### Abstract

Variational molecular calculations without assuming the Born-Oppenheimer approximation of states corresponding to zero total angular momentum require the use of spherically symmetric basis functions explicitly depending on the electron-electron, electron-nucleus, and nucleus-nucleus distances. In our calculations, such functions have been the explicitly correlated Gaussians. For molecules with three nuclei, the Gaussians have to be multiplied by powers of all three internuclear distances to describe the highly correlated motion of the nuclei. In this work we have derived formulae for the overlap and the Hamiltonian matrix elements for such basis functions. Implementation of the formulae presents some unconventional numerical difficulties related to maintaining the required precision of the calculation. The implementation problems are discussed.

Original language | English |
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Pages (from-to) | 1169-1182 |

Number of pages | 14 |

Journal | Molecular Physics |

Volume | 103 |

Issue number | 6-8 |

DOIs | |

Publication status | Published - Mar 20 2005 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Molecular Physics*,

*103*(6-8), 1169-1182. https://doi.org/10.1080/00268970512331339314

**Integrals for non-Born-Oppenheimer calculations of molecules with three nuclei.** / Bednarz, Eugeniusz; Bubin, Sergiy; Adamowicz, Ludwik.

Research output: Contribution to journal › Article

*Molecular Physics*, vol. 103, no. 6-8, pp. 1169-1182. https://doi.org/10.1080/00268970512331339314

}

TY - JOUR

T1 - Integrals for non-Born-Oppenheimer calculations of molecules with three nuclei

AU - Bednarz, Eugeniusz

AU - Bubin, Sergiy

AU - Adamowicz, Ludwik

PY - 2005/3/20

Y1 - 2005/3/20

N2 - Variational molecular calculations without assuming the Born-Oppenheimer approximation of states corresponding to zero total angular momentum require the use of spherically symmetric basis functions explicitly depending on the electron-electron, electron-nucleus, and nucleus-nucleus distances. In our calculations, such functions have been the explicitly correlated Gaussians. For molecules with three nuclei, the Gaussians have to be multiplied by powers of all three internuclear distances to describe the highly correlated motion of the nuclei. In this work we have derived formulae for the overlap and the Hamiltonian matrix elements for such basis functions. Implementation of the formulae presents some unconventional numerical difficulties related to maintaining the required precision of the calculation. The implementation problems are discussed.

AB - Variational molecular calculations without assuming the Born-Oppenheimer approximation of states corresponding to zero total angular momentum require the use of spherically symmetric basis functions explicitly depending on the electron-electron, electron-nucleus, and nucleus-nucleus distances. In our calculations, such functions have been the explicitly correlated Gaussians. For molecules with three nuclei, the Gaussians have to be multiplied by powers of all three internuclear distances to describe the highly correlated motion of the nuclei. In this work we have derived formulae for the overlap and the Hamiltonian matrix elements for such basis functions. Implementation of the formulae presents some unconventional numerical difficulties related to maintaining the required precision of the calculation. The implementation problems are discussed.

UR - http://www.scopus.com/inward/record.url?scp=27944438835&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27944438835&partnerID=8YFLogxK

U2 - 10.1080/00268970512331339314

DO - 10.1080/00268970512331339314

M3 - Article

AN - SCOPUS:27944438835

VL - 103

SP - 1169

EP - 1182

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 6-8

ER -