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Using our previously developed method for calculating parameter-free potential-energy surfaces for ionic molecular crystals, specifically sulfates, we study phase transitions in RbLiSO4 by means of lattice and molecular dynamics. We found that the high-temperature phase I (Pnam) is highly unstable and transforms to the observed lower temperature phase VI (P1121/n) at about 475–525 K. Compared with isomorphous CsLiSO4, there are more branches of unstable modes in the Pnam phase for RbLiSO4. The maximum instability of these modes occurs away from the zone center, q=(0.118a*,0,0), which implies that a high-order incommensurate phase could form during the phase transformation. The driving mechanism of these phase transitions is directly related to the rotational ordering of tetrahedral SO4 2- groups. The rms values of the deviations of the S-O bonds from their orientations in the Pnam phase to those in the P1121/n phase were found to be approximately ±23–25°.