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 Huc kel wave functions, is used in a study of second harmonic generation i n model systems related to KTiOPO4 (KTP). Clusters of one, three, and five interconnected TiO6 groups are constructed to simulate the extend ed--Ti--O--Ti--O--chains present in the crystal. To facilitate compari son and illuminate differences among systems of different sizes, we co mpute a specifically local nonlinear response. Ground and excited stat es are determined for the full structure, but only those portions of t he molecular orbitals relevant to a designated subsystem (typically th e central TiO6 group) are used to evaluate dipole transition moments i n the sum over states. Results show, first, that the nonresonant hyper polarizability is enhanced locally as more TiO6 units are added. An in tact and terminated structure, whether an isolated TiO6 monomer or tri mer, generally exhibits a smaller nonlinearity, with opposite sign, th an a fully integrated structure with the same number of TiO6 groups. A second observation is that, despite differences in magnitude, the cha nges in hyperpolarizability accompanying an axial distortion of each o ctahedron follow a nearly uniform pattern in chains of different lengt hs. These various effects are interpreted by comparing relative change s in total electronic density and by a detailed analysis of the matrix elements and molecular orbitals contributing to the perturbative expr ession. Indications are that simple molecular orbital pictures develop ed for isolated fragments may be insufficient to account for the coope rative nonlinear response of highly delocalized systems such as KTP.