  First principles calculations of magnetic and, to a lesser extent, electronic
properties of the novel LaFeAsO-based superconductors show substantial apparent
controversy, as opposed to most weakly or strongly correlated materials. Not
only do different reports disagree about quantitative values, there is also a
schism in terms of interpreting the basic physics of the magnetic interactions
in this system. In this paper, we present a systematic analysis using four
different first principles methods and show that while there is an unusual
sensitivity to computational details, well-converged full-potential
all-electron results are fully consistent among themselves. What makes results
so sensitive and the system so different from simple local magnetic moments
interacting via basic superexchange mechanisms is the itinerant character of
the calculated magnetic ground state, where very soft magnetic moments and
long-range interactions are characterized by a particular structure in the
reciprocal (as opposed to real) space. Therefore, unravelling the magnetic
interactions in their full richness remains a challenging, but utterly
important task.
