The responsiveness of metalloporphyrin skeletal mode vibrational frequencies to changes in the core size and in the planarity of the macrocycle have been investigated, using normal mode analysis with the recently developed empirical force field for NiOEP (nickel octaethylporphyrin) and NiTPP (meso-tetraphenylporphyrin). Crystallographic data for OEP and TPP show correlations of structure parameters with core size: as the core expands, so do the C,C, bridge bonds, the pyrrole C,C, and C,C, bonds, and the C,C,C, bridge angles, while the C,N bonds contract. These empirical correlations were used to define a structural model of core expansion in order to calculate the vibrational frequency dependence. The kinematic consequences of core expansion are negligible, but when the bond stretching force constants were scaled to the bond distances, using the empirical equation of Burgi and Dunitz, the frequency correlations were calculated nearly quantitatively. Core size effects were also examined with QCFF/Pi semiempirical calculations on a metallo-OEP model at a series of metal-nitrogen distances. The trends in geometry were in reasonable agreement with the crystallographic data except that C,C, was calculated to decrease strongly with core size, contrary to the observed trend. Consequently, the calculated frequency dependencies had slopes differing in sign from the observed slopes for modes having major C,C, contributions, vg and vI1. The kinematics of porphyrin ruffling and doming were calculated to produce appreciable downshifts in the vl0 and vI9 modes, involving out-of-phase stretching of the C,C, bridge bonds, due to out-of-plane displacements of the C, atoms. MND0/3 calculations, carried out on zinc(I1) porphine with dihedral angles artificially constrained to produce ruffled and domed structures, showed the ring bond distances to be essentially unaffected by the out-of-plane distortions. Consequently, the changes in frequency should be calculable from kinematics alone if the distortion is imposed externally, e.g. by crystal packing or by steric forces in proteins. Some ruffled or domed metalloporphyrins show additional deviations from expectations based on core size, however, probably because of electronic influences. Thus, the ruffled form of NiOEP shows downshifts of v2 and vI1, relative to the planar form, which are calculable by bond distance scaling, since the C,C, distance is observed to lengthen. Five-coordinate complexes of Fe(II), Co(II), and Mn(I1) show depressed vq frequencies; this effect is suggested to arise from interaction of the d,2 electrons with the filled azu T orbitals, an interaction permitted in these C,, complexes, and which is made effective by the low valency of the metal ions.
