Microscopic reaction rates in ion/molecule reactions: effects of uncoupled modes

Abstract

A new expression for microscopic rate coefficients is deduced for reactions with a simple-fission transition state wherein certain modes become uncoupled from the reaction coordinate at long range. The new expression, which involves a modification to the standard RRKM result, takes account of this uncoupling, thereby incorporating features inherent in capture models. Application to the case of ion/dipole reactions is considered, where only the hindered dipole rotation is coupled with the reaction coordinate at large separations. When implemented variationally, the new expression is shown analytically to produce in the high-pressure limit a capture-rate expression equivalent to that of Chesnavich, Su, and Bowers. This provides an important conceptual connection between the RRKM approach to ion/dipole reactions, which includes all degrees of freedom and may be applied at any pressure, and that of capture theories (which apply only in the high-pressure limit) in which only those degrees of freedom that are coupled with the reaction coordinate at long range are included. Neglect of uncoupling in conventional RRKM theory can lead to an overestimate (typically by ca. 50%) of ion/molecule rate coefficients at high pressures; the error is however negligible at low pressures.