Matsuzaki Yoichi, Nogami Atsushi, Tsuda Akihiko, Osuka Atsuhiro, Tanaka Kazuyoshi
Advanced Technology Research Laboratories, Nippon Steel Corporation, 20-1 Shintomi, Futtsu, Chiba 293-8511, Japan.
J Phys Chem A. 2006 Apr 13;110(14):4888-99. doi: 10.1021/jp0582989.
By using the Pariser-Parr-Pople (PPP) theory, the second hyperpolarizabilities (gamma) have been calculated for various pi-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((3)) (and even chi((1))) 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)) approximately 1/E(g)(x)(), is significantly improved by taking into account electron-electron interactions based on the comparison with experiments.
通过使用帕里泽-帕尔-波普尔（PPP）理论，计算了各种π共轭卟啉阵列的二阶超极化率（γ），包括“卟啉带”：中位-β双连接卟啉阵列Dn和中位-中位、β-β、β-β三连接阵列Tn。在卟啉单体和二聚体的情况下，通过与从头算哈特里-福克理论和B3LYP理论进行比较，检验了PPP理论的有效性。结果发现，与丁二炔桥连阵列Yn相比，Dn尤其是Tn随着卟啉单元数n的增加，γ/n呈现出更为显著的变化。因此，在n趋于无穷大的极限情况下，预计Dn和Tn的静态三阶极化率χ(3)比Yn的大1到3个数量级，并且考虑到阵列中卟啉单元的几何弛豫，卟啉带的这些优势变得更加突出。基于χ(1)和χ(3)与有效共轭长度（ECL）以及倒数HOMO-LUMO能隙（1/Eg）的标度行为，解释了包括卟啉阵列在内的各种共轭聚合物中的结构-性质关系。特别是，从χ(3)（甚至χ(1)）对1/Eg的主图中可以注意到，Tn的π共轭确实是特殊的，因为从普通一维共轭体系的标度行为无法预期其具有大的极化率。我们还指出，通过与实验比较考虑电子-电子相互作用，标度关系理论χ(3)≈1/Eg(x)得到了显著改进。
