Vibrational contributions to third-order nonlinear optical susceptibilities

Including vibrational levels in the perturbation theory sum for the third-order nonlinear optical susceptibility γ introduces terms which have a pure vibrational frequency in the denominator. These terms can be rewritten as a sum over Raman amplitudes. Model calculations on a diatomic system with two electronic states show that these terms are negligible, about 3% of the value obtained ignoring vibrations. In polyacetylene, the Herzberg–Teller contribution to the Raman amplitude is much larger than in the diatomic case. Within the tight binding and harmonic oscillator approximations, the sum over Raman amplitudes is 10% of the value for γ obtained ignoring vibrations.