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 SiIV, PV, GeIV, and AsV. The optimized geometries exhibit ruffling torsion angles ranging from 0° for (P)GeIVF2 and (P)SiIV(C⋮CPh)2 to about 55° for [(P)PVF2]+. 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 Å for sterically unhindered porphyrins and at 1.85−1.87 Å 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 Cα−Cmeso−Cα angle decreases with ruffling and the CβCβ distance and Cα−N−Cα angle increase with ruffling. These structural variations are reflected in a number of ruffling-sensitive vibrational frequencies.. The ruffled D2d geometries of [(P)PVF2]+ and [(P)PVCl2]+ are stabilized by 9.25 and 5.26 kcal/mol, respectively, relative to planar D4h symmetry-constrained optimized geometries. In contrast, the ruffled D2d geometries of [(Pz)PVF2]+ and of all the silicon complexes studied are more stable than the corresponding D4h 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°, 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(3dxy)-porphyrin(atu) orbital interactions in macrocycle ruffling. Also seen for certain low-spin ferrihemes, this orbital interaction is not important for manganese porphyrins.
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