THEORETICAL-STUDY OF THE NONLINEAR-OPTICAL PROPERTIES OF KTIOPO4 - COOPERATIVE EFFECTS IN EXTENDED --TI--O--TI--O-- CHAINS

The sum-over-states perturbative formalism, combined with extended Huckel wave functions, is used in a study of second harmonic generation in model systems related to KTiOPO4 (KTP). Clusters of one, three, and five interconnected TiO6 groups are constructed to simulate the extended--Ti--O--Ti--O--chains present in the crystal. To facilitate comparison and illuminate differences among systems of different sizes, we compute a specifically local nonlinear response. Ground and excited states are determined for the full structure, but only those portions of the molecular orbitals relevant to a designated subsystem (typically the central TiO6 group) are used to evaluate dipole transition moments in the sum over states. Results show, first, that the nonresonant hyperpolarizability is enhanced locally as more TiO6 units are added. An intact and terminated structure, whether an isolated TiO6 monomer or trimer, generally exhibits a smaller nonlinearity, with opposite sign, than a fully integrated structure with the same number of TiO6 groups. A second observation is that, despite differences in magnitude, the changes in hyperpolarizability accompanying an axial distortion of each octahedron follow a nearly uniform pattern in chains of different lengths. These various effects are interpreted by comparing relative changes in total electronic density and by a detailed analysis of the matrix elements and molecular orbitals contributing to the perturbative expression. Indications are that simple molecular orbital pictures developed for isolated fragments may be insufficient to account for the cooperative nonlinear response of highly delocalized systems such as KTP.