Optical properties of large systems

GW-Bethe Salpeter equation (GW-BSE) within many-body perturbation theory is a widely used method for accurate calculation of optical properties of materials. However, the high computational cost of the BSE interaction kernel limits its applicability to small systems (containing hundreds of atoms). One of the reasons for the high computational cost is the calculation of screened coulomb interaction, which using Adler-Wiser formula, requires sum over all unoccupied states. The stochastic GW method eliminates this sum over empty states using time dependent Hartree response. We propose an efficient method to compute the BSE interaction kernel using the self-consistent Hartree response of the system, thereby eliminating sum over empty states required for the screened coulomb interaction. Our method, combined with the stochastic GW method, enables the calculation of optical properties of large systems containing thousands of atoms. The number of self-consistent calculations are reduced using the interpolative separable density fitting method. We test this method for hydrogenated silicon clusters, and our results are in good agreement with available experiments and previous calculations.