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

TL;DR

This paper presents highly precise nonadiabatic calculations of electric polarizabilities and hyperpolarizabilities for low-lying vibrational-rotational states of hydrogen molecular ions, improving understanding of their electromagnetic properties for spectroscopy and interactions.

Contribution

It introduces a fully nonadiabatic computational approach using Hylleraas basis sets that avoids derivatives of energy functions, providing more accurate polarizability and hyperpolarizability data for hydrogen molecular ions.

Findings

Hyperpolarizability of HD+ ground state is seven orders of magnitude larger than dipole polarizability.

High-precision calculations enable treatment of near cancellations in excited states.

Identifies tune-out and magic wavelengths for HD+ in laser fields.

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.