π-Electronic Structure and Absorption Spectra of Carotenoids

The π-electronic structure and the absorption spectra of carotenods which contain a trans-conjugated chain of 2 N carbon atoms are considered within the framework of the HMO approximation. It is shown that the relation between the wavelengths of calculated absorption maxima and the number N of conjugated double bonds can be brought into very satisfactory agreement with the experiments, by determining parameter values for two resonance integrals phenomenologically. The bond orders and bond lengths are also calculated by using the resonance integrals thus determined. The transition moments and oscillator strengths, from which we can obtain the same selection rule with that of the FE model, are investigated as functions of N . Finally, the case of a set of MO's in which we can find a so-called surface state is considered.