 
Summary: Electron correlation in a hard spherical external potential: Wigner molecule formation
and hybridization
David C. Thompson and Ali Alavi*
Chemistry Department, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
Received 7 October 2003; revised manuscript received 17 December 2003; published 12 May 2004
We study a model of N electrons confined to a hard spherical box of radius R, for N 3, 4, and 5.
Unrestricted HartreeFock and full configurationinteraction calculations have been performed for high, me
dium, and low density regimes. Remarkable changes in electronic structure can be induced by varying the
effective Coulomb coupling. A lowspinhighspin transition occurs in the case of N 4 as R is increased. We
demonstrate a close connection between the propensity to form hybrid orbitals and the onset of Wigner
molecule formation.
DOI: 10.1103/PhysRevB.69.201302 PACS number s : 73.21. b, 31.10. z, 73.22. f
Studying electron correlation in model systems is a pow
erful way to obtain insight into complex phenomena associ
ated with it. In atomic and molecular systems, a distinction is
often made between dynamical and nondynamical correla
tion, the former being the principal type of correlation in the
light atoms, implying that the electrons move so as to avoid
each other in the short range. On the other hand, non
dynamical correlation is responsible for localizing electrons
