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An ab initio model is developed for the potentials in ionic molecular solids in which the electron covalency within the molecular ions substantially affects the interionic interactions. By treating the intermolecular and intramolecular interactions on the basis of the true electron charge densities of the molecular ions, this new model leads to an accurate parameter-free description of the potentialenergy surfaces for such crystals. We performed first-principles static structural relaxation, supercell molecular-dynamics simulation, and lattice-dynamics studies for the room-temperature paraelectric phase and the lower-temperature ferroelectric superstructure of K2SeO4 and predicted with good accuracy the transition from the former to the latter. Given the excellent agreement between theory and experiment, we then explored the delicately balanced potential-energy surfaces for K2SeO4 and found that they contain a double-well type of structure which is the essential origin of the incommensurate and the subsequent commensurate transitions in K2SeO4.