Relativistic Corrections for Calculating Ionization Energies of One- to Five-Electron Isoelectronic Atomic Ions

We have previously proposed a simple empirical equation to reproduce the literature values of the ionization energies of one-electron to four-electron atomic ions with very good agreement. However, we used a potential energy approach in our equation, which has no theoretical basis. This paper discusses an alternative kinetic energy expression for one to five electrons with simple corrections for relativistic and Lamb shift effects and for two- to-five electron ions additional effects including electron relaxation and residual interactions. For calculated values of one-electron (hydrogen-like) and two electron (helium like) atomic ions, the difference with the literature values is typically 0.001% or less. Agreement with the literature values for three-, four-, and five-electron ions is 99% or better. First electron affinities calculated by our expression also agree fairly well with generally recommended values. These results show that there is strong evidence that our methodology can be developed to reliably predict, with fairly good accuracy, ionization energies of multielectron atomic ions that have not been measured. 1. Introduction A knowledge of ionization energies is essential for understanding the chemistry of the elements and other fundamental concepts, such as lattice energies of inorganic solids. With the development of quantum theory, the two-particle problem can be solved exactly and the kinetic energy of the electron in a hydrogen atom can be calculated using the Schr？dinger equation. Since the Schr？dinger equation does not take account of relativistic effects, Dirac [1] produced an equation which included a relativistic correction for the electron energy levels. However, Lamb and Retherford [2–4] in a series of experiments showed that there is a small shift in the energy levels of the hydrogen atom not accounted for by the Dirac equation. This energy shift is now commonly called the Lamb shift. Theoretical atomic energy levels were calculated from a nonrelativistic model, and then relativistic and quantum electrodynamic effects were accounted for by treating them as perturbation corrections. General availability of powerful computers allowed highly complicated theoretical calculations of the energy levels and ionization energies of hydrogen [5] and helium-like ions [6] to be performed. These sophisticated equations for one- and two-electron atomic ions, which need complex computer routines to compute, include corrections for the variation of mass with velocity, reduced mass, mass polarization, and Lamb shift, and for two-electron ions,