### Abstract

The Brillouin theorem has been generalized for the coupling strength parameter (a) extended non-relativistic electronic Hamiltonian (H_{∇}+H_{ne}+aH_{ee}). The mathematical case a=0 generates an orto-normalized set of single Slater determinants which can be used as basis set for configuration interactions (CI) calculations for the physical case a=1, removing the known restriction by the original Brillouin theorem and opening a new way to practice.

Original language | English |
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Title of host publication | International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018 |

Editors | T.E. Simos, T.E. Simos, T.E. Simos, T.E. Simos, Ch. Tsitouras, T.E. Simos |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735418547 |

DOIs | |

Publication status | Published - Jul 24 2019 |

Event | International Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018 - Rhodes, Greece Duration: Sep 13 2018 → Sep 18 2018 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 2116 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | International Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018 |
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Country | Greece |

City | Rhodes |

Period | 9/13/18 → 9/18/18 |

### Fingerprint

### Keywords

- configuration interactions
- coupling strength parameter
- electron-electron repulsion energy participation in ground and excited states
- generalization of Brillouin theorem
- single determinant basis set
- totally non-interacting reference system

### ASJC Scopus subject areas

- Ecology, Evolution, Behavior and Systematics
- Ecology
- Plant Science
- Physics and Astronomy(all)
- Nature and Landscape Conservation

### Cite this

*International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018*[450061] (AIP Conference Proceedings; Vol. 2116). American Institute of Physics Inc.. https://doi.org/10.1063/1.5114528

**Single determinant basis set for the non-relativistic electronic Schrödinger equation using the coupling strength parameter generalized Brillouin theorem.** / Kristyán, S.

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

*International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018.*, 450061, AIP Conference Proceedings, vol. 2116, American Institute of Physics Inc., International Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018, Rhodes, Greece, 9/13/18. https://doi.org/10.1063/1.5114528

}

TY - GEN

T1 - Single determinant basis set for the non-relativistic electronic Schrödinger equation using the coupling strength parameter generalized Brillouin theorem

AU - Kristyán, S.

PY - 2019/7/24

Y1 - 2019/7/24

N2 - The Brillouin theorem has been generalized for the coupling strength parameter (a) extended non-relativistic electronic Hamiltonian (H∇+Hne+aHee). The mathematical case a=0 generates an orto-normalized set of single Slater determinants which can be used as basis set for configuration interactions (CI) calculations for the physical case a=1, removing the known restriction by the original Brillouin theorem and opening a new way to practice.

AB - The Brillouin theorem has been generalized for the coupling strength parameter (a) extended non-relativistic electronic Hamiltonian (H∇+Hne+aHee). The mathematical case a=0 generates an orto-normalized set of single Slater determinants which can be used as basis set for configuration interactions (CI) calculations for the physical case a=1, removing the known restriction by the original Brillouin theorem and opening a new way to practice.

KW - configuration interactions

KW - coupling strength parameter

KW - electron-electron repulsion energy participation in ground and excited states

KW - generalization of Brillouin theorem

KW - single determinant basis set

KW - totally non-interacting reference system

UR - http://www.scopus.com/inward/record.url?scp=85069970062&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069970062&partnerID=8YFLogxK

U2 - 10.1063/1.5114528

DO - 10.1063/1.5114528

M3 - Conference contribution

AN - SCOPUS:85069970062

T3 - AIP Conference Proceedings

BT - International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018

A2 - Simos, T.E.

A2 - Simos, T.E.

A2 - Simos, T.E.

A2 - Simos, T.E.

A2 - Tsitouras, Ch.

A2 - Simos, T.E.

PB - American Institute of Physics Inc.

ER -