  By carefully choosing parameters and including more semi-core orbitals as
valence electrons, we have constructed a high quality projected augmented wave
(PAW) dataset that yields results comparable to existing full-potential
linearized augmented plane-wave calculations. The dataset was then applied to
BaFe$_2$As$_2$ to study the effects of different levels of structure
optimization, as well as different choices of exchange-correlation functionals.
It is found that the LDA exchange-correlation functional fails to find the
correct SDW-AFM ground state under full optimization, while PBE
exchange-correlation functional obtains the correct state but significantly
overestimates the magnetism. The electronic structure of the SDW-AFM state is
not very sensitive to structure optimizations with the PBE exchange-correlation
functional because the position of the As atoms are preserved under
optimizations. We further investigated the Ba atom diffusion process on the
BaFe$_2$As$_2$ surface using the nudged elastic bands (NEB) method. The Ba atom
was found to be stable above the center of the squares formed by the surface As
atoms, and a diffusion barrier of 1.2 eV was found. Our simulated STM image
suggests an ordered surface Ba atom structure, in agreement with Ref.
