Formation energy of intrinsic defects in silicon from the Galitskii-Migdal formula

The work is devoted to the formation energy calculations of intrinsic defects in silicon based on the GW method and the Galitskii-Migdal formula. Two methods for calculating the electronic response function are applied. The first one uses direct integration over frequency to determine the response function. The diagonal form of the spectral function is the only assumption within the random phase approximation (RPA) framework, but the supercell calculations are very time consuming. Therefore, we propose the method in which the response function is calculated in the plasmon pole approximation, and the GW contribution to the exchange-correlation energy is taken with a certain mixing constant. The value of the constant is found from the correspondence with experimental data. This makes it possible to obtain accuracy comparable to the first method at significantly lower computational costs. The described method is used to calculate the formation energy of the neutral self-interstitial, vacancy, and two divacancy structures in supercells of 214-217 silicon atoms.