Understanding the Mechanism Stabilizing Intermediate Spin States in Fe(II)-Porphyrin

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 stabilization remain elusive. Here, it is demonstrated by using multiconfigurational quantum chemical approaches, including the novel Stochastic-CASSCF method, that electron delocalization between the metal center and the π system of the macrocycle differentially stabilizes the triplet spin states over the quintet. This delocalization takes place via charge-transfer excitations, involving the π system of the macrocycle and 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 toward the π 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. The breathing mechanism is made effective by strong electron correlation effects in the π system of the macrocycle. Reducing the correlation treatment on the macrocycle to second-order only also reverses the spin ordering. High order (beyond second-order) correlation on the macrocycle reduces the energetic cost of the additional electron to a sufficient extent to stabilize the triplet state. Our results find a qualitative analogue in six resonance structures involving the metal center in the Fe²⁺ and Fe³⁺ oxidation states.