Phonon density of states, free energy, and anharmonicity ofLiKSO4

${\mathrm{LiKSO}}_4$ has been investigated extensively by a variety of techniques recently. The phonon density of states of this material is now calculated for its two phases P$6_3$ ($C_6^6$) and P31c ($C_{3v}^4$) using the rigid molecular-ion model within the external mode formulation. The partial density of states associated with translations of each species of atoms and translations and rotations of the ‘‘molecules’’ ${\mathrm{SO}}_4$ ${\mathrm{}}^{\mathrm{-}2}$ are individually derived in the two phases. The free-energy difference and vibrational energy for the two phases are also evaluated. We have also analyzed the anharmonic behavior in the system at q≊0, using perturbation theory in order to understand its role in the rotational dynamics of ${\mathrm{SO}}_4$ ${\mathrm{}}^{\mathrm{-}2}$ ions.