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… 
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References

SHOWING 1-10 OF 33 REFERENCES

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

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

NATURAL ORBITALS IN THE QUANTUM THEORY OF TWO-ELECTRON SYSTEMS

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

Solitonic natural orbitals.

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.

Collective natural orbital occupancies of harmonium.

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

Wigner molecules: natural orbitals of strongly correlated two-electron harmonium.

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.

The ground state of harmonium

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 limits of few-electron harmonium atoms.

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.

Long-range interactions and the sign of natural amplitudes in two-electron systems.

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 electron correlation cusp

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)

Simple approximants for natural orbitals of harmonium.

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