# Natural occupation numbers: when do they vanish?

@article{Giesbertz2013NaturalON, title={Natural occupation numbers: when do they vanish?}, author={Klaas J. H. Giesbertz and Robert van Leeuwen}, journal={The Journal of chemical physics}, year={2013}, volume={139 10}, pages={ 104109 } }

The non-vanishing of the natural orbital (NO) occupation numbers of the one-particle density matrix of many-body systems has important consequences for the existence of a density matrix-potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the extended Koopmans' theorem. On the basis of Weyl's theorem we give a connection between the differentiability properties of the ground state wavefunction and the rate at which the natural occupations…

## 30 Citations

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

- PhysicsThe Journal of chemical physics
- 2013

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### Universalities among natural orbitals and occupation numbers pertaining to ground states of two electrons in central potentials.

- PhysicsThe 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…

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- 2017

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- 2018

Abstract
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- ChemistryThe Journal of chemical physics
- 2014

Extensions of the Löwdin-Shull functional for the breaking of a single electron pair bond in N-electron molecules are presented, using LiH, BeH(+), and Li2 molecules as prototypes.

### Reduced density-matrix functional theory: Correlation and spectroscopy

- Physics
- 2015

This thesis addresses the description of electron correlation and spectroscopy within the context of Reduced Density-Matrix Functional Theory (RDMFT).
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- 2016

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### Solitonic natural orbitals.

- PhysicsThe Journal of chemical physics
- 2018

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.

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

- PhysicsTheoretical Chemistry Accounts
- 2018

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…

### Natural amplitudes of the ground state of the helium atom: Benchmark calculations and their relevance to the issue of unoccupied natural orbitals in the H2 molecule.

- PhysicsThe 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.

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