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

Péter R. Surján, Ágnes Szabados

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish
Title of host publicationChallenges and Advances in Computational Chemistry and Physics
PublisherSpringer
Pages513-534
Number of pages22
DOIs
Publication statusPublished - Jan 1 2010

Publication series

NameChallenges and Advances in Computational Chemistry and Physics
Volume11
ISSN (Print)2542-4491
ISSN (Electronic)2542-4483

Fingerprint

Method of moments
Wave functions
Nonlinear equations
method of moments
perturbation theory
moments
iteration
wave functions
formalism
formulations
evaluation
matrices
configurations
energy

Keywords

  • Coupled cluster
  • Perturbative corrections
  • Stability analysis

ASJC Scopus subject areas

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

Cite this

Surján, P. R., & Szabados, Á. (2010). On The Coupled-Cluster Equations. Stability Analysis And Nonstandard Correction Schemes. In 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.

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 proceedingChapter

Surján, PR & Szabados, Á 2010, On The Coupled-Cluster Equations. Stability Analysis And Nonstandard Correction Schemes. in 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
Surján PR, Szabados Á. On The Coupled-Cluster Equations. Stability Analysis And Nonstandard Correction Schemes. In Challenges and Advances in Computational Chemistry and Physics. Springer. 2010. p. 513-534. (Challenges and Advances in Computational Chemistry and Physics). https://doi.org/10.1007/978-90-481-2885-3_19
Surján, Péter R. ; Szabados, Ágnes. / On The Coupled-Cluster Equations. Stability Analysis And Nonstandard Correction Schemes. Challenges and Advances in Computational Chemistry and Physics. Springer, 2010. pp. 513-534 (Challenges and Advances in Computational Chemistry and Physics).
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