Ab initiostatic dielectric matrices from the density-functional approach. I. Formulation and application to semiconductors and insulators

As a ground-state expectation value, the static dielectric response function can be obtained exactly within the density-functional approach. This approach is developed in the present paper within the local-density approximation. The ab initio pseudopotential method is used, extending the techniques that give excellent structural properties to the calculation of dielectric response functions. In particular, the full dielectric matrix is calculated, and so complete information about local fields is obtained. In contrast to recently proposed direct methods for obtaining the dielectric response matrices, the present approach is based on the usual perturbation formulation for the independent-particle polarizability. The results agree well with results obtained with use of direct methods. The advantage of the perturbative approach is that it allows calculation of the response matrices on a systematic grid of points in the Brillouin zone without significant extra computation or loss of accuracy for points of low symmetry. The response matrices for such a grid are required to describe the response to arbitrary perturbations, e.g., a local change in the potential due to an impurity or defect. The role of exchange and correlation is carefully developed and the relation of the response functions calculated within the density-functional approach to the usual random-phase approximation is illustrated. Results from first principles for the full static dielectric matrices are given for a series of semiconductors and insulators: diamond, Si, Ge, and LiCl. Comparison is made to previous results based on empirical potentials. The importance of local fields is illustrated for the macroscopic dielectric function and by using the concept of the dielectric band structure. Sufficient details of the method and results are included to serve as a reference for development of the dielectric matrix as a tool to be used in other applications. In particular, the additional terms in the long-wavelength dielectric matrix due to nonlocal terms in the ionic pseudopotential are presented.