Nonlinear optical properties of polyenoctupoles: a multipolar tensorial quantum analysis

This paper presents a theoretical analysis of the first-order hyperpolariza bility properties (beta) of polyenic molecules of octupolar C-3h symmetry ( polyenoctupoles), based on CNDO/S calculations, and interpreted in the fram e 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 e nd, the polyenoctupole properties are compared to those of dipolar analogue s having the same conjugation length rn, The general laws obtained for 1D d ipolar polyenes (linear variations of lambda with root m, exponential varia tions of beta with m) are also verified for the polyenoctupoles. The theory also reveals that, for the same conjugation length, the polyenoctupoles sh ould exhibit a better hyperpolarizability-absorption trade-off than the cor responding 1D polyenes. A multipolar tensorial analysis of the dipolar and octupolar components of beta in 1D polyenes demonstrates that the nonlinear anisotropy rho of the 1D polyenes effectively corresponds to ideal 1D chro mophores, with a octupolar/dipolar ratio close to its theoretical value of root 2/3 = 0.82. Finally, the octupolar interaction concept is introduced w ithin the frame of irreducible tensor representation. In this generally app licable representation, the beta tensor of a multipolar system is dissected into two separate tensor components, one (beta(A)) representing the sum of the contributions of the individual dipole subunits, the other(beta(1)) re flecting interactions (charge transfer or Coulombic) between the dipole uni ts constituting the multipole. The interaction term beta(1) could be determ ined in magnitude and in direction in the irreducible J = 3 space. In the C -3h octupoles considered in the present work, the octupolar interaction ter m beta(1) is found negligible for the smallest molecules and becomes relati vely important (up to 20-30% of beta(A)) Only for the octupoles having the largest size. (C) 1999 Elsevier Science B.V. All rights reserved.