Correspondences between the Classical Electrostatic Thomson Problem and Atomic Electronic Structure

  title={Correspondences between the Classical Electrostatic Thomson Problem and Atomic Electronic Structure},
  author={Tim LaFave},
  journal={Journal of Electrostatics},
  • T. LaFave
  • Published 1 December 2013
  • Physics
  • Journal of Electrostatics
Abstract Correspondences between the Thomson problem and atomic electron shell-filling patterns are observed as systematic non-uniformities in the distribution of potential energy necessary to change configurations of N ≤ 100 electrons into discrete geometries of neighboring N − 1 systems. These non-uniformities yield electron energy pairs, intra-subshell pattern similarities with empirical ionization energy, and a salient pattern that coincides with size-normalized empirical ionization… 

Figures from this paper

Discrete transformations in the Thomson Problem
Abstract A significantly lower upper limit to minimum energy solutions of the electrostatic Thomson Problem is reported. A point charge is introduced to the origin of each N -charge solution. This
Coulomb potential and energy of a uniformly charged cylindrical shell
Abstract Knowledge of electrical potential and energy is important to systems where electrostatic forces play a role. We calculate exactly the electrostatic potential of a uniformly charged
Electrostatic interaction energy between two coaxial parallel uniformly charged disks
Abstract We calculate exactly the electrostatic interaction energy between two coaxial parallel uniformly charged infinitely thin disks. For the sake of generality, it is assumed that the disks have
Spatial Relative Equilibria and Periodic Solutions of the Coulomb $$(n+1)$$-Body Problem
We study a classical model for the atom that considers the movement of n charged particles of charge −1 (electrons) interacting with a fixed nucleus of charge μ > 0. We show that two global branches
Electrostatic potential energy stored in a hemispherical surface with uniform surface charge distribution
Abstract We report an exact result for the electrostatic potential energy stored in a hemispherical surface with uniform surface charge density. This system lacks the spherical symmetry of a
Interaction energy of a pair of identical coplanar uniformly charged nanodisks
We consider a nanosystem consisting of two coplanar uniformly charged nanodisks that are coupled via Coulomb forces. Such a model represents a typical situation encountered in two-dimensional
"Star" morphologies of charged nanodrops comprised of conformational isomers.
Simulation-based phenomenology of the spatial distribution of conformational isomers surrounding a central macroion in a charged droplet with linear dimensions in the nanometer range finds that at a high charge state of the buckyball, the nearest layer to the macroion comprises the conformers with the highest dipole moment.
Minimizing Energy of P oint Charges on a Sphere using Symbiotic Organisms Search Algorithm
Determination of the optimal configurations of �� identical point charges on a unit sphere, known as Thomson's problem, is a well-known energy optimization problem in physics. In this paper we have
Computational and Analytical Modelling of Droplet-Macroion Interactions
Charged droplets involving macromolecules undergo distinct disintegration mechanisms and shape deformations as a consequence of droplet-macroion interactions. Three general classes of
Distributing many points on spheres: Minimal energy and designs
This survey discusses recent developments in the context of spherical designs and minimal energy point configurations on spheres, and proves that point sets minimising the discrete Riesz energy on S d in the hypersingular case are asymptotically uniformly distributed.


Shell filling of artificial atoms within density-functional theory
The electronic structures of three-dimensional quantum dots described by parabolic and nonparabolic confinements are calculated using spin-density-functional theory. For representative cases we
Structure and dynamics of spherical crystals characterized for the Thomson problem
Candidates for global minima of the Thomson problem for N charges on a sphere are located for N 400 and selected sizes up to N=972. These results supersede many of the lowest minima located in
Electronic structure of three-dimensional quantum dots
Abstract:We study the electronic structure of three-dimensional quantum dots using the Hartree-Fock approximation. The confining potential of the electrons in the quantum dot is assumed to be
Crystalline order on a sphere and the generalized Thomson problem.
Predictions from the continuum theory for the ground state energy agree with numerical simulations of long range power law interactions of the form 1/r(gamma) (0<gamma<2) to four significant figures.
Symmetric patterns of dislocations in Thomson’s problem
Determination of the classical ground state arrangement of $N$ charges on the surface of a sphere (Thomson's problem) is a challenging numerical task. For special values of $N$ we have obtained using
Structure and rearrangements of small trapped-ion clusters.
  • Wales, Lee
  • Physics, Medicine
    Physical review. A, Atomic, molecular, and optical physics
  • 1993
The potential-energy surfaces of clusters composed of identical charged particles confined by an isotropic harmonic potential are investigated with particular reference to rearrangement mechanisms. A
Ordering and phase transitions of charged particles in a classical finite two-dimensional system.
  • Bedanov, Peeters
  • Physics, Medicine
    Physical review. B, Condensed matter
  • 1994
A Monte Carlo study of phase transitions in a finite two-dimensional system of charged classical particles which are confined by a circular parabolic or hard-wall well and the results are compared with Wigner crystallization in the infinite 2D system.
Many-electron artificial atoms
Artificial atoms, i.e., systems of excess electrons confined in semiconductor quantum dots, are studied by the unrestricted Hartree-Fock method. We consider a spherical quantum dot embedded in an
Simulation of electronic properties and capacitance of quantum dots
The chemical potential and the capacitance of a 2D circular model quantum dot have been investigated for GaAs, InSb, and Si material parameters, covering a range from a few nanometers to micrometer
Why charges go to the surface: A generalized Thomson problem
We study a variant of the generalized Thomson problem in which n particles are confined to a neutral sphere and interacting by a 1/rγ potential. It is found that for γ ≤ 1 the electrostatic repulsion