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This work was supported by the Latvian Council of Science Grant No. 374/2012 and the Latvian National Research Program IMIS2. Many stimulating discussions with D. Vanderbilt, K.M. Rabe, M. Rohlfing, E. Heifets, J. Maier, G. Borstel and E.A. Kotomin are greatly acknowledged. ; By means of the hybrid exchange–correlation functionals, as it is implemented in the CRYSTAL computer code, ab initio calculations for main ABO3 perovskite (0 0 1) surfaces, namely SrTiO3, BaTiO3, PbTiO3, CaTiO3, SrZrO3, BaZrO3, PbZrO3 and CaZrO3, were performed. For ABO3 perovskite (0 0 1) surfaces, with a few exceptions, all atoms of the upper surface layer relax inward, all atoms of the second surface layer relax outward, and all third layer atoms, again, inward. The relaxation of (0 0 1) surface metal atoms for ABO3 perovskite upper two surface layers for both AO and BO2-terminations, in most cases, are considerably larger than that of oxygen atoms, what leads to a considerable rumpling of the outermost plane. The ABO3 perovskite (0 0 1) surface energies always are smaller than the (0 1 1) and especially (1 1 1) surface energies. The ABO3 perovskite AO and BO2-terminated (0 0 1) surface band gaps always are reduced with respect to the bulk values. The B–O chemical bond population in ABO3 perovskite bulk always are smaller than near the (0 0 1) and especially (0 1 1) surfaces. ; Latvian Council of Science Grant No. 374/2012; the Latvian National Research Program IMIS2; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union's Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART²

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