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 |
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Keywords
- Coupled cluster
- Perturbative corrections
- Stability analysis
ASJC Scopus subject areas
- Computer Science Applications
- Chemistry (miscellaneous)
- Physics and Astronomy (miscellaneous)
Cite this
On The Coupled-Cluster Equations. Stability Analysis And Nonstandard Correction Schemes. / Surján, Péter R.; Szabados, Ágnes.
Challenges and Advances in Computational Chemistry and Physics. Springer, 2010. p. 513-534 (Challenges and Advances in Computational Chemistry and Physics; Vol. 11).Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
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 -