Optimization of geometrical structure and simulation of the spectra of third-order nonlinear optical polarizabilities inC59SiandC58Si2heterofullerenes

Abstract

We report the optimized geometrical structures using the ab initio method, and the calculated frequency dependence of the third-order nonlinear optical polarizabilities $\ensuremath{\gamma}$ in the different optical processes of the third-harmonic generation, electric-field induced second-harmonic generation, and degenerate four-wave mixing using the INDO/SDCI method coupled with the sum-over-states method for ${\mathrm{C}}_{59}\mathrm{Si}$ and two isomers of ${\mathrm{C}}_{58}{\mathrm{Si}}_{2}$ heterofullerenes. The optimized structures show that the stabilization of the para isomer of ${\mathrm{C}}_{58}{\mathrm{Si}}_{2}$ is larger than that of the dia isomer of ${\mathrm{C}}_{58}{\mathrm{Si}}_{2},$ and the geometrical modifications of ${\mathrm{C}}_{59}\mathrm{Si}$ and ${\mathrm{C}}_{58}{\mathrm{Si}}_{2}$ isomers occur in the vicinity of the Si-doped atom after the replacement of one or two C atoms by Si atoms in the ${\mathrm{C}}_{60}$ fullerene. The calculated hyperpolarizabilities at nonresonant frequency show the varied trends in the order of ${\mathrm{C}}_{59}\mathrm{Si}\ensuremath{\approx}$ dia isomer of ${\mathrm{C}}_{58}{\mathrm{Si}}_{2}<$ para isomer of ${\mathrm{C}}_{58}{\mathrm{Si}}_{2}$ at ground state and the charge transfers of two-photon states make significant contributions to third-order optical polarizabilities for the para isomer of ${\mathrm{C}}_{58}{\mathrm{Si}}_{2}.$ The enhancement of first excited singlet state is about one or two order of magnitude at nonresonant frequency. The susceptibilities of $\ensuremath{\chi}(\ensuremath{-}\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega})$ of these Si-doped fullerene films are estimated to be about ${10}^{\ensuremath{-}10}$ esu at first excited state and ${10}^{\ensuremath{-}11}$ esu at ground state in nonresonant frequency.