A direct approach to calculate the phonon dispersion using an ab initi
o force constant method is introduced. The phonon dispersion and struc
tural instability of cubic ZrO2 are found using a supercell method in
the local-density approximation. The force constants are determined fr
om the Hellmann-Feynman forces induced by the displacement of an atom
in the 2 x 2 x 2 fcc supercell. This size of the supercell gives ''exa
ct'' phonon frequencies at Gamma,X,L,W Brillouin zone points. The phon
on dispersion curves show a pronounced soft mode at the X point, in ag
reement with the experimentally observed cubic to tetragonal phase tra
nsition.