[Shadow]

I have some doubts.

In PF₅ the hybridisation is sp³d. Why is the 3d orbital used instead of the 4s orbital when by the Aufbau principle 4s has lower energy than 3d?

When Fe gets ionized, why does an electron from 4s leave, but not a 3d electron, when 4s has lower energy?

[magician4]

there are some discussions whether indeed sp³d is involved with PF₅

for example:


(from: link, see also discussion in text )

if, however, you wish to construct hybrid orbitals resulting in a trigonal bipyramidal structure from s,p,d ... anyway, you'd need to include those orbital types that would result in named symmetry when "mixed".
with another s (in your case: 4 s) included, this is not possible (as s would add another spherical symmetry commitment, which however would be inapt here: we need something with a non-spherical "direction")
however, another d orbital would exactly fill the bill, and result in the desired symmetry of hybridorbitals constructed thereof

therefore, even if the energy of 4s (for a "naked" atom in vacuum! don't forget: in compounds, this might come out very different from that) is in theory lower than 3d, it still is the only game in town

with respect to your "iron" question: as I wrote above, this "aufbau principle" is valid for isolated, neutral atoms in gas phase  (ands even there, you'd have to take it with a pinch of salt: look at the huge list of "exceptions")
... and obviously, for the iron mono ion (which is a quite exotic particle at that) the configuration with a filled, stable d-shell seems to be more stable than the solution with a filled s shell
Quantum mechanical calculations might hold deeper insights why this is the case here
However, those "stability exchanges" do happen quite often, esp. with possible filled and half-filled d-shells involved


regards

Ingo