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Structural relaxations, molecular-dynamics simulations, and lattice-dynamics calculations were performed to study the phase transitions in Rb2ZnCl4, using intermolecular and intramolecular potentials generated from ab initio quantum-chemistry calculations for the whole molecular ion ZnCl4 2-. Compared with an earlier treatment of the system by a polarizable-ion model, the present approach emphasizes the static effect of the electron covalency within the molecular ions that affects strongly both the intermolecular and intramolecular interactions. The calculations gave a close agreement with experiment on the static structures of the Pnam and the Pna21 phases and the transition temperature from the former to the latter. For the lower-temperature, monoclinic phase of Rb2ZnCl4, the detailed structure of which is unknown, our simulations predict a structure with C1c1 space-group symmetry, which doubles the Pna21 structure along both the b and c axes and thus has 48 formula units per unit cell. The lattice-dynamics calculations for the Pna21 structure clearly revealed the lattice instability responsible for the Pna21-monoclinic transition and provided a more convincing explanation of a previous Raman measurement. We have shown that the potential-energy surface in Rb2ZnCl4 pertinent to the phase transitions contains a double-well structure, very similar to that of K2SeO4, except that the double well is much deeper, causing the much more severe disordering in the Pnam structure of Rb2ZnCl4 observed experimentally.