Exploratory Pariser-Parr-Pople investigation of the static first hyperpolarizability of polymethineimine chains

The in-plane components of the first hyperpolarizability per unit cell of model polymethineimine chains have been computed by the uncoupled and coupled Hartree-Fock procedures (UCHF and CHF) within the Pariser-Parr-Pople method. The effects of electron density alternation along the backbone are investigated using two different parametrizations. With the most realistic scheme, the longitudinal component of the first hyperpolarizability is, by far, the largest for large chains, although other in-plane components can be of importance under certain circumstances. Regardless of the parametrization, both UCHF and CHF treatments yield a longitudinal first hyperpolarizability per unit cell that goes through a maximum at small lengths when plotted against the chain length. The resulting 'dromedary-back' shape of the curve can be qualitatively explained in terms of the interplay between asymmetry and delocalization effects. The quantitative behavior in the vicinity of the maximum, which is related to the sign and magnitude of the limiting infinite chain value, is analyzed at the uncoupled Hartree-Fock level using a new approximation scheme for the sum over states. However, the latter becomes unsatisfactory as the length of the chain is increased. So called N-level models do not work even for small chains.