  One-body Green's function theories implemented on the real frequency axis
offer a natural formalism for the unbiased theoretical determination of
quasiparticle spectra in molecules and solids. Self-consistent Green's function
methods employing the imaginary axis formalism on the other hand can benefit
from the iterative implicit resummation of higher order diagrams that are not
included when only the first iteration is performed. Unfortunately, the
imaginary axis Green's function does not give direct access to the desired
quasiparticle spectra, which undermines its utility. To this end we investigate
how reliably one can calculate quasiparticle spectra from the Extended
Koopmans' Theorem (EKT) applied to the imaginary time Green's function in a
second order approximation (GF2). We find that EKT in conjunction with GF2
yields IPs and EAs that systematically underestimate experimental and accurate
coupled-cluster reference values for a variety of molecules and atoms. This
establishes that the EKT allows one to utilize the computational advantages of
an imaginary axis implementation, while still being able to acquire real axis
spectral properties. Because the EKT requires negligible computational effort,
and can be used with a Green's function from any level of theory, we conclude
that it is a potentially very useful tool for the systematic study of
quasiparticle spectra in realistic systems.
