  Whether the pairing mechanism for superconductivity in iron-based
superconductors is of itinerant or local character is a question still debated
on. In order to investigate the influence of Fermi surface nesting, we
calculate from first-principles the static susceptibility of FeSe under applied
pressures, both hydrostatic and non-hydrostatic. We show that the electronic
band structures are highly sensitive to the way pressure is applied and
confront our theoretical results with conclusions drawn from experiments. Given
that the critical temperature of FeSe is quite universal as function of
pressure, this is clear evidence that in FeSe the evolution of Fermi surface
nesting cannot account for the evolution of the critical temperature with
pressure. Hence we argue that the pairing in iron-chalcogenide compounds should
be of strong-coupling spin fluctuation origin.
