title: Collective natural orbital occupancies of harmonium.
abstract: In the harmonium atom, the collective occupancies {n(l)} of natural orbitals with different angular momenta l can be rigorously studied for those values of the confinement strength omega that lead to ground-state wave functions with correlation factors given by polynomials of kth order. Analysis of two such cases, with omega equal to 12 (k=1) and 110 (k=2), uncovers some interesting properties of {n(l)}, which turn out to be given by rational functions of pi(12) with simple coefficients. In particular, contrary to naive expectations, the collective occupancies for l>2 actually decrease upon strengthening of correlation. The explicit formulas for l-matrices and {n(l)} can be readily utilized in testing, calibration, and benchmarking of approximate implementations of the density matrix functional theory (DMFT).
authors.affiliation: Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, Germany.
authors.forename: Jerzy
authors.initials: J
authors.lastname: Cioslowski
authors.forename: Marcin
authors.initials: M
authors.lastname: Buchowiecki