Effect of the complexant shape on the large first hyperpolarizability of alkalides Li⁺(NH₃)₄M^-

The effect of complexant shape effect on the first hyperpolarizability β₀, of alkalides Li⁺(NH₃) ₄M^- (M=Li, Na, K) was explored. At the MP2/6-311 ++ G level, Li⁺(NH₃)₄M^- (M=Li, Na, K) have considerable β₀ values due to excess electrons from chemical doping and charge transfer. By comparison with the alkalides Li ⁺ (calix[4]pyrrole)M^-, a complexant shape effect in Li⁺(NH₃)₄M^- is detected. The β₀ values of Li⁺(NH₃)₄M ^- with the "smaller", inorganic, T_d-symmetric (NH₃)₄ complexant are more than four times larger than those of Li⁺(calix[4]pyrrole)M^- with the "larger", organic C_4v-symmetric calix[4]pyrrole complexant. The ratios of the β₀ values of Li⁺(NH ₃)₄M^- and Li⁺(calix[4]pyrrole)M ^- are 6.57 (M = Li), 6.55 (M = Na), and 5.77 (M = K). In the Li ⁺(NH₃)₄M^- systems, the NBO charge and oscillator strength are found to monotonically depend on the atomic number of the alkali metal anion. The order of the NBO charges of the alkali anions M^- is -0.667 (M = Li) > -0.644 (M = Na) > -0.514 (M = K), while the order of the oscillator strengths in the crucial transition is 0.351 (M = Li) < 0.360 (M = Na) < 0.467 (M = K). This indicates that complexant shape effects are strong, and consequently the β₀ values of Li ⁺(NH₃)₄M^- are found to be β₀ = 70 295 (M = Li) < 96 780 (M = Na) < 185 805 a.u. (M = K). This work reveals that the use of a high-symmetry complexant is an important factor that should be taken into account when enhancing the first hyperpolarizability of alkalides by chemical doping.