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PBE functional is used for its overall good description of the cohesive energies of all compounds involved (bulk: Ba, Ti, BaO, (Equation presented), and (Equation presented); molecule: (Equation presented)). It is worth noting that generalized gradient approximation functionals might overestimate the equilibrium volume of the paraelectric and ferroelectric phases of (Equation presented). Therefore, we have used the experimental lattice constants of (Equation presented) Å, (Equation presented) Å for the tetragonal phase [, ()]
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Our calculations well reproduce the atomic distortions and polarization of experiments (calculated: (Equation presented); experiment: (Equation presented)). Further test calculations using the PBEsol functional [, ()] show negligible effects on the results
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The selection of the bottom surface termination (i.e., (Equation presented)- or BaO-terminated bottom surface) has not been found to affect the results. We have also performed test calculations on the slab-thickness effect by adding an extra unit cell to the slab, which yields very close relative surface free energies and the same surface stability
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The selection of the bottom surface termination (i.e., (Equation presented)- or BaO-terminated bottom surface) has not been found to affect the results. We have also performed test calculations on the slab-thickness effect by adding an extra unit cell to the slab, which yields very close relative surface free energies and the same surface stability.
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