Iterative calculations of dielectric eigenvalue spectra

The eigenvalues and eigenvectors of the dielectric matrix $ϵ$ provide a compact representation of the screening properties of interacting electronic systems. We have previously shown that the dielectric eigenvalue spectrum may be efficiently computed by iterative linear-response calculations and that for nonmetallic systems $ϵ$ may be obtained through an eigenvalue-eigenvector decomposition where only a small number of eigenvalues are included. Here we investigate the spectral properties of the dielectric matrices of a variety of systems (solids, nanostructures, and molecules) as well as the convergence properties of the eigenvalue decomposition of $ϵ$ as a function of the number of eigenmodes. Our results provide guidance on how to perform practical calculations of dielectric matrices using iterative techniques.