A "Metallic" model for the spectra of conjugated polyenes

Abstract

The μ-electrons belonging to the double bonds of trans-conjugated polyenes are assumed to be a one-dimensional electron gas in a field of uniform potential energy whose length is approximately that of the conjugated system. The energy levels, the selection rule (Δn odd) and the transition intensities are deduced. The model predicts that the oscillator strength of the main absorption band of a trans-conjugated polyene is given by f=0.134(2N+l), where N is the number of double bonds. The calculated values are in good agreement with experimental data. The wave number of the main band is related to the length of the conjugated system and the number of double bonds with moderately good agreement with experiment. The second, weaker absorption band of trans-carotene is discussed briefly.