  Compared to experiment, the calculated bulk lattice constant of FeSe is too
small in LDA, PBEsol and PBE type exchange-correlation (xc) functionals even
though the mismatch decreases from LDA to PBE. In bulk SrTiO3 (STO) on the
other hand LDA over-binds, PBE under-binds and PBEsol agrees best with
experiment. With the errors in opposite directions, the strain in the FeSe
monolayer on STO depends on the xc functional and, especially in the
non-magnetic state, is strongly overestimated. In this work we investigate the
influence of the xc functional and magnetism in density functional calculations
on electronic bonding properties and charge transfer in the FeSe monolayer on a
STO substrate. Furthermore, we consider the effect of oxygen-vacancies within
the virtual crystal approximation. In agreement with earlier work, we find that
the band structure of the checkerboard antiferromagnetic configuration agrees
best with experiment where, in addition, the relative strain on FeSe is best
described. For a small vacancy concentration, in agreement with recent
experiment, the FeSe monolayer Ti layer distance increases while for higher
concentrations it decreases.
