Nonlinear optical properties of polyenoctupoles: a multipolar tensorial quantum analysis
Résumé
This paper presents a theoretical analysis of the first-order hyperpolarizability properties (β) of polyenic molecules of octupolar C3h symmetry (polyenoctupoles), based on CNDO/S calculations, and interpreted in the frame of a tensorial formalism. One of the goals of this analysis is to dissect the hyperpolarizability components in such a way as to reveal interactions within the different subunits constituting the octupolar system. To this end, the polyenoctupole properties are compared to those of dipolar analogues having the same conjugation length m. The general laws obtained for 1D dipolar polyenes (linear variations of λ with m, exponential variations of β with m) are also verified for the polyenoctupoles. The theory also reveals that, for the same conjugation length, the polyenoctupoles should exhibit a better hyperpolarizability–absorption trade-off than the corresponding 1D polyenes. A multipolar tensorial analysis of the dipolar and octupolar components of β in 1D polyenes demonstrates that the nonlinear anisotropy ρ of the 1D polyenes effectively corresponds to ideal 1D chromophores, with a octupolar/dipolar ratio close to its theoretical value of 2/3=0.82. Finally, the octupolar interaction concept is introduced within the frame of irreducible tensor representation. In this generally applicable representation, the β tensor of a multipolar system is dissected into two separate tensor components, one (βA) representing the sum of the contributions of the individual dipole subunits, the other (βI) reflecting interactions (charge transfer or Coulombic) between the dipole units constituting the multipole. The interaction term βI could be determined in magnitude and in direction in the irreducible J=3 space. In the C3h octupoles considered in the present work, the octupolar interaction term βI is found negligible for the smallest molecules and becomes relatively important (up to 20–30% of βA) only for the octupoles having the largest size.