Universalities among natural orbitals and occupation numbers pertaining to ground states of two electrons in central potentials
Although both the natural orbitals (NOs) {ψnlm(r→)} and their occupation numbers {νnl} pertaining to the ground state of two electrons confined by a central potential are completely determined by the spatial component Ψ(r→1,r→2) of the underlying wavefunction through a homogeneous Fredholm equation...
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Veröffentlicht in: | The Journal of chemical physics 2019-11, Vol.151 (18), p.184107-184107 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | Although both the natural orbitals (NOs) {ψnlm(r→)} and their occupation numbers {νnl} pertaining to the ground state of two electrons confined by a central potential are completely determined by the spatial component Ψ(r→1,r→2) of the underlying wavefunction through a homogeneous Fredholm equation of the second kind in which Ψ(r→1,r→2) plays the role of the kernel, for the species with a single positive-valued natural amplitude that corresponds to the strongly occupied NO (“the normal sign pattern”), these quantities turn out to depend almost entirely on the “on-top” wavefunction Ψ(r→,r→). For such species, for which the occupation numbers are found to have the large-n asymptotics of n−8, a universal expression involving only Ψ(r→,r→) that reproduces the weakly occupied NOs with remarkable accuracy is inferred from the electron-electron coalescence cusp in Ψ(r→1,r→2). These theoretical predictions are fully confirmed by comparisons among the benchmark-quality NOs computed for the helium atom, the isoelectronic cations with the nuclear charges ranging from 3 to 5, and the two-electron harmonium atom at the limit of an infinitely strong confinement. |
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ISSN: | 0021-9606 1089-7690 |
DOI: | 10.1063/1.5123669 |