Density Functional Theory Applied on Confined Many-Electron Atoms

Recent progress in confined atoms and molecules: Superintegrability and symmetry breakings

“…The asymptotic expansions for the energy, Eqs. (24), for the eigenfunctions in terms of the oscillator strengths, Eq. 28, were developed by the Author in its Ref.…”

“…In fact, its Refs. [20] Comment on the electron in the field of an electric dipole moment, [21] Ground-state energy shift of He close to a surface and its relation with the scattering potential: a confinement model, [22] The hydrogen atom in a semi-infinite space with an elliptical cone boundary, [23] Lamé spheroconal harmonics in atoms and molecules, [24] Rotations of asymmetric molecules and the hydrogen atom in free and confined configurations, [25] Ladder operators for Lamé spheroconal harmonic polynomials, [26] Ladder operators for quantum systems confined by dihedral angles, [27] Complete pure dipole spheroidal electrostatic fields and sources, [28] Surface current distribution on spheres and spheroids as sources of pure quadrupole magnetic fields were reviewed in Sections 2.1-2.5, illustrating further advances previewed in [4].…”

“…"Density Functional Theory Applied on Confined Many-Electron Atoms" [24] is connected with [9] and [11], some of those connections allow us to concentrate here on Section 3 Modified Thomas-Fermi Model and Section 4 Kohn-Sham Model.…”

“…This invited review article is written against the background of W. Jaskolski´s 1996 Physics Report on "Confined manyelectron systems" [1], the fifteen chapters of "Theory of Confined Quantum Systems" in Advances in Quantum Chemistry (AQC) 2009 Vols. 57 [2][3][4][5][6][7][8][9][10] and 58 [11][12][13][14][15][16], with S.A. Cruz as Special Editor, and the nine chapters of "Electronic Structure of Quantum Confined Atoms and Molecules" [17][18][19][20][21][22][23][24][25] edited by K. A. Sen in 2014. It is interesting to contrast [1] a review of the state-of-the-art in that year by a single author, with the two sets of reviews of specific topics in the field, twenty two and twenty six years later, illustrating advances and the diversification of the field in the respective periods.…”

“…In the Monograph, its Editor pointed out in the Preface that, it deals with the simplest among the quantum confined model systems, recording the significant developments in the field subsequent to the two published volumes of Advances in Quantum Chemistry . The titles and authors can be identified in [17][18][19][20][21][22][23][24][25], recognizing common topics and Contributors in [17][18][19][20] and [24] from the previous set of reviews; here we spell out the other titles [21] "Confined Quantum Systems Using the Finile Element and Discrete Variable Representation Methods", [22] "Bound and Resonant States in Confined Atoms", [23] "Spatial and Shell-Confined One Electron Atomic and Molecular Systems: Structure and Dipole Polarizability", and [25] Concerning the use of the words superintegrability and symmetry breakings in the title of this contribution, the reader may find in [4], and in [26] of [17] these respective uses for the one-electron hydrogen atom and quantum dot, in their free and confined configurations. In fact, the Schrödinger equation for the hydrogen atom can be separated and integrated in spherical, spheroconal, prolate spheroidal and parabolic coordinates; and for the harmonic oscillator modeling one-electron quantum dots in cartesian, cylindrical and also spherical and spheroconal coordinates.…”