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

Abstract

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, Sᵖ, in configuration space. Confinements imposed by impenetrable walls induce decrements on Sᵖ when the confinement radius, Rc, is reduced and the electron-density is localized. For confinements commanded by penetrable walls, Sᵖ exhibits an entirely different behavior, because when an atom starts to be confined, Sᵖ 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, Sᵖ 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.