Dipole moments and orientation polarizabilities of diatomic molecular ions for precision atomic mass measurement

In high precision Penning trap mass spectrometry the cyclotron frequency of a polarizable ion is perturbed due to the Stark interaction with the motional electric field. For polar diatomic molecular ions, which have adjacent rotational levels of opposite parity, these shifts can be particularly large—especially for the lowest rotational levels, which are those occupied by ions stored for many hours in cryogenic Penning traps. In order to provide corrections to precision atomic mass measurements, we consider the calculation of orientation polarizabilities of $\mathrm{C}{\mathrm{O}}^{+}$ and the positive ions of the first and second row diatomic hydrides, $\mathrm{Li}{\mathrm{H}}^{+}$ to $\mathrm{Ar}{\mathrm{H}}^{+}$. Dipole moments for these ions have been calculated using the restricted coupled cluster method with perturbative triples and large basis sets. Using these dipoles and an effective Hamiltonian, we have obtained rotational-state dependent polarizabilities of the open-shell diatomic ions $\mathrm{C}{\mathrm{O}}^{+}$, $\mathrm{N}{\mathrm{H}}^{+}$, $\mathrm{O}{\mathrm{H}}^{+}$, $\mathrm{F}{\mathrm{H}}^{+}$, $\mathrm{P}{\mathrm{H}}^{+}$, $\mathrm{S}{\mathrm{H}}^{+}$, and $\mathrm{Cl}{\mathrm{H}}^{+}$. Results are given for those rotational levels that are significantly populated at $4.2\mathrm{K}$, for magnetic fields up to $10\mathrm{T}$. For the remaining first and second row hydride cations, polarizabilities at the magnetic fields of interest can be obtained from a simple formula valid for closed-shell molecules. Conversely, in cases where the polarizability shifts can be measured, our results enable experimental determination of dipole moments.