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Natural occupation numbers: When do they vanish?

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Giesbertz, K., & van Leeuwen, R. (2013). Natural occupation numbers: When do they vanish?. Journal of Chemical Physics, 139(10), Article 104109. https://doi.org/10.1063/1.4820419
Published in
Journal of Chemical Physics
Authors
Giesbertz, Klaas |
van Leeuwen, Robert
Date
2013
Discipline
FysiikkaNanoscience CenterPhysicsNanoscience Center
Copyright
© 2013 AIP Publishing LLC. Published in this repository with the kind permission of the publisher.

 
The non-vanishing of the natural orbital (NO) occupation numbers of the one-particle density matrix of many-body systems has important consequences for the existence of a density matrix-potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the extended Koopmans’ theorem. On the basis of Weyl’s theorem we give a connection between the differentiability properties of the ground state wavefunction and the rate at which the natural occupations approach zero when ordered as a descending series. We show, in particular, that the presence of a Coulomb cusp in the wavefunction leads, in general, to a power law decay of the natural occupations, whereas infinitely differentiable wavefunctions typically have natural occupations that decay exponentially. We analyze for a number of explicit examples of two-particle systems that in case the wavefunction is non-analytic at its spatial diagonal (for instance, due to the presence of a Coulomb cusp) the natural orbital occupations are non-vanishing. We further derive a more general criterium for the non-vanishing of NO occupations for two-particle wavefunctions with a certain separability structure. On the basis of this criterium we show that for a two-particle system of harmonically confined electrons with a Coulombic interaction (the so-called Hookium) the natural orbital occupations never vanish. ...
Publisher
American Institute of Physics
ISSN Search the Publication Forum
1089-7690
Keywords
theoretical nanoscience
DOI
https://doi.org/10.1063/1.4820419
URI

http://urn.fi/URN:NBN:fi:jyu-201601191154

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/23208547

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