  Spin fluctuations in Fe(II)-porphyrins are at the heart of heme-proteins
functionality. Despite significant progress in porphyrin chemistry, the
mechanisms that rule spin state stabilisation remain elusive. Here, it is
demonstrated by using multiconfigurational quantum chemical approaches,
including the novel Stochastic-CASSCF method, that electron delocalization
between the metal centre and the pi system of the macrocycle differentially
stabilises the triplet spin states over the quintet. This delocalisation takes
place via charge-transfer excitations, involving the out-of-plane iron d
orbitals, key linking orbitals between metal and macrocycle. Through a
correlated breathing mechanism, the 3d electrons can make transitions towards
the pi orbitals of the macrocycle. This guarantees a strong coupling between
the on-site radial correlation on the metal and electron delocalization.
Opposite-spin 3d electrons of the triplet can effectively reduce electron
repulsion in this manner. Constraining the out-of-plane orbitals from breathing
hinders delocalization and reverses the spin ordering. Our results find a
qualitative analogue in Kekul\'e resonance structures involving also the metal
centre.
