Theoretical Estimation of the Radiative Association Rate between Mg⁺ and HCN(X¹Σ⁺)

The radiative association rate of HCN with Mg⁺, which is assumed to be the initial step in the formation of MgCN in the gas phase of circumstellar envelopes around evolved stars, is evaluated using quantum methods. To this end, an analytical model of the potential energy surface is obtained from a large grid of ab initio points. The bound states of the complex are computed for a few lower values of the total angular momentum but are found to be too numerous to allow a full close-coupling approach. The J-shifting approximation is then employed to determine the radiative association rate by solving the system's driven equations. The results obtained using this approach are compared with those obtained using a statistical approach and confirm the validity of the MgCN formation mechanism in these environments.