Nonlinear optical response of endohedral all-metal electride cages 2e-Mg2+(M@E12)2-Ca2+ (M = Ni, Pd, and Pt; E = Ge, Sn, and Pb)

To extend the interesting new concept of the all-metal electride, a series of endohedral all-metal electride cages 2e-Mg2+(M@E-12)Ca-2-(2+) (E = Ge, Sn, and Pb; M = Ni, Pd, and Pt) has been designed and investigated theoretically using the exchange-correlation functional CAM-B3LYP. In these electride cage molecules with excess electrons, interesting pull-push electron transfer relay occurs. The metal cage M@E-12 first pulls valence electrons from Ca atom forming a polyanion (M@E-12)(2), and then the formed polyanion pushes valence electrons of Mg atom out of its valence shell generating the isolated excess electrons that characterize this species as all-metal electrides. These endohedral all-metal electride cages display a large electronic first hyperpolarizability (beta(e)(0)) and so they could have a potential application as a new kind of second-order nonlinear optical (NLO) material. We have explored the structure-property relationships, which are significant. It is shown that, for a given central atom, the all-metal electrides with a Sn-cage correspond to the largest beta(e)(0), whereas, for a given metal cage, the all-metal electrides with Ni as the central atom correspond to the largest beta(e)(0). Owing to the two effects, the endohedral all-metal electride cage 2e-Mg2+(Ni@Sn-12)Ca-2-(2+) exhibits the largest beta(e)(0) value (16 893 a. u.). The same conclusions are also valid for the frequency-dependent b beta(e)(-2 omega; omega, omega) and beta(e)(-omega; omega, 0). Moreover, we have also explored the role of the vibrational contribution in the largest components (in x-axis) of static beta for endohedral all-metal electride cages. The vibrational contributions are significant for new all-metal electride NLO properties and therefore should be considered in the design of new NLO all-metal electrides.