First-principles calculation of bulk susceptibility for second-harmonic generation in crystalline C₆₀

The hyperpolarizabilities for electric dipole second-harmonic generation (SHG) due to the bilinear combination of an electric field and either the electric-field gradient (μ^eeq) or the associated magnetic field (τ^eem), and for electric quadrupole SHG quadratic in the electric field (μ^qee) have been calculated for the C₆₀ molecule at pump photon energies from 0.5 to 2.2 eV using the valence effective Hamiltonian method with a minimal STO-3G basis: magnetic dipole SHG quadratic in the electric field (τ^mee) is zero by symmetry in C₆₀. The coefficients exhibit resonances at photon energies near 1.9 for μ^eeq, 1.4 for μ^qee, and 2.0 eV for τ^eem. They are combined with empirical local-field factors and a theoretical local field-gradient tensor to calculate the composite susceptibility χ⁽²⁾ for SHG from crystalline C₆₀ in the same energy range. The susceptibility shows several resonances that arise from those in μ^eeq, μ^qee, and τ^eem. The results are able to reproduce the magnitudes and signs reported experimentally, subject to a sensitive dependence on photon energy near resonances.