Electronic and vibrational second hyperpolarizabilities of (MgO)n clusters.

In this work, we report results for the static second hyperpolarizability of magnesium oxide clusters including electronic and vibrational contributions. The comparison between second-order Møller-Plesset (MP2) perturbation theory and coupled cluster results to the electronic contribution points out that MP2 is a suitable method to compute this property. When computed at the MP2 level, the electronic contribution per atom converges to approximately 5000 a.u. Vibrational corrections were computed at the MP2 level through the perturbation theoretical method of Bishop and Kirtman. Results obtained showed that the term [α2]0,0 represents around 20% of the electronic counterpart while the term [µß]0,0 is comparable to it. Modes that contribute significantly to [α2]0,0 are those in which all or part of the bond lengths simultaneously increase and decrease, leading to large polarizability derivatives. In turn, modes that provide relevant contributions to [µß]0,0 are those in which oxygen anions move in opposite directions to the magnesium cations yielding large derivatives of the dipole moment and first hyperpolarizability.

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 [µß] 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.