Absorption and rotation of light by helical oligomers: The nearest neighbor approximation

Explicit expressions for the DK and RK associated with the excitation of regular oligomers from their ground states to the Kth exciton state as functions of N, P, μ, μ∥, μt, and μr have been derived on the assumption that the only perturbation Vij to the N singly excited states results from exciton transfer between adjacent residues, V12. The DK relation predicts the occurrence of a perpendicularly polarized absorption band arising from μ⟂ and a parallel polarized band from μ∥ with maxima at K = [2(N + 1)/P] and 1, which are shifted from the monomer band by 2V12 cos(2π/P) and 2V12cos[π/(N + 1)], respectively. Overlapping of the bands, which may occur in oligomers, decreases rapidly with N, leaving two perfectly polarized bands in the polymer. Within each band which includes only a few levels near the maxima, the most probable transition may be associated with all of the intensity for very short chains but only 40.2–50% (⟂) and 80.9% (∥) as N ∞ (polymer case). A relation was derived by which V12 may be simply calculated from μ, μr, μt, μ∥, a, and z. The nearest neighbor theory was compared with experiment by calculating a reasonable set of the relevant parameters which exactly account for known spectral shifts.