### Abstract

In this work we present very accurate quantum-mechanical calculations of all bound pure vibrational states of the HD+ ion performed without the Born-Oppenheimer (BO) approximation. All three particles forming the system are treated on equal footing. The approach involves separating the center-of-mass motion from the laboratory-frame nonrelativistic Hamiltonian and expending the wave function of each considered state in terms of all-particle explicitly correlated Gaussian functions. The Gaussian exponential parameters are variationally optimized with the aid of the analytical energy gradient calculated with respect to these parameters. For each state the leading relativistic corrections are calculated as expectation values of the corresponding operators with the non-BO wave function of the state. The non-BO approach allows us to directly describe the charge asymmetry in HD+ which is due to the nuclear-mass asymmetry. The effect increases with the vibrational excitation and affects the values of the relativistic corrections. This phenomenon is the focus of the present study.

Original language | English (US) |
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Article number | 032503 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 89 |

Issue number | 3 |

DOIs | |

State | Published - Mar 7 2014 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics