  Iron oxides and oxyhydroxides are challenging to model computationally as
competing phases may differ in formation energies by only several kJ/mol, they
undergo magnetization transitions with temperature, their structures may
contain partially occupied sites or long-range ordering of vacancies, and some
loose structures require proper description of weak interactions such as
hydrogen bonding and dispersive forces. If structures and transformations are
to be reliably predicted under different chemical conditions, each of these
challenges must be overcome simultaneously, while preserving a high level of
numerical accuracy and physical sophistication. Here we present comparative
studies of structure, magnetization, and elasticity properties of iron oxides
and oxyhydroxides using density functional theory calculations with plane-wave
and locally-confined-atomic-orbital basis sets, which are implemented in VASP
and SIESTA packages, respectively. We have selected hematite, maghemite,
goethite, lepidocrocite, and magnetite as model systems from a total of 13
known iron oxides and oxyhydroxides; and use same convergence criteria and
almost equivalent settings in order to make consistent comparisons. Our results
show both basis sets can reproduce the energetic stability and magnetic
ordering, and are in agreement with experimental observations. There are
advantages to choosing one basis set over the other, depending on the intended
focus. In our case, we find the method using PW basis set most appropriate, and
combine our results to construct the first phase diagram of iron oxides and
oxyhydroxides in the space of competing chemical potentials, generated entirely
from first principles
