Natural occupation numbers: When do they vanish?
Abstract
The nonvanishing of the natural orbital (NO) occupation numbers of the oneparticle density matrix of manybody systems has important consequences for the existence of a density matrixpotential 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 twoparticle systems that in case the wavefunction is nonanalytic at its spatial diagonal (for instance, due to the presence of a Coulomb cusp) the natural orbital occupations are nonvanishing. We further derive a more general criterium for the nonvanishing of NO occupations for twoparticle wavefunctions with a certain separability structure. On the basis of this criterium we show that for a twoparticle system of harmonically confined electrons with a Coulombic interaction (the socalled Hookium) the natural orbital occupations never vanish.
 Publication:

Journal of Chemical Physics
 Pub Date:
 September 2013
 DOI:
 10.1063/1.4820419
 arXiv:
 arXiv:1306.4142
 Bibcode:
 2013JChPh.139j4109G
 Keywords:

 density functional theory;
 ground states;
 manybody problems;
 orbital calculations;
 wave functions;
 31.15.ep;
 Variational particlenumber approach;
 Physics  Atomic Physics;
 Condensed Matter  Strongly Correlated Electrons;
 Quantum Physics
 EPrint:
 15 pages, 2 figures