In the present work, we report the multibranching effect on the dynamic first-order hyperpolarizability (β(−2ω; ω, ω)) of triphenylamine derivatives containing cyanopyridine onebranch (dipolar structure), two-branch (V-shaped structure), and three-branch (octupolar structure) structures. For this study, we used the hyper-Rayleigh scattering (HRS) technique involving picosecond pulse trains at 1064 nm. Our results show that β HRS increases from 2.02 × 10 −28 to 9.24 × 10 −28 cm 5 /esu when an extra branch is added to the molecule, configuring a change from a dipolar to a V-shaped (quadrupolar) molecular structure. When a third branch is added, leading to an octupolar structure, a decrease to 3.21 × 10 −28 cm 5 /esu is observed. Such a significant decrease in β HRS is attributed to a negative contribution presented in the β HRS description by using a three-level energy approach due to their electronic structure and considering a specific combination of the angle between the dipole moments. On the other hand, the enhancement of β HRS found for the quadrupolar structure is associated with the cooperative enhancement due to the electronic coupling between the branches that increases considerably the transition dipole moment and permanent dipole moment change. To explain the β HRS results obtained for different molecules, we employed the HRS figure of merit, FOM HRS = β HRS /N eff 3/2 , in which N eff is the effective number of π-conjugated bonds, and the few-energy level approach for β HRS within the Frenkel exciton model. To shed more light on the experimental results interpretation, we performed time-dependent density functional theory calculations combined with a polarizable continuum model to confirm the energy and oscillator strength of the electronic transitions assumed in the Frenkel exciton model employed here.

This paper reports on the static and dynamic first-order hyperpolarizabilities of a class of push-pull octupolar triarylamine derivatives dissolved in toluene. We have combined hyper-Rayleigh scattering experiment and the coupled perturbed Hartree-Fock method implemented at the Density Functional Theory (DFT) level of theory to determine the static and dynamic (at 1064 nm) first-order hyperpolarizability (βHRS) of nine triarylamine derivatives with distinct electron-withdrawing groups. In four of these derivatives, an azoaromatic unit is inserted and a pronounceable increase of the first-order hyperpolarizability is reported. Based on the theoretical results, the dipolar/octupolar character of the derivatives is determined. By using a polarizable continuum model in combination with the DFT calculations, it was found that although solvated in an aprotic and low dielectric constant solvent, due to solvent-induced polarization and the frequency dispersion effect, the environment substantially affects the first-order hyperpolarizability of all derivatives investigated. This statement is supported due to the solvent effects to be essential for the better agreement between theoretical results and experimental data concerning the dynamic first-order hyperpolarizability of the derivatives. The first-order hyperpolarizability of the derivatives was also modeled using the two- and three-level models, where the relationship between static and dynamic first hyperpolarizabilities is given by a frequency dispersion model. Using this approach, it was verified that the dynamic first hyperpolarizability of the derivatives is satisfactorily reproduced by the two-level model and that, in the case of the derivatives with an azoaromatic unit, the use of a damped few-level model is essential for, considering also the molecular size of such derivatives, a good quantitative agreement between theoretical results and experimental data to be observed.

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