  The work is devoted to the formation energy calculations of intrinsic defects
in silicon based on the GW method and the Galitskii-Migdal formula. The 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
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 an 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 divacansy structures in supercells of 214-217 silicon atoms.
