High energy two-photon states in finite versus infinite polyenes

Optical nonlinearity in π-conjugated polyenes depends crucially on a single two-photon state that is located above the one-photon allowed exciton. In the case of the infinite polyene this single state should be thought of as a collection of states with very narrow bandwidth. The location of this two-photon state in the infinite polyene is of considerable interest. We present numerical data for finite chains and discuss in detail why extrapolation of finite chain data to obtain the energies of the high energy states in the infinite polyene requires considerable care. Based on upper and lower bounds that we put on the energy of the two-photon state in question, we predict it to be extremely close to the one-photon excition in the infinite chain limit. We present recent experimental data for a polydiacetylene that is consistent with our prediction.