Reaction Rate Constant for Radiative Association of CF$^+$

Reaction rate constants and cross sections are computed for the radiative association of carbon cations ($\text{C}^+$) and fluorine atoms ($\text{F}$) in their ground states. We consider reactions through the electronic transition $1^1\Pi \rightarrow X^1\Sigma^+$ and rovibrational transitions on the $X^1\Sigma^+$ and $a^3\Pi$ potentials. Semiclassical and classical methods are used for the direct contribution and Breit--Wigner theory for the resonance contribution. Quantum mechanical perturbation theory is used for comparison. A modified formulation of the classical method applicable to permanent dipoles of unequally charged reactants is implemented. The total rate constant is fitted to the Arrhenius--Kooij formula in five temperature intervals with a relative difference of $<3\:\%$. The fit parameters will be added to the online database KIDA. For a temperature of $10$ to $250\:\text{K}$, the rate constant is about $10^{-21}\:\text{cm}^3\text{s}^{-1}$, rising toward $10^{-16}\:\text{cm}^3\text{s}^{-1}$ for a temperature of $30{,}000\:\text{K}$.