ↔ T dominance is that the effect of altering a term in the potential responsible for transferring energy between translation and rotation of the molecule is weakly dependent on the identity (HD or H₂) of the other molecule. (5) The influence of details in the potential on energy transfer in to or out of each of a pair of identical molecules is quite sensitive to the initial rotational energy of the molecules.