How Does a Heme Carbene Differ from Diatomic Ligated (NO, CO, and CN^-) Analogues in the Axial Bond?

Compared to well studied diatomic ligands (NO, CN^-, CO), the axial bonds of carbene hemes is much less known although its significance in biological chemistry. The unusually large quadrupole splitting (Δ E_Q = +2.2 mm·s^-1) and asymmetric parameter (η = 0.9) of the five-coordinate heme carbene [Fe(TTP)(CCl₂)], which is the largest among all known low spin ferrohemes, has driven investigations by means of Mössbauer effect Nuclear Resonance Vibrational Spectroscopy (NRVS). Three distinct measurements on one single crystal (two in-plane and one out-of-plane) have demonstrated comprehensive vibrational structures including stretch (429) and bending modes (472 cm^-1) of the axial Fe-CCl₂, and revealed iron vibrational anisotropy in three orthogonal directions for the first time. Frontier orbital analysis especially comparisons with diatomic analogues (NO, CN^-, CO) suggest that CCl₂, similar to NO, has led to strong but anisotropic π bonding in a ligand-based "4C"-coordinate which induced the vibrational anisotropies and very large Mössbauer parameters. This is contrasted to CN^- and CO complexes which possess a porphyrin-based "4N"-coordinate electronic and vibrational structures due to inherent on-axis linear ligation.