Spin-state energetics of iron(II) porphyrin from the particle-particle random phase approximation

The particle-particle random phase approximation (pp-RPA) has been deployed to study the spin-state energetics of transition metal (TM) complexes for the first time in this work. Namely, we designed and implemented a non-canonical reference pp-RPA protocol that is capable of capturing the singlet low-spin (LS) – triplet intermediate-spin (IS) excitation process of iron(II) complexes; herein we applied this method to iron-porphyrin related heme derivatives with clearly defined LS and IS electronic states. Coupled to the CAM-B3LYP functional and to Dunning-type basis sets, we utilized both the active-space and Davidson methods to solve the pp-RPA equation effectively to obtain vertical singlet–triplet excitation energies. Correcting these vertical metrics with a structural relaxation factor for each species, we evaluated the relative stability of LS and IS electronic states. Comparison of the pp-RPA results to established ab initio data revealed that pp-RPA describes well excitation energies and related relative spin state stabilities if the transition is based on non-bonding d-orbitals, such as complexes without an axial ligand in the investigated set of molecules. But it notably overestimates the stability of the singlet LS state to the triplet IS state in complexes, where the d-orbitals at which the excitation is centered have bonding or antibonding character.