This contribution explores the relation between molecular second hyperpolarizabilities (gamma) and molecular architecture in phenylacetylene dendrimers using the semiempirical molecular orbital method, that is, INDO/S method. The orientationally averaged gamma of a large-size phenylacetylene dendrimer, which is composed of 24 units of phenylacetylenes and is referred to as D25, is found to be about 50 times as large as that of the diphenylacetylene monomer. In contrast, the gamma(s)() value of D25 is found to be about 6 times as small as that of the para-substituted phenylacetylene oligomer (L25) composed of 24 units of phenylacetylenes. To investigate the structure-property relation in gamma for D25 and L25, we examine the spatial contributions of electrons to gamma values using gamma density analysis. The present analysis reveals that the dominant contributions of electrons to gamma of D25 are localized in the linear-leg regions parallel to the applied electric field and the contributions are also well segmented at the meta-connected points (benzene rings), while the spatial distribution of the gamma density of L25 is extended over the whole region of the chain, and the dominant contribution stems from the both-end regions. It is found for D25 that the magnitude of contributions to gamma in the internal region is more enhanced than that in the outer region. We further found that the magnitudes of contributions in internal linear-leg regions of D25 are somewhat larger than those of the same-size isolated linear-leg molecules. This suggests that the slightly remaining pi-conjugations via the meta-branching points still enhance the contributions to gamma localized in the linear-leg regions. These features of spatial contributions to gamma of D25 are found to originate in the fractal architecture, in which pi-conjugation lengths in the linear-leg region increase on going from the periphery to the core. Finally, fractal antenna dendrimers are expected to be promising novel nonlinear optical (NLO) substances with a controllability of the magnitude and spatial contribution of the third-order NLO properties.

Analytical expressions of total energies, effective exchange integrals, polyradical character, spin density, unpaired electron density, and information entropy are derived for allyl radical dimers and trimers on the basis of the Hubbard model in order to elucidate interrelationships among several broken-symmetry and symmetry-adapted approaches to molecular magnetism. Ab initio unrestricted Hartree-Fock and hybrid density functional theory (DFT) calculations of allyl radical dimers to decamers are also carried out for confirmation of characteristics revealed by the analytical investigations. A mesoscopic hydrogen radical cluster with 50 radical sites is studied by the ab initio hybrid DFT methods to elucidate functional behaviors of the above quantities with change of interatomic distance. The potential curves for the lowest and highest spin states of the cluster by these methods are depicted for the purpose. Implications of the present computational results are discussed in relation to size-consistent spin projection and size effects on effective exchange interactions in mesoscopic radical clusters.

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The two-parameter theory for radius of gyration and intrinsic viscosity was tested with experimental data on polystyrene and polyisobutylene published in preceding parts of this series. It was found