Efficient iterative method for calculations of dielectric matrices

A major bottleneck in first-principles calculations of excited and spectroscopic properties of materials is the evaluation of dielectric matrices. We show that by computing a relatively small number of eigenvectors via iterative linear-response calculations, we may construct the dielectric matrix of a system to high numerical accuracy. We demonstrate the procedure on several systems. The proposed method bypasses the need for the calculation of large numbers of excited states required by widely used expressions within the random-phase approximation and opens the way to efficient calculations of excited-state properties in materials and nanostructures.