Electronic and Vibrational Nonlinear Optical Properties of Five Representative Electrides

The electrides have a very special electronic structure with diffuse excess electrons not localized on any specific atom. Such systems are known to have huge electronic nonlinear optical (NLO) properties. Here, we determine and analyze the vibrational, as compared to the electronic, NLO properties for a representative set of electrides: Li@Calix, Na@Calix, Li@B10H14, Li2 •+TCNQ•–, and Na2 •+TCNQ•–. The static and dynamic vibrational (hyper)polarizabilities are computed by the nuclear relaxation method (with field-induced coordinates and the infinite optical frequency approximation) at the UB3LYP level using a hybrid Pople basis set. In general, the static vibrational βvec and γ∥ exceed the corresponding static electronic property values by up to an order of magnitude. The same comparison for dynamic vibrational hyperpolarizabilities shows a smaller ratio. For the intensity-dependent refractive index (IDRI) and dc-Kerr processes, the ratio is on the order of unity or somewhat larger; it is less for the dc-Pockels and the electric field induced second harmonic (EFISH) effects (as well as the static α̅) but still important. The role of anharmonicity, motion of the alkali atoms, and substitution of Na for Li is discussed along with specific aspects of the charge distribution associated with the excess electron.