Size-dependency of polarizabilities of fractal- and nonfractal-structured oligomers modeled after dendron parts in Cayley-tree-type dendrimers

Abstract

We investigate the size-dependency of static polarizabilities (α) (in the chain-length direction) of three types of model oligomers (made of phenylene vinylenes), i.e., para-oligomers and meta-oligomers with fractal and nonfractal structures by the finite-field method using molecular orbital calculations. The fractal-structured meta-oligomers are considered to be models of dendron parts involved in Cayley-tree-type dendrimers. The chain-length dependence of α of para-oligomers is found to be much larger than that of nonfractal-structured meta-oligomers, while the fractal-structured meta-oligomers exhibit an attractive chain-length dependence of α; the α values of meta-structured oligomers are near to those of nonfractal-structured meta-oligomers in small chain-length region, while they are close to those of para-oligomers in sufficiently large chain-length region. Using the polarizability density analysis, the spatial contributions of π-electrons to α of nonfractal-structured meta-oligomers are found to be smaller than those of para-oligomers and to be well decoupled at the meta-substituted benzene rings. In contrast, it is found that the spatial contributions of π-electrons to α in linear-leg regions for fractal-structured meta-oligomers are similar to those for the para-oligomers though the α density distributions for fractal-structured meta-oligomers are also well decoupled at the meta-substituted benzene rings. Such features, which reflect the fractal structure, is predicted to cause the attractive size-dependency of α for fractal-structured meta-oligomers.