The formulation of Bardsley et al (Phys. Rev. A 11 1911) for evaluating the asymptotic electron exchange interaction between an alkali ion and its parent atom is extended by the use of a more accurate representation of the asymptotic wavefunction of the isolated atom and also by the inclusion of a further term in the series that accounts for the presence of the ion. The Bardsley analysis is compared with a purely numerical approach in which the Holstein–Herring integrand is constructed from a polarized wavefunction built from numerical solutions of the differential equations of Rayleigh–Schrodinger perturbation theory and the ¨ required quadrature is performed numerically. Values of the asymptotic exchange interactions are given for the molecular ions Li+ 2 , Na+ 2 , K+ 2 , Rb+ 2 and Cs+ 2 . As an example, exchange interactions for Cs+ 2 evaluated by an ab initio method are compared to those predicted by the Bardsley formula. Potentials for the lowest states of Cs+ 2 are constructed from the ab initio values matched to the asymptotic exchange and long-range polarization interactions, and these potentials are used to predict the 12+ g and 12+ u scattering lengths and low-energy charge transfer cross sections.
