High-precision nonadiabatic calculations of dynamic polarizabilities and hyperpolarizabilities for the lowlying vibrational-rotational states of hydrogen molecular ions

Abstract

The static and dynamic electric multipolar polarizabilities and second hyperpolarizabilities of the H${}_2^{+}$, D${}_2^{+}$, and HD${}^{+}$ molecular ions in the ground and first excited states are calculated nonrelativistically using explicitly correlated Hylleraas basis sets. The calculations are fully nonadiabatic; the Born-Oppenheimer approximation is not used. Comparisons are made with published theoretical and experimental results, where available. In our approach, no derivatives of energy functions nor derivatives of response functions are needed. In particular, we make contact with earlier calculations in the Born-Oppenheimer calculation where polarizabilities were decomposed into electronic, vibrational, and rotational contributions and where hyperpolarizabilities were determined from derivatives of energy functions. We find that the static hyperpolarizability for the ground state of HD${}^{+}$ is seven orders of magnitude larger than the corresponding dipole polarizability. For the dipole polarizability of HD${}^{+}$ in the first excited-state the high precision of the present method facilitates treatment of a near cancellation between two terms. For applications to laser spectroscopy of trapped ions we find tune-out and magic wavelengths for the HD${}^{+}$ ion in a laser field. In addition, we also calculate the first few leading terms for long-range interactions of a hydrogen molecular ion interacting with a ground-state H, He, and Li atoms.

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References in corpus (6)

• Species-specific optical lattices
• Relativistic corrections of mα^6 order to the ro-vibrational spectrum of H_2^+ and HD^+ molecular ions
• Non-relativistic ab initio calculations for $2^{2}S$, $2^{2}P$ and $3^{2}D$ lithium isotopes: Applications to polarizabilities and dispersion interactions
• The static and dynamic polarisability, and the Stark and black-body radiation frequency shifts of the molecular hydrogen ions H2+, HD+, and D2+
• Precision spectroscopy of the hydrogen molecular ions HD${}^{+}$
• Calculations of polarizabilities and hyperpolarizabilities for the Be${}^{+}$ ion

Cited by in corpus (3)

• Be optical lattice clocks with the fractional Stark shift up to the level of 10${}^{-19}$
• Static field-gradient polarizabilities of small atoms and molecules in finite temperature
• Leading order relativistic corrections to the dipole polarizability of the hydrogen molecular ions