### Abstract

(i) The coupled-cluster equations being nonlinear, they have to be solved iteratively. An insight into the convergence properties of this iteration can be obtained by analyzing the stability of the converged solutions as fixed points. (ii) The usual form of coupled-cluster equations represents an example to the method of moments, with the number of unknown amplitudes being equal to the number of equations. The method of moments generates nonsymmetric equations loosing the variational character of the coupled-cluster method, but enabling efficient evaluation of the matrix elements. Taking higher moments into account, one may obtain more equations than parameters, thus the latter must be determined by minimizing the sum-of-squares of all moments. This leads to additional effort but improved coupled-cluster wave functions and/or energies. (iii) Another way of improving the coupled-cluster method is perturbation theory, which needs special formulations due to the nonsymmetric nature of the formalism. An efficient way to do this is offered by multi-configuration perturbation theory.

Original language | English |
---|---|

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

Publisher | Springer |

Pages | 513-534 |

Number of pages | 22 |

DOIs | |

Publication status | 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

- Coupled cluster
- Perturbative corrections
- Stability analysis

### ASJC Scopus subject areas

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

### Cite this

*Challenges and Advances in Computational Chemistry and Physics*(pp. 513-534). (Challenges and Advances in Computational Chemistry and Physics; Vol. 11). Springer. https://doi.org/10.1007/978-90-481-2885-3_19

**On The Coupled-Cluster Equations. Stability Analysis And Nonstandard Correction Schemes.** / Surján, Péter R.; Szabados, Ágnes.

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. 513-534. https://doi.org/10.1007/978-90-481-2885-3_19

}

TY - CHAP

T1 - On The Coupled-Cluster Equations. Stability Analysis And Nonstandard Correction Schemes

AU - Surján, Péter R.

AU - Szabados, Ágnes

PY - 2010/1/1

Y1 - 2010/1/1

N2 - (i) The coupled-cluster equations being nonlinear, they have to be solved iteratively. An insight into the convergence properties of this iteration can be obtained by analyzing the stability of the converged solutions as fixed points. (ii) The usual form of coupled-cluster equations represents an example to the method of moments, with the number of unknown amplitudes being equal to the number of equations. The method of moments generates nonsymmetric equations loosing the variational character of the coupled-cluster method, but enabling efficient evaluation of the matrix elements. Taking higher moments into account, one may obtain more equations than parameters, thus the latter must be determined by minimizing the sum-of-squares of all moments. This leads to additional effort but improved coupled-cluster wave functions and/or energies. (iii) Another way of improving the coupled-cluster method is perturbation theory, which needs special formulations due to the nonsymmetric nature of the formalism. An efficient way to do this is offered by multi-configuration perturbation theory.

AB - (i) The coupled-cluster equations being nonlinear, they have to be solved iteratively. An insight into the convergence properties of this iteration can be obtained by analyzing the stability of the converged solutions as fixed points. (ii) The usual form of coupled-cluster equations represents an example to the method of moments, with the number of unknown amplitudes being equal to the number of equations. The method of moments generates nonsymmetric equations loosing the variational character of the coupled-cluster method, but enabling efficient evaluation of the matrix elements. Taking higher moments into account, one may obtain more equations than parameters, thus the latter must be determined by minimizing the sum-of-squares of all moments. This leads to additional effort but improved coupled-cluster wave functions and/or energies. (iii) Another way of improving the coupled-cluster method is perturbation theory, which needs special formulations due to the nonsymmetric nature of the formalism. An efficient way to do this is offered by multi-configuration perturbation theory.

KW - Coupled cluster

KW - Perturbative corrections

KW - Stability analysis

UR - http://www.scopus.com/inward/record.url?scp=85073186468&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073186468&partnerID=8YFLogxK

U2 - 10.1007/978-90-481-2885-3_19

DO - 10.1007/978-90-481-2885-3_19

M3 - Chapter

AN - SCOPUS:85073186468

T3 - Challenges and Advances in Computational Chemistry and Physics

SP - 513

EP - 534

BT - Challenges and Advances in Computational Chemistry and Physics

PB - Springer

ER -