false
en
2018-12-01
https://scigraph.springernature.com/explorer/license/
research_article
173
articles
The radial components of the natural orbitals (NOs) pertaining to the 1S+ ground state of the two-electron harmonium atom are found to satisfy homogeneous differential equations at the values of the confinement strength ω at which the respective correlation factors are given by polynomials. Together with the angular momentum l of the NOs, the degrees of these polynomials determine the orders of the differential equations, eigenvalues of which (arising from well-defined boundary conditions) yield the natural amplitudes. In the case of l=0, analysis of these equations uncovers certain properties of the NOs whereas application of a WKB-like approximation produces asymptotic expressions for both the NOs and the corresponding natural amplitudes that hold when the latter are small negative numbers. Extensive numerical calculations reveal that these expressions remain valid for arbitrary values of ω. The approximate s-type NOs, which are remarkably accurate at sufficiently small radial distances and exhibit universal scaling, differ qualitatively from the eigenfunctions of the core Hamiltonian even at the ω→∞ limit of vanishing electron correlation.
2019-04-10T17:45
2018-12
https://link.springer.com/10.1007%2Fs00214-018-2362-5
Natural orbitals of the ground state of the two-electron harmonium atom
readcube_id
f44b8a7b20e6a01d9c4bbbbb3462665a59d10f67dc31a095e5a452ac7b039b86
Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451, Szczecin, Poland
Max Planck Institute for the Physics of Complex Systems
Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187, Dresden, Germany
12
Jerzy
Cioslowski
Numerical and Computational Mathematics
Springer Nature - SN SciGraph project
137
doi
10.1007/s00214-018-2362-5
1432-881X
1432-2234
Theoretical Chemistry Accounts
Mathematical Sciences
pub.1109809107
dimensions_id