Symmetry-breaking phenomena in metalloporphyrin π-cation radicals

Density functional theory (DFT) calculations of the energetics, molecular structures, and spin density profiles of metalloporphyrin pi-cation radicals suggest that the common practice of describing these radicals in terms of a universal A(1u)/A(2u) dichotomy is often not justified, confirming a possibility first foreseen by Prendergast and Spiro (ref 15) over a decade ago on the basis of vibrational spectroscopy and semiempirical calculations. Because of near-degeneracy of the a(1u) and a(2u) HOMOs of many metalloporphyrins, the cation radicals derived from these compounds undergo a pseudo-Jahn-Teller (pJT) distortion and are, therefore, best described as 2 A. with reference to the C-4h point group, rather than as(2) A(1u) (D-4h) or (2)A(2u) (D-4h).We find that the porphyrin cation radicals undergo a pJT distortion if the energy difference between the (2)A(1u) and (2)A(2u) pi-cation radicals, optimized under D-4h symmetry constraints, is less than 0.15 eV. According to this criterion, metallo-porphine and metallo-OEP pi-cation radicals should always be pJT-distorted and metallo-meso-tetrahalogenoporphyrin radicals should not. For [Zn(TPP.)](+), the (2)A(1u)/(2)A(2u) energy difference is almost exactly at the threshold of 0.15 eV, consistent with the experimental observation of both symmetry-broken and undistorted structures for this species. The (2)A(1u)/(2)A(2u) energy difference (when the molecular geometries are optimized under a D-4h symmetry constraint) also appears to govern whether the real pJT-distorted cation radical is more A(1u)- or A(2u)-like in terms of its spin density profile. Because many metalloporphyrin pi-cation radicals exist as cofacial dimers in the crystalline phase, we examined the symmetries and structures of the model compounds [{Zn(P)}(2)](+,2+) by means of DFT geometry optimizations. The results showed that dimerization has relatively little impact on the bond length alternation in the individual rings. A final interesting result, consistent with experiment, is that the bond length alternation in the delocalized mixed-valence dimer [ {Zn(P)}(2)](+) is about half that found for [{Zn(P)}(2)](2+).