MIXED-SPACE FORMALISM FOR THE DIELECTRIC RESPONSE IN PERIODIC-SYSTEMS

We present a useful formalism for the calculation of the polarizabilit y and dielectric response of periodic systems. Our approach is to intr oduce intermediate ''mixed-space'' functions with the full translation al periodicity of the lattice. This is a considerable advantage over e xisting real-space methods since the decay length of a response functi on [such as epsilon(r,r'\omega)] can be significantly larger than the Wigner-Seitz cell radius. Further, we show that, in supercell calculat ions, these mixed-space functions decay as fast as the corresponding r eal-space quantities within one supercell, so that the present scheme can be combined with usual real-space cutoff techniques. The advantage of the present method compared to a standard reciprocal space approac h is exemplified for the case of bulk silicon and for the case of a Si surface in a slab geometry.