Collisions in a noncentral field: A variational and trajectory investigation of ion–dipole capture

Variational rate theory and trajectory methods are used to investigate the classical dynamics of capture on a noncentral long range potential. The ion–dipole surface is investigated in detail. An upper bound to the true thermal capture rate constant is derived using the variational approach. The upper bound is independent of the moment of inertia of the rotor and has only a multiplicative inverse square root dependence on the system reduced mass. For the ion–dipole surface the upper bound is in excellent agreement with trajectory calculations of the true capture rate constant and with experimental data on thermal heavy particle transfer rate constants between ions and polar neutrals. The trajectory calculations are done using an angular momentum conserved coordinate system which eliminates the need to solve two sets of Hamilton’s equations. A precise criterion for capture is derived and is used in the trajectory calculations. Reduced variables are introduced for the ion–dipole surface and it is shown that the ratio of the true thermal capture rate constant to the Langevin rate constant depends at most on only two reduced variables. An upper bound to the values of the impact parameter that can lead to capture is also derived and is compared to some earlier trajectory results of Dugan and Magee. It is shown that the upper bound arises from a noncentral field periodic orbit.