# Perspective: Explicitly correlated electronic structure theory for complex systems

## Abstract

The explicitly correlated approach is one of the most important breakthroughs in ab initio electronic structure theory, providing arguably the most compact, accurate, and efficient ansatz for describing the correlated motion of electrons. Since Hylleraas first used an explicitly correlated wave function for the He atom in 1929, numerous attempts have been made to tackle the significant challenges involved in constructing practical explicitly correlated methods that are applicable to larger systems. These include identifying suitable mathematical forms of a correlated wave function and an efficient evaluation of many-electron integrals. R12 theory, which employs the resolution of the identity approximation, emerged in 1985, followed by the introduction of novel correlation factors and wave function ansätze, leading to the establishment of F12 theory in the 2000s. Rapid progress in recent years has significantly extended the application range of explicitly correlated theory, offering the potential of an accurate wave-function treatment of complex systems such as photosystems and semiconductors. In conclusion, this perspective surveys explicitly correlated electronic structure theory, with an emphasis on recent stochastic and deterministic approaches that hold significant promise for applications to large and complex systems including solids.

- Authors:

- Max Planck Inst. for Solid State Research, Stuttgart, (Germany); Technische Univ. Munchen, Garching (Germany). Dept. Chemie; Kobe Univ. (Japan). Graduate School of Science, Technology, and Innovation
- Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Chemistry
- Kobe Univ. (Japan). Graduate School of System Informatics
- Kobe Univ. (Japan). Graduate School of Science, Technology, and Innovation, and Graduate School of System Informatics

- Publication Date:

- Research Org.:
- Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Chemistry

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1473851

- Alternate Identifier(s):
- OSTI ID: 1349358

- Grant/Contract Number:
- FG02-11ER16211; SC0006028

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 146; Journal Issue: 8; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS

### Citation Formats

```
Grüneis, Andreas, Hirata, So, Ohnishi, Yu-ya, and Ten-no, Seiichiro.
```*Perspective: Explicitly correlated electronic structure theory for complex systems*. United States: N. p., 2017.
Web. doi:10.1063/1.4976974.

```
Grüneis, Andreas, Hirata, So, Ohnishi, Yu-ya, & Ten-no, Seiichiro.
```*Perspective: Explicitly correlated electronic structure theory for complex systems*. United States. doi:10.1063/1.4976974.

```
Grüneis, Andreas, Hirata, So, Ohnishi, Yu-ya, and Ten-no, Seiichiro. Fri .
"Perspective: Explicitly correlated electronic structure theory for complex systems". United States.
doi:10.1063/1.4976974. https://www.osti.gov/servlets/purl/1473851.
```

```
@article{osti_1473851,
```

title = {Perspective: Explicitly correlated electronic structure theory for complex systems},

author = {Grüneis, Andreas and Hirata, So and Ohnishi, Yu-ya and Ten-no, Seiichiro},

abstractNote = {The explicitly correlated approach is one of the most important breakthroughs in ab initio electronic structure theory, providing arguably the most compact, accurate, and efficient ansatz for describing the correlated motion of electrons. Since Hylleraas first used an explicitly correlated wave function for the He atom in 1929, numerous attempts have been made to tackle the significant challenges involved in constructing practical explicitly correlated methods that are applicable to larger systems. These include identifying suitable mathematical forms of a correlated wave function and an efficient evaluation of many-electron integrals. R12 theory, which employs the resolution of the identity approximation, emerged in 1985, followed by the introduction of novel correlation factors and wave function ansätze, leading to the establishment of F12 theory in the 2000s. Rapid progress in recent years has significantly extended the application range of explicitly correlated theory, offering the potential of an accurate wave-function treatment of complex systems such as photosystems and semiconductors. In conclusion, this perspective surveys explicitly correlated electronic structure theory, with an emphasis on recent stochastic and deterministic approaches that hold significant promise for applications to large and complex systems including solids.},

doi = {10.1063/1.4976974},

journal = {Journal of Chemical Physics},

number = 8,

volume = 146,

place = {United States},

year = {Fri Feb 24 00:00:00 EST 2017},

month = {Fri Feb 24 00:00:00 EST 2017}

}

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