A SIMPLE, ACCURATE MODEL FOR PORPHYRIN RING-CURRENT SHIFTS

A computationally simple, but accurate, model for porphyrin ring-current shifts is presented and calibrated by using X-ray and n.m.r. data from cytochrome c, cytochrome c551, cytochrome b5, and pyridine and picoline complexes of zinc porphyrin. The model involves a multipole expansion in terms of Legendre polynomials of the cosine of the polar angle and reciprocal powers of the distance between the centre of the porphyrin ring and the atom of interest. The multipole model offers a simple analytical expression for the ring-current shift in contrast to the complex expressions derived from the Johnson-Bovey and Haigh-Mallion models. The model was tested with a series of capped porphyrins and gave cap-to-porphyrin separations in excellent agreement with the X-ray structures at low temperature. Excellent agreement is also observed between calculated and observed ring-current shifts, even for protons in close proximity to the porphyrin ring.