Dispersion coefficients for first hyperpolarizabilities using coupled cluster quadratic response theory

The frequency dependence of third-order properties can in the normal disper sion region be expanded in a Taylor series in the frequency arguments. The dispersion coefficients thus obtained provide an efficient way of expressin g the dispersion of frequency-dependent properties and are transferable bet ween different optical processes. We derive analytic expressions for the di spersion coefficients of third-order properties in coupled cluster quadrati c response theory and report an implementation for the three coupled cluste r models CCS, CC2, and CCSD. Calculations are performed for the first hyper polarizability of the NH3 molecule. The convergence of the dispersion expan sion with the order of the coefficients is examined and we find good conver gence up to about half the frequency at which the first pole in the hyperpo larizability occurs. Pade approximants improve the convergence dramatically and extend the application range of the dispersion expansion to frequencie s close to the first pole. The sensitivity of the dispersion coefficients o n the dynamic correlation treatment and on the choice of the one-electron b asis set is investigated. The results demonstrate that, contrary to presump tions in the literature, the dispersion coefficients are sensitive to basis set effects and correlation treatment similar to the static hyperpolarizab ilities.