EFFECTS OF ELECTRON CORRELATION ON THE NONLINEAR OPTICAL-PROPERTIES OF POLYACETYLENE

Within the independent-electron approximation, the perturbation-theory expression for the second hyperpolarizability-gamma can be written as a sum over two classes of terms: electron-hole (e-h) pair migration terms, which involve only singly excited states, and terms involving doubly excited states. In the long-chain limit, this separation of terms corresponds to the two integrals in the band-theory expression for gamma. In polyacetylene, the e-h pair migration terms are dominant with the doubly excited states accounting for a 20% decrease in gamma. On inclusion of electron correlation, tightly bound excitons are formed and the terms in the perturbation-theory expression for gamma can be separated into two new classes: exciton migration terms and terms involving biexciton states. The exciton migration terms are explicitly evaluated using the Pariser-Parr-Pople Hamiltonian and a basis set composed of all single excitations from the Hartree-Fock ground state, i.e., the intermediate exciton formalism. Since 98% of the optical intensity is in the lowest-energy excitons, the free electron-hole pair states can be ignored in the calculation of gamma. The exciton migration terms are similar in magnitude to the e-h pair migration terms of Huckel theory, provided that the Huckel parameters are adjusted to give the same long-chain band gap as that obtained in exciton theory. This may account for the success of Huckel theory in predictions of gamma for long chains. The contribution from the biexciton states is not evaluated.