| Abstract
| - By using the Pariser−Parr−Pople (PPP) theory, the second hyperpolarizabilities (γ) have been calculated forvarious π-conjugated porphyrin arrays including “porphyrin tapes”: the meso-β doubly linked porphyrinarray Dn and the meso−meso, β−β, β−β triply linked array Tn. The validity of the PPP theory is checkedvia a comparison with both the ab initio Hartree−Fock and the B3LYP theories in the case of porphyrinmonomers and dimers. It is found that Dn and especially Tn exhibit much more remarkable evolution of γ/nalong with an increasing number of porphyrin units n compared with the butadiyne-bridged array, Yn. As aresult, the static third-order susceptibilities χ(3) of Dn and Tn are expected to be 1 and 3 orders of magnitudelarger than that of Yn in the limit n → ∞, and these advantages of porphyrin tapes become more prominentby taking into account geometrical relaxations of porphyrin units in the arrays. The structure−propertyrelationship in various conjugated polymers including porphyrin arrays is interpreted on the basis of thescaling behaviors of χ(1) and χ(3) with the effective conjugation length (ECL) as well as the reciprocal HOMO−LUMO energy gap (1/Eg). In particular, from the master plot of χ(3) (and even χ(1)) versus 1/Eg, the π-conjugationof Tn is noted to indeed be exceptional, because its large susceptibilities cannot be expected from the scalingbehavior of ordinary one-dimensional conjugated systems. We also point out that the theory of scalingrelationship, χ(3) ∼ 1/Egx, is significantly improved by taking into account electron−electron interactionsbased on the comparison with experiments.
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