Nonlinear optical response of conjugated polymers: Essential excitations and scattering

The computations presented here investigate the role that electron-electron interactions play in establishing the magnitude of the nonresonant second hyperpolarizability of conjugated polymers. A sum-over-states formalism is used so that the connection between the structure of the excited electronic states and the nonlinear response may be explored. The inclusion of electron correlation in calculations of the long-chain limit is made possible by an essential excitation/scattering formalism. This approach identifies the important excitations and explicitly calculates the scattering between these excitations that can occur in a two-photon process. The approach has two important advantages. First, it provides a balanced description of the one-photon and two-photon states, as required to obtain a size-consistent prediction for the hyperpolarizability when using a sum over electronic states generated by an approximate but nonperturbative method. Second, the use of a contracted, scattering basis set makes it computationally feasible to include both single- and double-electron-hole pair configurations in calculations on long chains. Using the Pariser-Parr-Pople Hamiltonian of polyacetylene with the unscreened Coulomb interactions of the Ohno parametrization, the essential excitation/scattering approach yields a nonresonant hyperpolarizability that agrees with that of the independent electron model, provided that the independent electron model is parametrized to yield the same optical gap as the correlated model. This agreement is significant, since the excited states obtained in the correlated calculations exhibit large effects from electron correlation, such as exciton formation and low-energy ${}_{}{}^1{}_{}{}^{}$ ${\mathit{A}}_{\mathit{g}}$ states. This suggests that even relatively strong electron-electron interactions need not be explicitly included in a model of the polymeric limit of the nonresonant response, but can instead be absorbed into the effective parameters of an independent electron model. © 1996 The American Physical Society.