Abstract: Applying difference equation method,a decomposed expression of the eigene-quation for one type of the single-linked chain polymers is discussed,and the formulae for the molecular orbitals are given in closed form. The analytical energy expressions of polyenes which have alternatively long and short bond lengths are obtained by using the interpolation that is based on an approximate model proposed by us. In terms of this, the ionization energies of various homologous serieses of conjugate systems can be well correlated linearly by means of unified parameters for different energy levels.Asimilar treatment is also presented for double-linked systems.At last,a more rigorous criterion for deciding relative quality of correlation coefficients is proposed.