A simple formula to calculate the ionization energies of two-, three-, and four-electron atomic ions

We have previously proposed a simple equation that is able to reproduce literature values (Moore 1970) for the ionization energies of one-electron (Lang and Smith 1981) and two-electron (Sabir Ali et al. 1984) atomic ions with very good agreement. However, our proposed equation has no firm theoretical basis, only that we consider our potential energy approach a logical alternative to the usual kinetic relativistic/quantum mechanical methodology. The results calculated from the equation give excellent agreement with literature values and differ by less than 1 eV and less than 0.02% in all cases from hydrogen up to atomic number 20. This paper provides an updated version of the two-electron equation adapted to calculate the ionization energies of three and four electron ions. Our equation also gives fairly good estimates of first electron affinities. Comparisons are made with another published equation, sources of data are described, and the calculated results are discussed.