Transition metal dichalcogenides (TMDs), such as MoS$_2$, are known to undergo a structural phase transformation as well as a change in the electronic conductivity upon Li intercalation. These properties make them candidates for charge-tunable ion-insertion materials that could be used in electro-chemical devices. In this work we study the phase stability and electronic structure of H and T$^prime$ Li-intercalated MoX$_2$ bilayers with X=S, Se, or Te. Using first-principles calculations in combination with classical and machine learning modeling approaches, we find that the H phase is more stable at low Li concentration for all X, and the critical Li concentration at which the T$^primeto$H transition occurs decreases with increasing mass of X. Furthermore the relative free energy of the two phases becomes less sensitive to Li insertion with increasing atomic mass of the chalcogen atom X. While the electronic conductivity increases with increasing ion concentration at low concentrations, we do not observe a (positive) conductivity jump at the phase transition from H to T$^prime$.
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