A theoretical study on the third-order nonlinear optical properties of π-conjugated linear porphyrin arrays

By using the Pariser-Parr-Pople (PPP) theory, the second hyperpolarizabilities (gamma) have been calculated for various T-conjugated porphyrin arrays including "porphyrin tapes": the meso-beta doubly linked porphyrin array Dn and the meso-meso, beta-beta, beta-beta triply linked array Tn. The validity of the PPP theory is checked via a comparison with both the ab initio Hartree-Fock and the B3LYP theories in the case of porphyrin monomers and dimers. It is found that Dn and especially Tn exhibit much more remarkable evolution of gamma/n along with an increasing number of porphyrin units n compared with the butadiyne-bridged array, Yn. As a result, the static third-order susceptibilities chi((3)) of Dn and Tn are expected to be 1 and 3 orders of magnitude larger than that of Yn in the limit n -> infinity, and these advantages of porphyrin tapes become more prominent by taking into account geometrical relaxations of porphyrin units in the arrays. The structure-property relationship in various conjugated polymers including porphyrin arrays is interpreted on the basis of the scaling behaviors of chi((1)) and chi((3)) with the effective conjugation length (ECL) as well as the reciprocal HOMO-LUMO energy gap (1/E-g). In particular, from the master plot of chi((1)) (and even chi((3))) versus 1/E-g, the pi-conjugation of Tn is noted to indeed be exceptional, because its large susceptibilities cannot be expected from the scaling behavior of ordinary one-dimensional conjugated systems. We also point out that the theory of scaling relationship, chi((3)) similar to 1/E-g(x), is significantly improved by taking into account electron-electron interactions based on the comparison with experiments.