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We study the effect of the correlated hopping term and the intersite Coulombinteraction term on principal features of the $d$-$wave$ superconducting (SC)state, in both the electron and hole doped regimes within the t-J-U model. Inour analysis we use the approach based on the diagrammatic expansion of theGutzwiller wave function (DE-GWF) which allows us to go beyond the renormalizedmean field theory (RMFT). We show that the correlated hopping term enhances thepairing at the electron-doped side of the phase diagram. Moreover, theso-called non-BCS regime (which manifests itself by the negative kinetic energygain at the transition to the SC phase) is narrowed down with the increasingmagnitude of the correlated hopping $\sim K$. Also, the doping dependences ofthe nodal Fermi velocity and Fermi momentum, as well as the average number ofdouble occupancies, are analyzed with reference to the experimental data forselected values of the parameter $K$. For the sake of completeness, theinfluence of the intersite Coulomb repulsion on the obtained results isprovided. Additionally, selected results concerning the Hubbard-model case arealso presented. A complete model with all two-site interactions is brieflydiscussed in the Appendix for reference.

physical review. b./physical review. b

Universal properties of high-temperature superconductors from real-space  pairing III: The role of correlated hopping and intersite Coulomb interaction  within the t-J-U model