caa a22 4500 605487340 CHVBK 20210128100450.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00214-015-1705-8 doi (NATIONALLICENCE)springer-10.1007/s00214-015-1705-8 Cioslowski Jerzy Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451, Szczecin, Poland aut Partial-wave decomposition of the ground-state wavefunction of the two-electron harmonium atom [Elektronische Daten] [Jerzy Cioslowski] An exact formula for the collective occupancy of natural orbitals with an angular momentum l is derived for the ground state of the two-electron harmonium atom. For confinement strengths $$\omega $$ ω that correspond to polynomial correlation factors as well as at the weak ( $$\omega \rightarrow \infty $$ ω → ∞ ) and strong ( $$\omega \rightarrow 0$$ ω → 0 ) correlations limits, it reduces to closed-form expressions. At the former limit, a similar result obtains for the partial-wave contributions to the ground-state energy. Slow convergence of the collective occupancies to their leading large-l asymptotics provided by Hill's formula is uncovered. As the rate of convergence decreases strongly with $$\omega $$ ω , a complete breakdown of Hill's formula ensues upon the confinement strength becoming infinitesimally small. The relevance of these findings to the performance of the extrapolation schemes for the estimation of the complete-basis-set limits of quantum-mechanical observables is discussed. The Author(s), 2015 Partial-wave decomposition nationallicence Two-electron harmonium atom nationallicence Electron correlation nationallicence Theoretical Chemistry Accounts Springer Berlin Heidelberg 134/9(2015-09-01), 1-7 1432-881X 134:9<1 2015 134 214 https://doi.org/10.1007/s00214-015-1705-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00214-015-1705-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Cioslowski Jerzy Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451, Szczecin, Poland aut NATIONALLICENCE 773 0- Theoretical Chemistry Accounts Springer Berlin Heidelberg 134/9(2015-09-01), 1-7 1432-881X 134:9<1 2015 134 214