# Generalization of the Kohn-Sham system that can represent arbitrary one-electron density matrices

## Abstract

Density functional theory is currently the most widely applied method in electronic structure theory. The Kohn-Sham method, based on a fictitious system of noninteracting particles, is the workhorse of the theory. The particular form of the Kohn-Sham wave function admits only idempotent one-electron density matrices whereas wave functions of correlated electrons in post-Hartree-Fock methods invariably have fractional occupation numbers. Here we show that by generalizing the orbital concept and introducing a suitable dot product as well as a probability density, a noninteracting system can be chosen that can represent the one-electron density matrix of any system, even one with fractional occupation numbers. This fictitious system ensures that the exact electron density is accessible within density functional theory. It can also serve as the basis for reduced density matrix functional theory. Moreover, to aid the analysis of the results the orbitals may be assigned energies from a mean-field Hamiltonian. This produces energy levels that are akin to Hartree-Fock orbital energies such that conventional analyses based on Koopmans' theorem are available. Lastly, this system is convenient in formalisms that depend on creation and annihilation operators as they are trivially applied to single-determinant wave functions.

- Authors:

- Publication Date:

- Research Org.:
- Brookhaven National Lab. (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23)

- OSTI Identifier:
- 1287089

- Alternate Identifier(s):
- OSTI ID: 1254212

- Report Number(s):
- BNL-112150-2016-JA

Journal ID: ISSN 2469-9926

- Grant/Contract Number:
- SC00112704; DESC0012704

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review A

- Additional Journal Information:
- Journal Volume: 93; Journal Issue: 5; Journal ID: ISSN 2469-9926

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Kohn-Sham system; density; matrices; correlated electrons; one-electron

### Citation Formats

```
Hubertus J. J. van Dam. Generalization of the Kohn-Sham system that can represent arbitrary one-electron density matrices. United States: N. p., 2016.
Web. doi:10.1103/PhysRevA.93.052512.
```

```
Hubertus J. J. van Dam. Generalization of the Kohn-Sham system that can represent arbitrary one-electron density matrices. United States. doi:10.1103/PhysRevA.93.052512.
```

```
Hubertus J. J. van Dam. Wed .
"Generalization of the Kohn-Sham system that can represent arbitrary one-electron density matrices". United States. doi:10.1103/PhysRevA.93.052512. https://www.osti.gov/servlets/purl/1287089.
```

```
@article{osti_1287089,
```

title = {Generalization of the Kohn-Sham system that can represent arbitrary one-electron density matrices},

author = {Hubertus J. J. van Dam},

abstractNote = {Density functional theory is currently the most widely applied method in electronic structure theory. The Kohn-Sham method, based on a fictitious system of noninteracting particles, is the workhorse of the theory. The particular form of the Kohn-Sham wave function admits only idempotent one-electron density matrices whereas wave functions of correlated electrons in post-Hartree-Fock methods invariably have fractional occupation numbers. Here we show that by generalizing the orbital concept and introducing a suitable dot product as well as a probability density, a noninteracting system can be chosen that can represent the one-electron density matrix of any system, even one with fractional occupation numbers. This fictitious system ensures that the exact electron density is accessible within density functional theory. It can also serve as the basis for reduced density matrix functional theory. Moreover, to aid the analysis of the results the orbitals may be assigned energies from a mean-field Hamiltonian. This produces energy levels that are akin to Hartree-Fock orbital energies such that conventional analyses based on Koopmans' theorem are available. Lastly, this system is convenient in formalisms that depend on creation and annihilation operators as they are trivially applied to single-determinant wave functions.},

doi = {10.1103/PhysRevA.93.052512},

journal = {Physical Review A},

number = 5,

volume = 93,

place = {United States},

year = {2016},

month = {4}

}

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