Phonons from *ab initio* calculations

In bulk crystals, crystals with defects, clusters, surfaces, etc.
the phonons can be calculated from the Hellmann-Feynman (HF) forces
by the direct method. The HF forces should be calculated with an
*ab initio* program for a number of atoms displaced from
equilibrium positions, one atom at a time. Program Phonon is
able to extract the force constants from the HF forces in
a symmetry controlled manner, build the dynamical matrix
and provide the phonon dispersion relations, and total and
partials phonon density of states. The thermodynamic functions
in harmonic approximation, i.e. the internal and free energy,
entropy and heat capacity, the Debye-Waller factor for
diffraction peak intensities, the coherent and incoherent
inelastic neutron, or X-ray scattering intensities on a single,
or polycrystals, including the multiphonon contributions can be found.
For polar crystals the LO/TO spliting can be included in a semi
phenomenological way. The Phonon tool can be used to find the
Raman and infrared absorption frequencies and their irreducible
representations.

One may check a dynamical stability of an ab initio optimized supercell, serach for possible soft modes which might indicate stable lower symmetry phases. Within the quasiharmonic approximation the finite temperature properties of the system, including a phase transitions under temperature, can be studied. For more see: http://wolf.ifj.edu.pl/phonon/.