An ab initio calculation of the potential energies was made for the electronic states of ionic excimer molecules consisting of rare gases (Rg = Ne, Ar, Kr and Xe) and alkali metals (A = K and Rb). The calculation included the ground 11∑+ states and the first excited singlet 21∑+, which correspond to the Rg(1S) + A+(1S) and Rg+(2P) + A(2S) separate limits, respectively. The calculated results predict that the emission based on transitions from the 21∑+(ν'=0) states to the higher ν'' levels of the 11∑+ states is characterised by the highest relative transition probabilities, which are promising for lasing in the vacuum and extreme ultraviolet (VUV/XUV) spectral ranges. Moreover, bound — free VUV emission bands were observed for electron-beam-pumped gas mixtures of Xe or Kr with a hot Rb or Cs alkali vapour. The observed four emission bands were assigned to the 21∑+ →11∑+ transitions in the rare-gas — alkali ionic excimers Xe+Rb, Kr+Rb, Xe+Cs, and Kr+Cs, respectively.