The relationship between hyperpolarizability (beta) and spectral intensities has been investigated for polyene (or oligoene) systems. The vibrational polarizability, first hyperpolarizability, and second hyperpolarizability have been derived for the geometrical and electrical potentials with anharmonic terms included. This relationship has been tested by performing ab initio calculations on polyene derivative systems of X-(HC=CH)(n)-Y, where 1 less than or equal to n less than or equal to 5 for X/Y=H/NH2, H/NO2, and NH2/NO2. Particular attention has been given to the first hyperpolarizability. The electronic hyperpolarizability shows a linear relationship with the square root of the product of IR and Raman intensities of the concurrent C=C stretching vibrational mode. The spectral intensities represent the vibrational hyperpolarizabilities which are of equivalent magnitude to the electronic hyperpolarizabilities. In the presence of an external electric field, the C=C bond stretches are responsible for the electronic hyperpolarizability, while the effects by other bond stretches are not significant. Thus the hyperpolarizability can be estimated by obtaining the LR and Raman intensities of C=C stretching vibration. This relationship would be valid for poly pi-conjugated molecules. (C) 1997 American Institute of Physics. [S0021-9606(97)00141-4].