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Using a newly developed first-principles approach to simulations of ionic molecular crystals, we performed static relaxation, molecular-dynamics simulation, and lattice-dynamics calculations, and measurements of the Raman spectrum, for the Pnam structure of K2SO4. It was found that the structure does not have the zone-center instability present in isomorphous K2SeO42 found in an earlier study. This difference between the two systems is attributed to the different charge distributions in the molecular ions. The calculated Raman-active zone-center frequencies for the Pnam structure of K2SO4 were found to be in general agreement with the experimental Raman frequencies.