The Five-Electron Case of Thomson's Problem

We give a rigorous computer-assisted proof that the triangular bipyramid is the unique configuration of five points on the sphere that globally minimizes the Coulomb (1/r) potential. We also prove the same result for the (1/r 2 ) potential. The main mathematical contribution of the paper is a fairly...

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Bibliographic Details
Published in:Experimental mathematics 2013-04, Vol.22 (2), p.157-186
Main Author: Schwartz, Richard Evan
Format: Article
Language:English
Subjects:
5-electron problem
51-04
electron configurations
power-law potential
triangular bi-pyramid
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Summary:We give a rigorous computer-assisted proof that the triangular bipyramid is the unique configuration of five points on the sphere that globally minimizes the Coulomb (1/r) potential. We also prove the same result for the (1/r 2 ) potential. The main mathematical contribution of the paper is a fairly efficient energy estimate that works for any number of points and any power-law potential.
ISSN:1058-6458
1944-950X
DOI:10.1080/10586458.2013.766570