Vibrational corrections to the second hyperpolarizabilities of Al(n)P(n) clusters

In this work, we report results of vibrational corrections to the second hyperpolarizabilities of Al2P2, Al3P3, Al4P4, Al6P6, and Al9P9 clusters. The vibrational corrections were calculated through the perturbation theoretic method of Bishop and Kirtman and also using a variational methodology at the second order Møller-Plesset perturbation theory level with the aug-cc-pVDZ basis set. Results show that the vibrational corrections are important, accounting for more than half of the corresponding electronic second hyperpolarizabilities at the static limit. Comparisons between results obtained through both methods show very good agreements for the terms [α(2)] and [μβ] but significant differences for the term [μ(2)α]. Dynamic vibrational corrections to the second hyperpolarizabilities related to the dc-second harmonic generation, intensity dependent refractive index, and dc-Kerr nonlinear optical processes are also reported.