Molecular Structure and Absorption Spectra of Carotenoids

An assemblage of π-electrons in the chain of carotenoid molecules is discussed, according to Tomonaga's method, on the basis of an assumption that the electrons are kept in a pipe whose length is equal to the chain length of conjugated double bonds. The spin degrees of freedom of electrons are taken into account though Tomonaga disregarded them. The one-dimensional potential of two-electron forces is assumed to be given by an average of the Coulomb repulsive potential over a section of the pipe. The calculated values of absorption maxima are in good agreement with experiment for carotenoids. The adequacy of the method is discussed.