Dominant electronic oscillators in the optical nonlinearities of conjugated polyenes

In the coupled-oscillator representation [Takahashi and Mukamel, J. Chem. Phys. 100 (1994) 2366], the optical properties of conjugated polymers are calculated by mapping the system into a collection of coupled normal modes representing electron-hole pairs. Optical nonlinearities are induced by anharmonic couplings among oscillators and with the external field. Tree diagrams are developed which visualize the relevant nonlinearities and dominant oscillators and provide an efficient algorithm for computing the hyperpolarizabilities.