### Abstract

An eclectic combination of cluster, perturbation, and linear expansions often provides the most compact mathematical descriptions of molecular electronic wave functions. A general theory is introduced to define a hierarchy of systematic electron-correlation approximations that use two or three of these expansion types. It encompasses coupled-cluster and equation-of-motion coupled-cluster methods and generates various perturbation corrections thereto, which, in some instances, reduce to the standard many-body perturbation methods. Some of these methods are also equipped with the ability to use basis functions of interelectronic distances via the so-called R12 and F12 schemes. Two computer algebraic techniques are devised to dramatically expedite implementation, verification, and validation of these complex electron-correlation methods. Numerical assessments support the unmatched utility of the proposed approximations for a range of molecular problems.

Original language | English (US) |
---|---|

Title of host publication | Challenges and Advances in Computational Chemistry and Physics |

Publisher | Springer |

Pages | 191-217 |

Number of pages | 27 |

DOIs | |

State | Published - Jan 1 2010 |

### Publication series

Name | Challenges and Advances in Computational Chemistry and Physics |
---|---|

Volume | 11 |

ISSN (Print) | 2542-4491 |

ISSN (Electronic) | 2542-4483 |

### Fingerprint

### Keywords

- Automated derivation and implementation
- Coupled cluster
- Equation-of-motion coupled cluster
- Explicitly correlated
- Perturbation corrections

### ASJC Scopus subject areas

- Computer Science Applications
- Chemistry (miscellaneous)
- Physics and Astronomy (miscellaneous)

### Cite this

*Challenges and Advances in Computational Chemistry and Physics*(pp. 191-217). (Challenges and Advances in Computational Chemistry and Physics; Vol. 11). Springer. https://doi.org/10.1007/978-90-481-2885-3_8

**Eclectic Electron-Correlation Methods.** / Hirata, So; Shiozaki, Toru; Valeev, Edward F.; Nooijen, Marcel.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Challenges and Advances in Computational Chemistry and Physics.*Challenges and Advances in Computational Chemistry and Physics, vol. 11, Springer, pp. 191-217. https://doi.org/10.1007/978-90-481-2885-3_8

}

TY - CHAP

T1 - Eclectic Electron-Correlation Methods

AU - Hirata, So

AU - Shiozaki, Toru

AU - Valeev, Edward F.

AU - Nooijen, Marcel

PY - 2010/1/1

Y1 - 2010/1/1

N2 - An eclectic combination of cluster, perturbation, and linear expansions often provides the most compact mathematical descriptions of molecular electronic wave functions. A general theory is introduced to define a hierarchy of systematic electron-correlation approximations that use two or three of these expansion types. It encompasses coupled-cluster and equation-of-motion coupled-cluster methods and generates various perturbation corrections thereto, which, in some instances, reduce to the standard many-body perturbation methods. Some of these methods are also equipped with the ability to use basis functions of interelectronic distances via the so-called R12 and F12 schemes. Two computer algebraic techniques are devised to dramatically expedite implementation, verification, and validation of these complex electron-correlation methods. Numerical assessments support the unmatched utility of the proposed approximations for a range of molecular problems.

AB - An eclectic combination of cluster, perturbation, and linear expansions often provides the most compact mathematical descriptions of molecular electronic wave functions. A general theory is introduced to define a hierarchy of systematic electron-correlation approximations that use two or three of these expansion types. It encompasses coupled-cluster and equation-of-motion coupled-cluster methods and generates various perturbation corrections thereto, which, in some instances, reduce to the standard many-body perturbation methods. Some of these methods are also equipped with the ability to use basis functions of interelectronic distances via the so-called R12 and F12 schemes. Two computer algebraic techniques are devised to dramatically expedite implementation, verification, and validation of these complex electron-correlation methods. Numerical assessments support the unmatched utility of the proposed approximations for a range of molecular problems.

KW - Automated derivation and implementation

KW - Coupled cluster

KW - Equation-of-motion coupled cluster

KW - Explicitly correlated

KW - Perturbation corrections

UR - http://www.scopus.com/inward/record.url?scp=85073223658&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073223658&partnerID=8YFLogxK

U2 - 10.1007/978-90-481-2885-3_8

DO - 10.1007/978-90-481-2885-3_8

M3 - Chapter

AN - SCOPUS:85073223658

T3 - Challenges and Advances in Computational Chemistry and Physics

SP - 191

EP - 217

BT - Challenges and Advances in Computational Chemistry and Physics

PB - Springer

ER -