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The electronic structure of the (LiYb)$^+$ molecular ion is investigated withtwo variants of the coupled cluster method restricted to single, double, andnoniterative or linear triple excitations. Potential energy curves for theground and excited states, permanent and transition electric dipole movements,and long-range interaction coefficients $C_4$ and $C_6$ are reported. The datais subsequently employed in scattering calculations and photoassociationstudies. Feshbach resonances are shown to be measurable despite the ion'smicromotion in the Paul trap. Molecular ions can be formed in their singletelectronic ground state by one-photon photoassociation and in triplet states bytwo-photon photoassociation; and control of cold atom-ion chemistry based onFeshbach resonances should be feasible. Conditions for sympathetic cooling ofan Yb$^+$ ion by an ultracold gas of Li atoms are found to be favorable in thetemperature range of 10$\,$mK to 10$\,$nK; and further improvements usingFeshbach resonances should be possible. Overall, these results suggestexcellent prospects for building a quantum simulator with ultracold Yb$^+$ ionsand Li atoms.

Cold interactions between an Yb$^+$ ion and a Li atom: Prospects for sympathetic cooling, radiative association, and Feshbach resonances