  The applicability of a broken symmetry version of the $G_0W_0$ approximation
to the calculation of isotropic exchange coupling constants has been studied.
Using a simple H--He--H model system the results show a significant and
consistent improvement of the results over both broken symmetry Hartree--Fock
and broken symmetry density functional theory. In the case of more realistic
bimetallic Cu(II) complexes, inclusion of the $G_0W_0$ correction does not lead
to obvious improvement in the results. The discrepancies are explained by
improved description of the interactions within the magnetic orbital space upon
inclusion of the $G_0W_0$ corrections but deterioration of the description of
charge- and spin-polarization effects outside the magnetic orbital space.
Overall the results show that computational methods based on the $GW$ method
have a potential to improve computational estimates of exchange coupling
constants.
