Many‐electron atom confinement by a penetrable spherical box

Abstract

AbstractA confinement model for many‐electron atoms enclosed by a spherical boundary with finite‐barrier potential height is presented. The model is based on the Thomas–Fermi–Dirac–Weizsäcker (TFDλW) functional formalism using known properties of the orbital electron densities and constitutes a natural extension of a previously published report for the case of infinitely hard walls [Cruz et al., Int J Quantum Chem, 2005, 102, 897]. The confining barrier potential is considered as a step‐like function of finite height V0. This assumption demands of the appropriate description of the TFDλW energy functional for both the interior and exterior regions together with corresponding ansatz orbital density representations, subject to continuity boundary conditions at the wall. For a given cage radius R and confining barrier height V0, the total ground‐state energy is variationally optimized with respect to the characteristic parameters defining the interior and exterior orbital densities. The total ground‐state energy and corresponding electronic density are obtained as function of barrier height and cage radius for many‐electron atoms and ions. The model is explicitly applied to He, Li, C, and Ne and various ionic species for barrier heights (atomic units) V0 = 0, 5, and ∞. Given a barrier height V0, the results are presented for the critical cage size to produce one or more unbound electrons—yet, confined by the box—until reaching threshold size values for which electron escape from the confinement region take place. © 2008 Wiley Periodicals, Inc. Int. J. Quantum Chem, 2008