# Natural orbitals of the ground state of the two-electron harmonium atom

@article{Cioslowski2018NaturalOO,
title={Natural orbitals of the ground state of the two-electron harmonium atom},
author={Jerzy Cioslowski},
journal={Theoretical Chemistry Accounts},
year={2018},
volume={137},
pages={1-11}
}
• J. Cioslowski
• Published 11 November 2018
• Physics
• Theoretical Chemistry Accounts
AbstractThe radial components of the natural orbitals (NOs) pertaining to the $$^1S_+$$1S+ ground state of the two-electron harmonium atom are found to satisfy homogeneous differential equations at the values of the confinement strength $$\omega$$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…
7 Citations
• Physics
The Journal of chemical physics
• 2019
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
• Physics
The Journal of chemical physics
• 2019
The numerical trends observed in the present calculations strongly suggest that in the case of the ground state of the helium atom, the only positive-valued natural amplitude is that pertaining to the strongly occupied orbital, i.e., λ10.
• Physics
Journal of chemical theory and computation
• 2021
The leading L-3 dependence of the errors in the energies computed with nuclei-centered basis sets comprising functions with angular momenta not exceeding L is rigorously proven for the 1Σ states of
• J. Cioslowski
• Physics, Chemistry
The Journal of chemical physics
• 2020
The power-law decay of the occupation numbers of the natural orbitals is demonstrated for 1S states of systems composed of arbitrary even numbers of electrons and the implications of the presence of this cusp upon electronic structure calculations of quantum chemistry and solid-state physics are elucidated.
• Physics, Chemistry
International Journal of Quantum Chemistry
• 2019
Atoms under pressure undergo a series of processes and modification of its electronic structure. Examples are the spontaneous ionization, stabilization of excited-state configurations that result in
• Mathematics
Journal of chemical theory and computation
• 2021
The resulting formalism, in which the "on-top" two-electron density ρ2(r⃗, rₗ) solely controls the asymptotic behavior of both ψn(r ⃗) and νn at the limit of the latter becoming infinitesimally small, produces surprisingly accurate values of both quantities even for small n.

## References

SHOWING 1-10 OF 33 REFERENCES

AbstractAn 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
• Mathematics
• 1956
The wave functions for the singlet and triplet states of a two-electron system in a given nuclear framework are investigated as superpositions of configurations and are shown to be transformationally
It is shown that unusual, weakly occupied natural orbitals corresponding to additional positive-valued natural amplitudes emerge upon sufficient weakening of the confinement of the harmonium atom.
• Mathematics
The Journal of chemical physics
• 2005
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
• Physics
The Journal of chemical physics
• 2006
The occupancies at the omega-->0 limit are vanishingly small and asymptotically independent of the angular momentum, forming a geometric progression with the scale factor proportional to omega(1/3) and the common ratio of 0.0186.
• Physics
• 2000
A detailed analysis that benefits from a slate of new approximate numerical and exact asymptotic results produces highly accurate properties of the ground state of the harmonium atom as functions of
The weak-correlation asymptotics of electronic properties of harmonium atoms comprising up to four electrons are investigated and closed-form expressions are derived for the first- and second-order contributions to the Hartree-Fock and correlation energies of eight electronic states, six of which are singly determinantal and two are multi-determinantal.
• Physics
The Journal of chemical physics
• 2013
It is demonstrated that the amplitudes show an avoided crossing behavior as function of a parameter in the Hamiltonian and this feature is used to show that these amplitudes never become zero, except for special interactions in which infinitely many of them can become zero simultaneously when changing the interaction strength.
The Kais function is an exact solution of the Schrödinger equation for a pair of electrons trapped in a parabolic potential well with r12−1 electron-electron interaction. Partial wave analysis (PWA)
• Mathematics
The Journal of chemical physics
• 2005
Simple approximations to the natural orbitals (NOs) of harmonium with enforced correct short- and long-range asymptotics yield accurate bounds for the NO occupancies. In particular, expressions