  We present a fast and accurate method to calculate vibrational properties for
mechanically unstable high temperature phases that suffer from imaginary
frequencies at zero temperature. The method is based on standard
finite-difference calculations with optimized large displacements and is
significantly more efficient than other methods. We demonstrate its application
for calculation of phonon dispersion relations, free energies, phase transition
temperatures, and vacancy formation energies for body-centered cubic
high-temperature phases of Ti, Zr, and Hf.
