Partial-wave decomposition of the ground-state wavefunction of the two-electron harmonium atom

  • Jerzy CioslowskiEmail author
Part of the Highlights in Theoretical Chemistry book series (HITC, volume 12)


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 ω that correspond to polynomial correlation factors as well as at the weak (\(\omega \to \infty\)) and strong (\(\omega \to 0\)) correlations limits, it reduces to closedform expressions. At the former limit, a similar result obtains for the partial-wave contributions to the groundstate 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 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.


Partial-wave decomposition Two-electron harmonium atom Electron correlation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of SzczecinSzczecinPoland

Personalised recommendations