Electronic structure and nonlinear optical properties of the fullerenesC60andC70: A valence-effective-Hamiltonian study

Abstract

Based on the geometries optimized by the AM1 semiempirical technique (Austin Model 1 of Dewar et al.), we exploit the valence-effective-Hamiltonian (VEH) method to study the electronic structures of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$. The valence-electronic density of states (DOS) calculated is found to be in excellent agreement with the high-resolution energy-distribution curves obtained from synchrotron-photoemission experiments in terms of both positions and relative intensities of the peaks. The maximum difference in peak position between theory and experiment is 0.4 eV. This shows that the VEH method provides a very reasonable description of these two fullerenes. We then apply the VEH-SOS (sum-over-states) approach to study the nonlinear optical response of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$. We obtain that the off-resonance third-order susceptibility ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ is on the order of ${10}^{\mathrm{-}12}$ esu. Our results are fully consistent with the electric-field-induced second-harmonic generation and third-harmonic-generation (THG) measurements by Wang and Cheng and the degenerate-four-wave-mixing measurements by Kafafi et al., but about three to four orders of magnitude lower than the data reported by Blau et al. and by Yang et et al. The static ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$ values of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ are compared to those of polyacetylene. We also investigate the dynamic nonlinear optical response by calculating the THG spectrum. We find that the lowest two-photon and three-photon resonances occur at almost the same frequency for ${\mathrm{C}}_{60}$, because of the symmetry of the molecule.