Correspondences between the Classical Electrostatic Thomson Problem and Atomic Electronic Structure

@article{LaFave2013CorrespondencesBT,
  title={Correspondences between the Classical Electrostatic Thomson Problem and Atomic Electronic Structure},
  author={Tim LaFave},
  journal={Journal of Electrostatics},
  year={2013},
  volume={71},
  pages={1029-1035}
}
  • 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… 

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References

SHOWING 1-10 OF 88 REFERENCES
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.
TLDR
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
TLDR
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
...
1
2
3
4
5
...