Higher Ionization Energies of Atoms with Density Functional Theory

Uri Argaman, Eli Kraisler and Guy Makov

To calculate the ground state energy of many-electron systems, such as atoms, molecules and solids, it is necessary to solve the many-electron Schrödinger equation. This equation does not have an analytic solution, and the numerical solution is not straightforward. DFT is an alternative formulation of quantum mechanics in which it is possible to calculate the total energy and the charge density of many electron systems in the ground state. In practice, it is necessary to use uncontrolled approximations that must be verified against experimental data.  Atoms and ions are simple systems, where the approximations of DFT can be easily tested. The ionization energy is a quantity that has been measured experimentally to high accuracy, and can also be easily calculated as the difference between the ground state energy of the atom or ion and that of the ion with one electron less. We have calculated the higher ionization energies using DFT of all the experimentally measured light elements. We find that the overall agreement with experiment is very good, less than 3%. However, surprisingly we find that the error relative to experimental data depends on the electronic configuration of the ion and exhibits a specific pattern of dependence.