Beratan, DN; Onuchic, JN; Perry, JW, *Nonlinear susceptibilities of finite conjugated organic polymers*,
The Journal of Physical Chemistry, vol. 91 no. 11
(1987),
pp. 2696-2698 [pdf] .
**Abstract:**

*Tight-binding calculations of the length dependence of the third-order molecular hyperpolarizability for polyenes and polyynes are reported. The π-electron wave functions were determined by exploiting the limited translational symmetry of the molecules. Perturbation theory was used to calculate the longitudinal component of the electronic nonresonant hyperpolarizability. To our knowledge, this is the first two-"band" calculation of third-order hyperpolarizabilities on finite π-electron systems of varying length. In contrast to the results of the one-"band" models, the hyperpolarizability densities increase rapidly and then, after about 10-15 repeating units, approach an asymptotic value. © 1987 American Chemical Society.*