Within Huckel theory, the nonresonant third-order nonlinear optical susceptibility of a conjugated polymer is directly proportional to the bandwidth raised to the third power, and inversely proportional to the optical gap raised to the sixth power, This functional dependence, if correct, implies that polyacetylene is already an optimal organic material with regards to the magnitude of the nonresonant hyperpolarizability. Therefore, any improvement,, in the figure-of-merit for optical switching applications will come at the expense of the magnitude of the hyperpolarizability. Here, singles configuration-interaction (S-CI) theory is used to solve the Pariser-Parr-Pople (PPP) Hamiltonian of polyacetylene, treating both the strength of electron-electron interactions and the degree of bond alternation as model parameters. The results show that the hyperpolarizability is independent of the strength of electron-electron interactions and thus the degree of electron-hole correlation, and instead depends almost exclusively on the optical gap and the bandwidth. Furthermore, the functional dependence on the optical gap and bandwidth is nearly identical to that obtained from Huckel theory, giving strong support to the Huckel description of long chains, and its implications for materials optimization. In addition, the inverse-sixth power dependence of the hyperpolatizability is shown to imply a strong dependence of the transition moments on the optical gap. Finally. the resonant hyperpolarizability associated with two-photon absorption is found to tend toward an inverse-sixth power dependence on optical gap, although deviations from this dependence are considerably larger than for the resonant response.