Direct ab initio calculation of the dynamical matrix

In this paper there is presented method for ab initio calculation of the phonon spectra. The method is based upon a direct calculation of the dynamical matrix via second derivatives of the total energy. The pseudopotential technique in plane-wave basis set was used to calculate the total energy within the local density approximation (LDA). For the change of the electron density there is derived the self-consistent equation which is solved analytically with no use of iterations. In this paper the attention is paid only to non-metallic systems.