Ion–polar molecule encounters

It is permissible to assume that the rate coefficient for collisions between ions and polar molecules does not depend on the moment of inertia of the latter because the rotation time is brief compared with the collision time. On taking the moment of inertia to be vanishingly small the classical collision problem can be solved exactly when the angular momentum vector is normal to the orbital plane. Use is made of the adiabatic invariance of ∮ p d q /2π in which p is an appropriate momentum and q is the conjugate coordinate. This adiabatic invariant fixes the change in the rotational energy in moving from an infinite separation to any chosen position. The average dipole orientation is thereby determined, which fixes the force acting. The potential energy function (including due allowance for the rotational energy stored) is now written down and an integral expression for the primitive rate coefficient is thence obtained. The ratio of the primitive rate coefficient to the Langevin rate coefficient depends only on the initial rotational energy and on the dimensionless parameter β = 2 αkT/D 2 , where α is the polarizability, D is the dipole moment and T is the temperature. Extensive computations have been performed. Tables are presented giving the primitive rate coefficient and also approximations to the thermally averaged rate coefficients for linear and for spherical top molecules.