Structural relaxations, molecular-dynamics simulations, and lattice-dynamics calculations were performed to study the phase transitions in ${\mathrm{Rb}}_{2}$${\mathrm{ZnCl}}_{4}$, using intermolecular and intramolecular potentials generated from ab initio quantum-chemistry calculations for the whole molecular ion ${\mathrm{ZnCl}}_{4}^{2\mathrm{\ensuremath{-}}}$. Compared with an earlier treatment of the system by a polarizable-ion model, the present approach emphasizes the static effect of the electron covalency within the molecular ions that affects strongly both the intermolecular and intramolecular interactions. The calculations gave a close agreement with experiment on the static structures of the Pnam and the Pna${2}_{1}$ phases and the transition temperature from the former to the latter. For the lower-temperature, monoclinic phase of ${\mathrm{Rb}}_{2}$${\mathrm{ZnCl}}_{4}$, the detailed structure of which is unknown, our simulations predict a structure with C1c1 space-group symmetry, which doubles the Pna${2}_{1}$ structure along both the b and c axes and thus has 48 formula units per unit cell. The lattice-dynamics calculations for the Pna${2}_{1}$ structure clearly revealed the lattice instability responsible for the Pna${2}_{1}$-monoclinic transition and provided a more convincing explanation of a previous Raman measurement. We have shown that the potential-energy surface in ${\mathrm{Rb}}_{2}$${\mathrm{ZnCl}}_{4}$ pertinent to the phase transitions contains a double-well structure, very similar to that of ${\mathrm{K}}_{2}$${\mathrm{SeO}}_{4}$, except that the double well is much deeper, causing the much more severe disordering in the Pnam structure of ${\mathrm{Rb}}_{2}$${\mathrm{ZnCl}}_{4}$ observed experimentally.