Frequency dispersion of the first hyperpolarizabilities of reference molecules for nonlinear optics

The frequency dispersion of the hyper-Rayleigh scattering first hyperpolarizabilities (β<inf>HRS</inf>) of five reference molecules for nonlinear optics, namely, carbon tetrachloride, chloroform, dichloromethane, acetonitrile, and trichloroacetonitrile, is described using the coupled-cluster singles and doubles quadratic response function (CCSD-QRF) as well as approximate schemes. Comparisons to approximate schemes in which the frequency dispersion is evaluated as either a multiplicative or an additive correction to the static hyperpolarizability yield the following observations: (i) errors of the order of 10% or less are usually encountered when using the multiplicative scheme for photon energies far from the lowest dipole-allowed excitation energies, (ii) spurious cases cannot be excluded as evidenced by carbon tetrachloride where the multiplicative scheme predicts a decrease of β<inf>HRS</inf> in contradiction to the increase obtained using the CCSD-QRF method, and (iii) the additive scheme is at best as reliable as the multiplicative approximation. The two-state approximation presents the advantage of correcting the wrong behavior of the additive and multiplicative schemes for carbon tetrachloride, but it is not an improved solution for the other compounds, while the question of selecting the appropriate dominant excited state remains unanswered. Finally, a new β<inf>xyz</inf> value of 18.9 a.u. is proposed for carbon tetrachloride in gas phase at λ = 1064 nm, to be compared with the measured 16.9 ± 1.4 a.u. value due to Shelton.