Electron-density delocalization in many-electron atoms confined by penetrable walls: A Hartree-Fock study

The electronic structure of several many-electron atoms, confined within a penetrable spherical box, was studied using the Hartree-Fock (HF) method, coupling the Roothaan's approach with a new basis set to solve the corresponding one-electron equations. The resulting HF wave-function was employed to evaluate the Shannon entropy, S, in configuration space. Confinements imposed by impenetrable walls induce decrements on S when the confinement radius, R-c, is reduced and the electron-density is localized. For confinements commanded by penetrable walls, S exhibits an entirely different behavior, because when an atom starts to be confined, S delivers values less than those observed for the free system, in the same way that the results presented by impenetrable walls. However, from a confinement radius, S shows increments, and precisely in these regions, the spatial restrictions spread to the electron density. Thus, from results presented in this work, the Shannon entropy can be used as a tool to measure the electron density delocalization for many-electron atoms, as the hydrogen atom confined in similar conditions.