# 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

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.

### 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…

### Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model

- Physics
- 2017

The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle…

### Approximate energy functionals for one-body reduced density matrix functional theory from many-body perturbation theory

- MathematicsThe European Physical Journal B
- 2018

Abstract
We develop a systematic approach to construct energy functionals of the one-particle reduced density matrix (1RDM) for equilibrium systems at finite temperature. The starting point of our…

### 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).
Within RDMFT the ground-state properties of a…

### Invertibility of the retarded response functions for initial mixed states: application to one-body reduced density matrix functional theory

- Physics
- 2016

ABSTRACT Recently, I have derived conditions to characterise the kernel of the retarded response function, under the assumption that the initial state is a ground state. In this paper, I demonstrate…

### 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.

### Invertibility of retarded response functions for Laplace transformable potentials: Application to one-body reduced density matrix functional theory.

- MathematicsThe Journal of chemical physics
- 2015

A theorem for the invertibility of arbitrary response functions is presented under the following conditions: the time dependence of the potentials should be Laplace transformable and the initial…

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