  We demonstrate in the present study that self-consistent calculations based
on the self-energy functional theory (SFT) are possible for the electronic
structure of realistic systems in the context of quantum chemistry. We describe
the procedure of a self-consistent SFT calculation in detail and perform the
calculations for isolated $3 d$ transition metal atoms from V to Cu as a
preliminary study. We compare the one-particle Green's functions (GFs) obtained
in this way and those obtained from the coupled-cluster singles and doubles
(CCSD) method. Although the SFT calculation starts from the spin-unpolarized
Hartree--Fock (HF) state for each of the target systems, the self-consistency
loop correctly leads to degenerate spin-polarized ground states. We examine the
spectral functions in detail to find their commonalities and differences among
the atoms by paying attention to the characteristics of the two approaches. It
is demonstrated via the two approaches that calculations based on the density
functional theory (DFT) can fail in predicting the orbital energy spectra for
spherically symmetric systems. It is found that the two methods are quite
reliable and useful beyond DFT.
