### Abstract

This paper presents the calculation of the electric transition dipole moment in a pre-Born-Oppenheimer framework. Electrons and nuclei are treated equally in terms of the parametrization of the non-relativistic total wave function, which is written as a linear combination of basis functions constructed from explicitly correlated Gaussian functions and the global vector representation. The integrals of the electric transition dipole moment are derived corresponding to these basis functions in both the length and the velocity representation. The calculations are performed in laboratory-fixed Cartesian coordinates without relying on coordinates which separate the center of mass from the translationally invariant degrees of freedom. The effect of the overall motion is eliminated through translationally invariant integral expressions. The electric transition dipole moment is calculated between two rovibronic levels of the H2 molecule assignable to the lowest rovibrational states of the X ^{1}Σ_{g}
^{+} B ^{1}Σ_{u}
^{+} electronic states in the clamped-nuclei framework. This is the first evaluation of this quantity in a full quantum mechanical treatment without relying on the Born-Oppenheimer approximation.

Original language | English |
---|---|

Article number | 154105 |

Journal | The Journal of Chemical Physics |

Volume | 141 |

Issue number | 15 |

DOIs | |

Publication status | Published - Oct 21 2014 |

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### ASJC Scopus subject areas

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

### Cite this

*The Journal of Chemical Physics*,

*141*(15), [154105]. https://doi.org/10.1063/1.4897632

**Electric transition dipole moment in pre-Born-Oppenheimer molecular structure theory.** / Simmen, Benjamin; Mat́yus, E.; Reiher, Markus.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 141, no. 15, 154105. https://doi.org/10.1063/1.4897632

}

TY - JOUR

T1 - Electric transition dipole moment in pre-Born-Oppenheimer molecular structure theory

AU - Simmen, Benjamin

AU - Mat́yus, E.

AU - Reiher, Markus

PY - 2014/10/21

Y1 - 2014/10/21

N2 - This paper presents the calculation of the electric transition dipole moment in a pre-Born-Oppenheimer framework. Electrons and nuclei are treated equally in terms of the parametrization of the non-relativistic total wave function, which is written as a linear combination of basis functions constructed from explicitly correlated Gaussian functions and the global vector representation. The integrals of the electric transition dipole moment are derived corresponding to these basis functions in both the length and the velocity representation. The calculations are performed in laboratory-fixed Cartesian coordinates without relying on coordinates which separate the center of mass from the translationally invariant degrees of freedom. The effect of the overall motion is eliminated through translationally invariant integral expressions. The electric transition dipole moment is calculated between two rovibronic levels of the H2 molecule assignable to the lowest rovibrational states of the X 1Σg + B 1Σu + electronic states in the clamped-nuclei framework. This is the first evaluation of this quantity in a full quantum mechanical treatment without relying on the Born-Oppenheimer approximation.

AB - This paper presents the calculation of the electric transition dipole moment in a pre-Born-Oppenheimer framework. Electrons and nuclei are treated equally in terms of the parametrization of the non-relativistic total wave function, which is written as a linear combination of basis functions constructed from explicitly correlated Gaussian functions and the global vector representation. The integrals of the electric transition dipole moment are derived corresponding to these basis functions in both the length and the velocity representation. The calculations are performed in laboratory-fixed Cartesian coordinates without relying on coordinates which separate the center of mass from the translationally invariant degrees of freedom. The effect of the overall motion is eliminated through translationally invariant integral expressions. The electric transition dipole moment is calculated between two rovibronic levels of the H2 molecule assignable to the lowest rovibrational states of the X 1Σg + B 1Σu + electronic states in the clamped-nuclei framework. This is the first evaluation of this quantity in a full quantum mechanical treatment without relying on the Born-Oppenheimer approximation.

UR - http://www.scopus.com/inward/record.url?scp=84908042885&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908042885&partnerID=8YFLogxK

U2 - 10.1063/1.4897632

DO - 10.1063/1.4897632

M3 - Article

VL - 141

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 15

M1 - 154105

ER -