Molecular Orbital Model for Ion Polar-Molecule Capture Collisions

Abstract

This article presents a molecular orbital model for ion polar molecule capture collisions which was developed by building on classical theoretical treatments. We replace the polarization potential with a perturbation molecular orbital potential, and assume that the molecular dipole does not change as a result of electron exchange at distances greater than or equal to the critical radius in the collision complex. Overlap integrals are introduced in this treatment of ion−molecule collision rates. For calculation of the perturbation molecular orbital potential, the overlap integral is approximated by use of Gaussian wave functions with scaled Slater atomic radii. The molecular dipole is assumed to be “locked” by the ion at the critical radius. The rotational mode of the molecular dipole along the locked axis is excited by coupling with the ion−molecule motion. The gain in rotational energy by the molecular dipole under the torque of the ion is approximated by a first-order Stark effect. Use of a Stark effect model results in the conservation of both energy and angular momentum. The net contribution of the ion−dipole interaction potential to ion−molecule capture collisions is to remove the rotational energy of the ion and dipole. The decrease in the ion polar molecule interaction potential caused by Stark effect excitation of dipole rotation accounts for the fact that the locked dipole approximation without Stark effect coupling significantly overestimates the rates of ion polar molecule collisions. Ab initio molecular orbital calculations on model systems were conducted to convert Slater atomic orbital radii into approximate molecular orbital radii by evaluating a scaling parameter, f. Experimental hydride transfer rates reflect the convolution of collision rates and subsequent hydride transfer rates. The reaction efficiency for hydride transfer is the ratio of the experimental reaction rate divided by the collision rate. Reaction efficiencies obtained using the collision model developed here are in qualitative agreement with Golden Rule reaction rate models. This result is in contrast with reaction efficiencies calculated by classical potentials that show a monotonic increase in reaction efficiency with increasing reaction free energy.