Variational–perturbational treatment for the polarizabilities of conjugated chains. II. Hyperpolarizabilities of polyenic chains

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Abstract
We use a perturbative density matrix treatment to investigate the behavior of the first and second static hyperpolarizabilities of linear conjugated chains CNHN+2 described by a Pariser–Parr–Pople Hamiltonian. We examine the evolution of the hyperpolarizabilities with increasing chain lengths, and the effect of different conformations (such as those corresponding to soliton and polaron defects) and of different charge states on the polarizability response of the chains. It is shown that charged soliton chains have large first hyperpolarizabilities β, and that the behavior of the different components of the second hyperpolarizability tensor γiiii is highly dependent on the geometry and charge of the conjugated chain. In all cases, the contribution of the longitudinal component is shown to dominate the orientationally averaged hyperpolarizability of the chains.