  By means of density functional theory (DFT) calculations (with and without
inclusion of spin-orbit (SO) coupling) we present a detailed study of the
electronic structure and corresponding microscopic Hamiltonian parameters of
Na2IrO3. In particular, we address the following aspects: (i) We investigate
the role of the various structural distortions and show that the electronic
structure of Na2IrO3 is exceptionally sensitive to structural details. (ii) We
discuss both limiting descriptions for Na2IrO3; quasi-molecular orbitals (small
SO limit, itinerant) versus relativistic orbitals (large SO limit, localized)
and show that the description of Na2IrO3 lies in an intermediate regime. (iii)
We investigate whether the nearest neighbor Kitaev-Heisenberg model is
sufficient to describe the electronic structure and magnetism in Na2IrO3. In
particular, we verify the recent suggestion of an antiferromagnetic Kitaev
interaction and show that it is not consistent with actual or even plausible
electronic parameters. Finally, (iv) we discuss correlation effects in Na2IrO3.
We conclude that while the Kitaev-Heisenberg Hamiltonian is the most general
expression of the quadratic spin-spin interaction in the presence of spin-orbit
coupling (neglecting single-site anisotropy), the itinerant character of the
electrons in Na2IrO3 makes other terms beyond this model (including, but not
limited to 2nd and 3rd neighbor interactions) essential.
