Linear-response theory and lattice dynamics: A muffin-tin-orbital approach

A detailed description of a method for calculating static linear-response functions in the problem of lattice dynamics is presented. The method is based on density-functional theory and it uses linear muffin-tin orbitals as a basis for representing first-order corrections to the one-electron wave functions. This makes it possible to greatly facilitate the treatment of the materials with localized orbitals. We derive variationally accurate expressions for the dynamical matrix. We also show that large incomplete-basis-set corrections to the first-order changes in the wave functions exist and can be explicitly calculated. Some useful hints on the k-space integration for metals and the self-consistency problem at long wavelengths are also given. As a test application we calculate bulk phonon dispersions in Si and find good agreement between our results and experiments. As another application, we calculate lattice dynamics of the transition-metal carbide NbC. The theory reproduces the major anomalies found experimentally in its phonon dispersions. The theory also predicts an anomalous behavior of the lowest transverse acoustic mode along the (0) direction. Most of the calculated frequencies agree within a few percent with those measured. 1996 The American Physical Society.