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<p>Optical cycling, a continuous photon scattering off atoms or molecules, plays a
central role in the quantum information science. While optical cycling has been
experimentally achieved for many neutral species, few molecular ions have been investigated. We present a systematic theoretical search for diatomic molecular ions
suitable for optical cycling using equation-of-motion coupled-cluster methods. Inspired by the electronic structure patterns of laser-cooled neutral molecules, we establish the design principles for molecular ions and explore various possible cationic
molecular frameworks. The results show identifying a perfect molecular ion for optical cycling is challenging, yet possible. Among various possible diatomic molecules
we suggest several candidates, which require further attention from both theory and
experiment: YF+, SiO+, PN+, SiBr+, and BO+.
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