### Abstract

We have obtained some exact solutions for a solvable model for the hydrogen molecular ion where the Coulomb interaction between the electron and the nuclei is replaced by a harmonic potential. We have also obtained the solutions to this model within the ordinary Born-Oppenheimer (BO) approximation for the electronic and nuclear degrees of freedom. The model shows some of the qualitative features of the real system and allows for a detailed study of non-adiabatic effects on the electronic structure through the calculation of the first-order corrections to the BO approximation, resulting from the nuclear kinetic energy and the vibronic coupling. The results are of interest in the context of non-adiabatic treatment of molecules and for the description of molecules in external magnetic fields.

Original language | English |
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Pages (from-to) | 4537-4544 |

Number of pages | 8 |

Journal | Journal of Physics B: Atomic, Molecular and Optical Physics |

Volume | 31 |

Issue number | 20 |

DOIs | |

Publication status | Published - Oct 28 1998 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)

### Cite this

**Non-Born-Oppenheimer corrections in an exactly solvable model of the hydrogen ion molecule.** / Pino, Ramiro; Mujica, Vladimiro.

Research output: Contribution to journal › Article

*Journal of Physics B: Atomic, Molecular and Optical Physics*, vol. 31, no. 20, pp. 4537-4544. https://doi.org/10.1088/0953-4075/31/20/012

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TY - JOUR

T1 - Non-Born-Oppenheimer corrections in an exactly solvable model of the hydrogen ion molecule

AU - Pino, Ramiro

AU - Mujica, Vladimiro

PY - 1998/10/28

Y1 - 1998/10/28

N2 - We have obtained some exact solutions for a solvable model for the hydrogen molecular ion where the Coulomb interaction between the electron and the nuclei is replaced by a harmonic potential. We have also obtained the solutions to this model within the ordinary Born-Oppenheimer (BO) approximation for the electronic and nuclear degrees of freedom. The model shows some of the qualitative features of the real system and allows for a detailed study of non-adiabatic effects on the electronic structure through the calculation of the first-order corrections to the BO approximation, resulting from the nuclear kinetic energy and the vibronic coupling. The results are of interest in the context of non-adiabatic treatment of molecules and for the description of molecules in external magnetic fields.

AB - We have obtained some exact solutions for a solvable model for the hydrogen molecular ion where the Coulomb interaction between the electron and the nuclei is replaced by a harmonic potential. We have also obtained the solutions to this model within the ordinary Born-Oppenheimer (BO) approximation for the electronic and nuclear degrees of freedom. The model shows some of the qualitative features of the real system and allows for a detailed study of non-adiabatic effects on the electronic structure through the calculation of the first-order corrections to the BO approximation, resulting from the nuclear kinetic energy and the vibronic coupling. The results are of interest in the context of non-adiabatic treatment of molecules and for the description of molecules in external magnetic fields.

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U2 - 10.1088/0953-4075/31/20/012

DO - 10.1088/0953-4075/31/20/012

M3 - Article

VL - 31

SP - 4537

EP - 4544

JO - Journal of Physics B: Atomic, Molecular and Optical Physics

JF - Journal of Physics B: Atomic, Molecular and Optical Physics

SN - 0953-4075

IS - 20

ER -