Simple Physical Model for the Estimation of Irreversible Dissociation Rates for Bimolecular Complexes

In this article, we propose a simple method of estimating
dissociation
rates of bimolecular van der Waals complexes (“wells”),
rooted in rigid body dynamics, requiring as input parameters only
the bimolecular binding energy, together with the intermolecular equilibrium
distance and moments of inertia of the complex. The classical equations
of motion are solved for the intermolecular and rotational degrees
of freedom in a coordinate system considering only the relative motion
of the two molecules, thus bypassing the question of whether the energy
of the complex is statistically distributed. Well-escaping trajectories
are modeled from these equations, and the escape rate as a function
of relative velocity and angular momentum is fitted to an empirical
function, which is then integrated over a probability distribution
of said quantities. By necessity, this approach makes crude assumptions
on the shape of the potential well and neglects the impact of energy
quantization, and, more crucially, the coupling between the degrees
of freedom included in the equations of motion with those that are
not. We quantify the error caused by the first assumption by comparing
our model potential with a quantum chemical potential energy surface
(PES) and show that while the model does make several compromises
and may not be accurate for all classes of bimolecular complexes,
it is able to produce physically consistent dissociation rate coefficients
within typical atmospheric chemistry confidence intervals for triplet
state alkoxyl radical complexes, for which the detailed balance approach
has been shown to fail.