Longrange interactions and the sign of natural amplitudes in twoelectron systems
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.
 Publication:

Journal of Chemical Physics
 Pub Date:
 September 2013
 DOI:
 10.1063/1.4820418
 arXiv:
 arXiv:1306.4556
 Bibcode:
 2013JChPh.139j4110G
 Keywords:

 atomphoton collisions;
 energy level crossing;
 wave functions;
 32.80.Xx;
 31.15.X;
 Level crossing and optical pumping;
 Alternative approaches;
 Physics  Atomic Physics;
 Condensed Matter  Strongly Correlated Electrons;
 Physics  Computational Physics;
 Quantum Physics
 EPrint:
 10 pages, 4 figures