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The multielectron LDA+GTB approach has been developed to calculate electronicstructure of strongly correlated cuprates. At low energies the effectiveHamiltonian of the $t - t' - t" - {t_ \bot } - {J^ * } - {J_ \bot }$-model hasbeen derived with parameters coming from the ab initio calculation for LSCO.The electronic structure of LSCO has been calculated self-consistently with theshort-range antiferromagnetic order for various doping level. Two Lifshitz-typequantum phase transitions with Fermi surface topology changes have been foundat dopings $x_{c1}=0.15$ and $x_{c2}=0.24$. Its effect on normal andsuperconducting properties has been calculated. The interatomic exchangeparameter and its pressure dependence has been calculated within LDA+GTBscheme. The magnetic mechanisms of d-wave pairing induced by static anddynamical spin correlations are discussed. Simultaneous treatment of magneticand phonon pairing results in the conclusion that both contributions are of thesame order. For two layer cuprates like YBCO the interlayer hopping andexchange effects on the electronic structure and doping dependence of $T_c$ isdiscussed as well as the Coulomb interaction induced mechanism of pairing.

Magnetic mechanisms of pairing in strongly correlated electron system of copper oxides