The slabs for the rutile TiO2 （110） surface

Traditionally, we use a slab to mimic a surface and we constrain the slab to have the bulk-terminated 2D lattice constants. Here we propose a different model in which we impose no constraints, allowing all coordinates including the 2D slab itself to relax. We perform DFT calculations on both models. We find that the unconstrained slabs yield better agreement with experimental results and they have lower total energies. The optimized 2D lattice constants of the unconstrained slabs eventually converge to the attached bulk value. The total energy difference reveals that, with odd number trilayers, the unconstrained slab is much closer to the corresponding constrained slab. The surface energies both converge to the individual values with the number of atomic layers.