# A well-scaling natural orbital theory

## Abstract

Here, we introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled approximations to the two-particle density matrix that yield algebraic scaling in general, and Hartree–Fock scaling in its seniority-zero version. Results from the latter version for small molecular systems are compared with those of highly accurate quantum-chemical computations. The energies lie above full configuration interaction calculations, close to doubly occupied configuration interaction calculations. Their accuracy is considerably greater than that obtained from current density-functional theory approximations and from current functionals of the oneparticle density matrix.

- Authors:

- The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste (Italy)
- Rutgers Univ., Piscataway, NJ (United States). Dept. of Physics and Astronomy; Princeton Univ., NJ (United States). Dept. of Chemistry
- Princeton Univ., NJ (United States). Dept. of Chemistry and Dept. of Physics

- Publication Date:

- Research Org.:
- Princeton Univ., NJ (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1430121

- Grant/Contract Number:
- FG02-05ER46201

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Proceedings of the National Academy of Sciences of the United States of America

- Additional Journal Information:
- Journal Volume: 113; Journal Issue: 46; Journal ID: ISSN 0027-8424

- Publisher:
- National Academy of Sciences, Washington, DC (United States)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEAR CHEMISTRY; electronic structure; correlation; density matrix

### Citation Formats

```
Gebauer, Ralph, Cohen, Morrel H., and Car, Roberto.
```*A well-scaling natural orbital theory*. United States: N. p., 2016.
Web. doi:10.1073/pnas.1615729113.

```
Gebauer, Ralph, Cohen, Morrel H., & Car, Roberto.
```*A well-scaling natural orbital theory*. United States. doi:10.1073/pnas.1615729113.

```
Gebauer, Ralph, Cohen, Morrel H., and Car, Roberto. Tue .
"A well-scaling natural orbital theory". United States.
doi:10.1073/pnas.1615729113. https://www.osti.gov/servlets/purl/1430121.
```

```
@article{osti_1430121,
```

title = {A well-scaling natural orbital theory},

author = {Gebauer, Ralph and Cohen, Morrel H. and Car, Roberto},

abstractNote = {Here, we introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled approximations to the two-particle density matrix that yield algebraic scaling in general, and Hartree–Fock scaling in its seniority-zero version. Results from the latter version for small molecular systems are compared with those of highly accurate quantum-chemical computations. The energies lie above full configuration interaction calculations, close to doubly occupied configuration interaction calculations. Their accuracy is considerably greater than that obtained from current density-functional theory approximations and from current functionals of the oneparticle density matrix.},

doi = {10.1073/pnas.1615729113},

journal = {Proceedings of the National Academy of Sciences of the United States of America},

number = 46,

volume = 113,

place = {United States},

year = {Tue Nov 01 00:00:00 EDT 2016},

month = {Tue Nov 01 00:00:00 EDT 2016}

}

*Citation information provided by*

Web of Science

Web of Science

Works referenced in this record:

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- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868

##
Self-Consistent Equations Including Exchange and Correlation Effects

journal, November 1965

- Kohn, W.; Sham, L. J.
- Physical Review, Vol. 140, Issue 4A, p. A1133-A1138