One-electron reduced density matrices of strongly correlated harmonium atoms

The Journal of Chemical Physics
Jerzy Cioslowski

Abstract

Explicit asymptotic expressions are derived for the reduced one-electron density matrices (the 1-matrices) of strongly correlated two- and three-electron harmonium atoms in the ground and first excited states. These expressions, which are valid at the limit of small confinement strength ω, yield electron densities and kinetic energies in agreement with the published values. In addition, they reveal the ω(5/6) asymptotic scaling of the exchange components of the electron-electron repulsion energies that differs from the ω(2/3) scaling of their Coulomb and correlation counterparts. The natural orbitals of the totally symmetric ground state of the two-electron harmonium atom are found to possess collective occupancies that follow a mixed power/Gaussian dependence on the angular momentum in variance with the simple power-law prediction of Hill's asymptotics. Providing rigorous constraints on energies as functionals of 1-matrices, these results are expected to facilitate development of approximate implementations of the density matrix functional theory and ensure their proper description of strongly correlated systems.

References

Sep 1, 2006·The Journal of Chemical Physics·Jerzy Cioslowski, Marcin Buchowiecki
Sep 1, 2006·The Journal of Chemical Physics·Jerzy Cioslowski, Katarzyna Pernal
Dec 3, 2008·The Journal of Chemical Physics·Daniel R RohrEvert Jan Baerends
Oct 5, 2010·Physical Chemistry Chemical Physics : PCCP·Paola Gori-Giorgi, Michael Seidl
May 23, 2012·The Journal of Chemical Physics·Jerzy CioslowskiEduard Matito
Sep 26, 2012·Physical Review Letters·David A Mazziotti
Dec 18, 2013·The Journal of Chemical Physics·Jerzy Cioslowski

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Citations

Feb 8, 2016·The Journal of Chemical Physics·Vincent Tognetti, Pierre-François Loos
Dec 10, 2015·The Journal of Chemical Physics·Jerzy CioslowskiEduard Matito
Jun 24, 2016·The Journal of Chemical Physics·Krzysztof Strasburger
Aug 9, 2016·The Journal of Chemical Physics·Jerzy Cioslowski
Jan 26, 2017·Physical Chemistry Chemical Physics : PCCP·Mauricio Rodriguez-MayorgaEduard Matito

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