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We present and discuss results of the calculations for BaTiO_3 and SrTiO_3 surface relaxation with different terminations using a semi-empirical shell model (SM) as well as ab initio methods based on Hartree-Fock (HF) and Density Functional Theory (DFT) formalisms. Using the SM, the positions of atoms in 16 near-surface layers placed atop a slab of rigid ions are optimized. This permits us determination of surface rumpling and surface-induced dipole moments (polarization) for different terminations of the (100) and (110) surfaces. We also compare results of the ab initio calculations based on both HF with the DFT-type electron correlation corrections, several DFT with different exchange-correlation functionals, and hybrid exchange techniques. Our SM results for the (100) surfaces are in a good agreement with both our ab initio calculations and LEED experiments. For the (110) surfaces O-termination is predicted to be the lowest in energy.

First principles and semi-empirical calculations of atomic and electronic structure for the (100) and (110) perovskite surfaces