Molecular orbital expressions for approximate uncoupled Hartree-Fock second hyperpolarizabilities. A Pariser-Parr-Pople assessment for model polyacetylene chains

Various partitioning schemes to the uncoupled Hartree-Fock second hyperpolarizability and three of its approximations have been derived. One-electron eigenstate formula have been determined. The validity of these schemes for studying polymeric systems has been assessed by investigating the evolution with chain length of the longitudinal second hyperpolarizability per unit cell of model polyacetylene chains. This study of the size-consistency of the various contributions has been carried out within the Pariser-Parr-Pople method. It is shown that all the approximations and partitioning schemes work well for the smallest chains. The less alternating the electron distribution along the polymeric backbone, the better the approximations and partitioning schemes.