Practical methods in ab initio lattice dynamics

A popular method of extracting phonon frequencies from ab initio calculations is to find the equilibrium structure of a material and then build up the matrix of force constants by calculating forces acting due to small displacements of the atoms. If the range of the force constants is assumed to be short, as it typically is in parametrized force-model calculations, the entire dispersion relation can be evaluated from data taken from small ab initio calculations. In this paper we highlight the practical difficulties introduced by low-symmetry structures with free internal parameters and present practical solutions to them. By way of example, we present a number of calculations where solution of these problems is essential. These include ab initio calculation of phonon dispersion in a non-centrosymmetric structure (silver gallium diselenide) and good agreement between calculations and neutron scattering data for a structure with free internal parameters (germanium sulphide).