Abstract
In singlet twoelectron systems, the natural occupation numbers of the oneparticle reduced density matrix are given as squares of the natural amplitudes which are defined as the expansion coefficients of the twoelectron wave function in a natural orbital basis. In this work, we relate the sign of the natural amplitudes to the nature of the twobody interaction. We show that longrange Coulombtype interactions are responsible for the appearance of positive amplitudes and give both analytical and numerical examples that illustrate how the longdistance structure of the wave function affects these amplitudes. We further demonstrate that the amplitudes show an avoided crossing behavior as function of a parameter in the Hamiltonian and use this feature to show that these amplitudes never become zero, except for special interactions in which infinitely many of them can become zero simultaneously when changing the interaction strength. This mechanism of avoided crossings provides an alternative argument for the nonvanishing of the natural occupation numbers in Coulomb systems. © 2013 AIP Publishing LLC.
Original language  English 

Article number  104110 
Pages (fromto)  19 
Number of pages  9 
Journal  Journal of Chemical Physics 
Volume  139 
Issue number  10 
DOIs  
Publication status  Published  Sep 2013 
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Journal of Chemical Physics Editor's choice
Giesbertz, Klaas (Recipient) & Robert van Leeuwen (Recipient), 2013
Prize › Academic