A first-principles quantum chemical analysis of the factors controlling ruffling deformations of porphyrins: Insights from the molecular structures and potential energy surfaces of silicon, phosphorus, germanium, and arsenic porphyrins and of a peroxidase compound I model

Using nonlocal density functional theory calculations, we have examined several factors influencing ruffling deformations of porphyrin and porphyrazine complexes. Because a ruffling distortion is often a direct result of a small macrocycle core size, which, in turn, is brought about by complexation of a central ion with a small ionic radius, this study focuses on the conformations and potential energy surfaces of porphyrin complexes with small central ions (herafter symbolized M) such as Si-IV, P-V, Ge-IV, and As-V. The optimized geometries exhibit ruffling torsion angles ranging from 0 degrees for (P)(GeF2)-F-IV and (P)Si-IV(C = CPh)(2) to about 55 degrees for [(P)(PF2)-F-V](+). For relatively substantial ruffling distortions, a good linear correlation has been found between the ruffling torsion angle and the M-N distance for a wide variety of central ions including transition metals, for sterically unhindered porphyrins, and for a database including both experimental and optimized structures. The threshold between ruffling and planar structures is at M-N bond distances of 2.00-2.02 Angstrom for sterically unhindered porphyrins and at 1.85-1.87 Angstrom for porphyrazines. The calculations confirm an experimental observation that electron-withdrawing axial ligands lead to increased ruffling, especially for phosophorous and silicon porphyrins. The ortho hydrogens of axial phenyl ligands and the 2- and 6- hydrogens of axial pyridine ligands can sterically interfere with the porphyrin and contribute to ruffling. In addition to the M-N distance, a number of other geometrical parameters also vary systematically with the ruffling distortion. Thus, the C-alpha-C-meso-C-alpha angle decreases with ruffling and the CbetaCbeta distance and C-alpha-N-C-alpha angle increase with ruffling. These structural Variations are reflected in a number of ruffling-sensitive vibrational frequencies.. The ruffled D-2d geometries of [(P)(PF2)-F-V](+) and [(P)(PCl2)-Cl-V](+) are stabilized by 9.25 and 5.26 kcal/mol, respectively, relative to planar D-4h symmetry-constrained optimized geometries. In contrast, the ruffled D2d geometries of [(Pz)(PF2)-F-V](+) and of all the silicon complexes studied are more stable than the corresponding D-4h symmetry-constrained optimized geometries by less than 0.01 kcal/mol. This underscores the extreme softness of ruffling deformations and shows that even fairly large distortions, where the ruffling torsion angle changes by up to 25 degrees, can occur with almost no expenditure of energy. Finally, through a reinvestigation of a recent study of a peroxidase compound I model, we have uncovered a heretofore unsuspected role of Fe(3d(xy))-porphyrin(a(tu)) orbital interactions in macrocycle ruffling. Also seen for certain low-spin ferrihemes, this orbital interaction is not important for manganese porphyrins.