Computational methods to study the formation of small molecules by radiative association

Abstract

To form a stable molecule by association of two colliding fragments, energy must be removed or else the fragments will eventually dissociate again. Energy can be removed by a third body and by emission of a photon, where the latter process is termed radiative association. Radiative association is a ubiquitous process for forming molecules, albeit not so well known as on Earth it is normally outcompeted by three body collisions. In interstellar space however, particularly in regions with little dust (few grains), it can be important. There are only few experimental studies of radiative association as the process is improbable and therefore hard to measure. We will briefly mention the experimental work but our main focus is on theoretical approaches to calculate radiative association cross sections and thermal rate constants. We limit the descriptions to the formation of diatomic molecules. We begin with an introduction to and overview of radiative association. This is followed by a brief section on how cross sections are related to the thermal rate constant. Thereafter we describe methods for obtaining radiative association cross sections, with a bias towards methods that are our own favorites. This will include quantum mechanically based perturbation theory and an optical potential approach that is also quantum mechanically based. From the optical potential method the derivation of a semi-classical method is given. We also describe a recent classical approach that is applicable to transitions within the same electronic state, which the semi-classical approach is not. The semi-classical and classical methods do not treat resonances, which are of quantal origin. We therefore describe Breit–Wigner theory for treating the resonance contribution to the cross sections. Thereafter we review the techniques that are used in the quantum dynamics calculations themselves. The methods discussed are then illustrated in three applications to the formation of diatomic molecules, viz. HF, CO and CN. We end with concluding remarks and summary. In this review we do not discuss electronic structure calculations for obtaining the potential energy and dipole curves that are used in the dynamics calculations.