Frequency-dependent second hyperpolarizabilities using coupled cluster cubic response theory

The coupled cluster cubic response function is derived using a time-averaged quasienergy Lagrangian and Fourier component variational perturbation theory. The obtained expressions are in accord with the 2n+1 and 2n+2 rules. The first implementation of the cubic response function is reported for frequency-dependent second hyperpolarizabilities for a coupled cluster singles and doubles wavefunction and sample calculations are presented for hyperpolarizabilities of N2 for several third-order optical processes. The results are in excellent agreement with recent experiments for electric field induced second harmonic generation.