Elimination of unoccupied-state summations in ab initio self-energy calculations for large supercells

We present a method for the computation of self-energy corrections in large supercells. It eliminates the explicit summation over unoccupied states, and uses an iterative scheme based on an expansion of the Green\textquoterights function around a set of reference energies. This improves the scaling of the computational time from the fourth to the third power of the number of atoms for both the inverse dielectric matrix and the self-energy, yielding improved efficiency for eight or more silicon atoms per unit cell.