  The $d$-$wave$ superconductivity is analyzed within the three-band $d$-$p$
model with the use of the diagrammatic expansion of the Guztwiller wave
function method (DE-GWF). The determined stability regime of the
superconducting state appears in the range of hole doping $\delta\lesssim
0.35$, with the optimal doping close to $\delta\approx 0.19$. The pairing
amplitudes between the $d$-orbitals due to copper and $p_x/p_y$ orbitals due to
oxygen are analyzed together with the hybrid $d$-$p$ pairing. The $d$-$d$
pairing between the nearest neighboring atomic sites leads to the dominant
contribution to the SC phase. Moreover, it is shown that the decrease of both
the Coulomb repulsion on the copper atomic sites ($U_d$) and the charge
transfer energy between the oxygen and copper atomic sites ($\epsilon_{dp}$)
increases the pairing strength as it moves the system from the strong to the
intermediate-correlation regime, where the pairing is maximized. Such a result
is consistent with our analysis of the ratio of changes in the hole content at
the $d$ and $p$ orbitals due to doping, which, according to experimental study,
increases with the increasing maximal critical temperature [cf. Nat. Commun. 7,
11413 (2016)]. Furthermore, the results for the three-band model are compared
to those for the effective single-band picture and similarities between the two
approaches are discussed. For the sake of completeness, the normal-state
characteristics determined from the DE-GWF approach are compared with those
resulting from the Variational Quantum Monte Carlo method with inter-site
correlations included through the appropriate Jastrow factors.
