Structural characterization of synthetic and protein-bound porphyrins in terms of the lowest-frequency normal coordinates of the macrocycle

The X-ray crystal structures of synthetic and protein-bound metalloporphyrins are analyzed using a new normal structural decomposition method for classifying and quantifying their out-of-plane and in-plane distortions. These distortions are characterized in terms of equivalent displacements along the normal coordinates of the D4h-symmetric porphyrin macrocycle (normal deformations) by using a computational procedure developed for this purpose. Often it turns out that the macrocyclic structure is, even in highly distorted porphyrins, accurately represented by displacements along only the lowest-frequency normal coordinates. Accordingly, the macrocyclic structure obtained from just the out-of-plane normal deformations of the saddling (sad, B2u)-, ruffling (ruf, B1u)-, doming (dom, A2u)-, waving [wav(x), wav(y); Eg]-, and propellering (pro, A1u)-type essentially simulates the out-of-plane distortion of the X-ray crystal structure. Similarly, the observed in-plane distortions are decomposed into in-plane norm...