Length dependence of excitation energies in linear polyenes: Localized and delocalized descriptions

The length dependence of the lowest allowed transition energy of linear polyenes is studied using delocalized SCF and localized excitonic approaches. Within the PPP SCF approximations the calculated transition energies converge to a finite values as N^?1 as the number of double bonds (N) becomes large, when the excited state contains all singly excited configurations. On the other hand, the fully localized excitonic method at the level of single excitations, although it predicts a gap in the excitation spectrum of an infinite polyene, gives results which converge to this value as N^?2. The inclusion of double and triple excitations into the excitonic method by means of perturbation theory does not appear to change this behavior. The reasons for the discrepancy between the two approaches is analyzed. Experimentally, the transition energies in solution converge to a finite value as N^?1 to a good degree of approximation. If it is assumed that the solvent shift is constant for long polyenes, the available experimental results favour the delocalized approach as the starting point in describing the length dependence of the excitation energy of long polyenes.