### Abstract

We report the derivation of the orbit-orbit relativistic correction for calculating pure vibrational states of diatomic molecular systems with electrons within the framework that does not assume the Born-Oppenheimer (BO) approximation. The correction is calculated as the expectation value of the orbit-orbit interaction operator with the non-BO wave function expressed in terms of explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. With that we can now calculate the complete relativistic correction of the order of α2 (where α=1c). The new algorithm is applied to determine the full set of the rotationless vibrational levels and the corresponding transition frequencies of the H2 molecule. The results are compared with the previous calculations, as well as with the frequencies obtained from the experimental spectra. The comparison shows the need to include corrections higher than second order in α to further improve the agreement between the theory and the experiment.

Original language | English (US) |
---|---|

Article number | 114313 |

Journal | The Journal of Chemical Physics |

Volume | 128 |

Issue number | 11 |

DOIs | |

State | Published - 2008 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of Chemical Physics*,

*128*(11), [114313]. https://doi.org/10.1063/1.2834926

**Orbit-orbit relativistic corrections to the pure vibrational non-Born-Oppenheimer energies of H2.** / Stanke, Monika; Kȩdziera, Dariusz; Bubin, Sergiy; Molski, Marcin; Adamowicz, Ludwik.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 128, no. 11, 114313. https://doi.org/10.1063/1.2834926

}

TY - JOUR

T1 - Orbit-orbit relativistic corrections to the pure vibrational non-Born-Oppenheimer energies of H2

AU - Stanke, Monika

AU - Kȩdziera, Dariusz

AU - Bubin, Sergiy

AU - Molski, Marcin

AU - Adamowicz, Ludwik

PY - 2008

Y1 - 2008

N2 - We report the derivation of the orbit-orbit relativistic correction for calculating pure vibrational states of diatomic molecular systems with electrons within the framework that does not assume the Born-Oppenheimer (BO) approximation. The correction is calculated as the expectation value of the orbit-orbit interaction operator with the non-BO wave function expressed in terms of explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. With that we can now calculate the complete relativistic correction of the order of α2 (where α=1c). The new algorithm is applied to determine the full set of the rotationless vibrational levels and the corresponding transition frequencies of the H2 molecule. The results are compared with the previous calculations, as well as with the frequencies obtained from the experimental spectra. The comparison shows the need to include corrections higher than second order in α to further improve the agreement between the theory and the experiment.

AB - We report the derivation of the orbit-orbit relativistic correction for calculating pure vibrational states of diatomic molecular systems with electrons within the framework that does not assume the Born-Oppenheimer (BO) approximation. The correction is calculated as the expectation value of the orbit-orbit interaction operator with the non-BO wave function expressed in terms of explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. With that we can now calculate the complete relativistic correction of the order of α2 (where α=1c). The new algorithm is applied to determine the full set of the rotationless vibrational levels and the corresponding transition frequencies of the H2 molecule. The results are compared with the previous calculations, as well as with the frequencies obtained from the experimental spectra. The comparison shows the need to include corrections higher than second order in α to further improve the agreement between the theory and the experiment.

UR - http://www.scopus.com/inward/record.url?scp=41049117260&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41049117260&partnerID=8YFLogxK

U2 - 10.1063/1.2834926

DO - 10.1063/1.2834926

M3 - Article

C2 - 18361577

AN - SCOPUS:41049117260

VL - 128

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 11

M1 - 114313

ER -