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In this article we report results for the electronic and vibrational hyperpolarizabilities of ten molecules: Li@benzene, Li@pyridine, Li@pyrimidine, and Li@pyrazine; Li@naphthalene, Li@quinoline, Li@isoquinoline, Li@cinnolin, Li@quinazoline, and Li@quinoxaline. An electron correlation study shows that second-order many-body perturbation theory and density functional theory with CAM-B3LYP and M05-2X functionals give results for the electronic hyperpolarizabilities in good agreement with coupled cluster with single and doubles reference values. Static and dynamic vibrational corrections were computed through the perturbation theoretical method of Bishop and Kirtman and using a variational approach. In general, we obtained notable discrepancies between the results obtained by the two methods for the pure vibrational corrections because of the deficiency of the perturbation method to properly treat low-frequency normal modes present in the investigated systems. However, both methods give results similar to the zero-point vibrational average corrections.

This work reports the results of the vibrational corrections and frequency dependence to the first hyperpolarizabilities of the alkali-and alkaline-earth-doped boron nitride nanotubes. The electronic contributions were computed by means of the density functional theory with the M06-2X functional, and the vibrational corrections were calculated using the perturbation theoretical method and the field-induced coordinates methodology. The results for the electronic contribution show that such materials exhibit large first hyperpolarizabilities and electride characteristic. We also show that the distribution of the excess electron, which originates from the doping atoms, plays an important role in the large electronic hyperpolarizabilities (β el). Moreover, our findings strongly indicate that the effect of vibrations on the hyperpolarizabilities can be quite important and can even be much larger than the electronic counterpart.