  The three band p-d model of strongly correlated electrons interacting with
optical phonon via diagonal and off-diagonal electron-phonon interaction is
considered within cluster perturbation theory. At first step the exact
diagonalization of the Hamiltonian of CuO4 cluster results in the construction
of local polaronic eigenstates |p> with hole numbers nh=0,1,2 per unit cell.
The inter cluster hoppings and interactions are exactly written in terms of
Hubbard operators X(pq)= |p><q| determined within the multielectron polaronic
eigenstates |p>. The Fermi type single electron quasiparticle dispersion and
spectral weight are calculated for the undoped antiferromagnetic parent
insulator like La2CuO4. The quasiparticle dispersion of Hubbard polarons is
determined by a hybridization of the several Hubbard subbands with local
Franck-Condon resonances. For small electron-phonon interaction the
conductivity band is stronger renormalized then the valence band. Nevertheless
for large electron-phonon interaction both bands are strongly renormalized with
quasiparticle localization. Effect of partial compensation of diagonal and
off-diagonal electron-phonon interaction at intermediate coupling is found.
