### Abstract

A computational scheme for approximate lower bound to eigenvalues of linear operators is elaborated, based on Löwdin's bracketing function. Implementation in direct full configuration interaction algorithm is presented, generating essentially just input-output increase. While strict lower bound property is lost due to approximations, test calculations result lower bounds of the same order of magnitude, as the usual upper bound, provided by the expectation value. Difference of upper and lower bounds gives an error bar, characterizing the wavefunction at the given iteration step.

Original language | English |
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Article number | 084112 |

Journal | The Journal of Chemical Physics |

Volume | 143 |

Issue number | 8 |

DOIs | |

Publication status | Published - aug. 28 2015 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*The Journal of Chemical Physics*,

*143*(8), [084112]. https://doi.org/10.1063/1.4928977

**Energy error bars in direct configuration interaction iteration sequence.** / Tóth, Zsuzsanna; Szabados, A.

Research output: Article

*The Journal of Chemical Physics*, vol. 143, no. 8, 084112. https://doi.org/10.1063/1.4928977

}

TY - JOUR

T1 - Energy error bars in direct configuration interaction iteration sequence

AU - Tóth, Zsuzsanna

AU - Szabados, A.

PY - 2015/8/28

Y1 - 2015/8/28

N2 - A computational scheme for approximate lower bound to eigenvalues of linear operators is elaborated, based on Löwdin's bracketing function. Implementation in direct full configuration interaction algorithm is presented, generating essentially just input-output increase. While strict lower bound property is lost due to approximations, test calculations result lower bounds of the same order of magnitude, as the usual upper bound, provided by the expectation value. Difference of upper and lower bounds gives an error bar, characterizing the wavefunction at the given iteration step.

AB - A computational scheme for approximate lower bound to eigenvalues of linear operators is elaborated, based on Löwdin's bracketing function. Implementation in direct full configuration interaction algorithm is presented, generating essentially just input-output increase. While strict lower bound property is lost due to approximations, test calculations result lower bounds of the same order of magnitude, as the usual upper bound, provided by the expectation value. Difference of upper and lower bounds gives an error bar, characterizing the wavefunction at the given iteration step.

UR - http://www.scopus.com/inward/record.url?scp=84940398886&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940398886&partnerID=8YFLogxK

U2 - 10.1063/1.4928977

DO - 10.1063/1.4928977

M3 - Article

AN - SCOPUS:84940398886

VL - 143

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 8

M1 - 084112

ER -