The three-band Emery model, describing the holes in the CuO2 planes of
the high-temperature superconducting oxides, is considered. The model
includes the direct oxygen-oxygen hopping integral t(pp). The exact B
ogolyubov transformation is used to exclude one oxygen band and obtain
a two-dimensional Anderson model. Afterward, the effective Hamiltonia
n is obtained by eliminating the second oxygen band with the use of tw
o approximate canonical transformations. The effective Hamiltonian des
cribes the spins residing on the copper sites and interacting through
an indirect interaction J(SX)(R), where R is the distance between two
copper ions. J(SX)(R) depends on the doping rate delta and is a decayi
ng function of R. Numerical results for J(SX)(R) are given for differe
nt doping rates delta for the case of parabolic bands. The obtained in
teraction J(SX)(R), when added to the original antiferromagnetic inter
action (present in oxides at delta = 0), might lead to a frustration o
f the long-range antiferromagnetic ordering upon doping.