Calculation of optical properties and density of states for systems with huge unit cells

Abstract

We present a method for the ab initio calculation of spectral properties of systems with huge unit cells. Translationally invariant systems with elementary cells containing several hundred atoms in the unit cell are characterized by a large number of bands in a very small Brillouin zone. This makes the allocation of energies at different $\mathbf{k}$ points to one band impossible. For that reason a quadratic extrapolation of the band energies is performed starting from a single $\mathbf{k}$ point ${\mathbf{k}}_{0}.$ The band energies and momentum operator matrix elements are calculated at ${\mathbf{k}}_{0}$ using the projector augmented wave method. The Brillouin-zone integration is carried out by means of the linear tetrahedron method following a resampling procedure. The viability of the method is demonstrated for nonprimitive large supercells by reproducing the absorption coefficient and the density of states of an ideal crystal. The method is applied to 216- and 512-atom simple-cubic supercells. A germanium cluster embedded in a host material is treated as an example of a perturbed system.