The classical Langevin rate constant for ion/molecule capture: when, if at all, is it constant?

Abstract

Using the statistical adiabatic channel model (SACM) to estimate the rate of capture of an ion by a spherically symmetrical molecule, and including quantization of the orbital momentum, leads to the reduced capture rate constant that depends on two dimensionless parameters characterizing the system. The form of such a dependence indicates, however, that for all of the typical ions as well as for all of the typical spherical molecules the capture rate constant approximates to the classical Langevin rate constant. The rate can only be appreciably faster if the system features a very small reduced mass, for instance, a thermal electron plus a molecule. Also the importance of two quantum effects, the overbarrier reflection from the potential barrier and the tunnelling through this barrier, was examined with the use of three different barriers to approximate the potential barrier for the polarization complex. The functions that describe this barrier realistically, the symmetrical Eckart function and the Dirac comb, indicate that any contribution to the capture rate constant for all of the ion-molecule systems considered from the former effect can be ignored over the whole range of temperatures. The latter effect, tunnelling through the barrier, is important but only from the systems that feature reduced masses so small as to become physically unrealistic. The physically realistic systems do not undergo any tunnelling unless the temperature is extremely low, decreasing below the characteristic rotational temperature of the molecule.