  Self consistent GW approach (scGW) has been applied to calculate the ground
state properties (equilibrium Wigner-Seitz radius $S_{WZ}$ and bulk modulus
$B$) of 3d transition metals Sc, Ti, V, Fe, Co, Ni, and Cu. The approach
systematically underestimates $S_{WZ}$ with average relative deviation from the
experimental data about 1% and it overestimates the calculated bulk modulus
with relative error about 25%. It is shown that scGW is superior in accuracy as
compared to the local density approximation (LDA) but it is less accurate than
the generalized gradient approach (GGA) for the materials studied. If compared
to the random phase approximation (RPA), scGW is slightly less accurate, but
its error for the 3d metals looks more systematic. The systematic nature of the
deviation from the experimental data suggests that the next order of the
perturbation theory should allow one to reduce the error.
