The Screened Atomic Potential—A Simple Explanation of the Aufbau Model

The hydrogen atom, whose electronic structure is well understood by most students of chemistry, forms the basis for the development of theories and descriptions of many-electron atoms with considerably more complex and less easily understood electronic structures. The common textbook description of many-electron atoms is generally in terms of the empirical Aufbau rules and screened nuclei, while researchers often utilize complex computations where physical transparency and understanding are often lost. In this paper we seek to provide a simple physical understanding of many-electron atoms by developing a simple but remarkably accurate representation of the screening mechanism, which explains in simple terms the crucial role of electron–electron repulsion in the energy and orbital structure of atoms. We briefly review the well-known properties of the hydrogen atom and discuss Slater’s rules, formulated in the early days of electronic structure theory. The latter provide insight and understanding of the structure of atoms at a qualitative and semi-quantitative level, achieved via the concept of shell-dependent screened effective nuclear charges. The atomic potential we propose incorporates exponential screening. The effective nuclear charge is exponentially damped, so that it varies from Z to +1 with increasing separation from the nucleus. The resulting orbital energies are not only consistent with the Aufbau rules, but also agree well with Hartree–Fock results. This model of screening is, therefore, well-suited to the study of many-electron atoms, in particular, the role of electron–electron repulsion and its simple treatment via nuclear screening.