Transition metal-induced excess electron localization driving the giant first hyperpolarizability in alkaline earthides: a DFT and TD-DFT study

Abstract

The rational design of alkaline earthides with high stability and superior nonlinear (NLO) response remains a significant challenge. In this work, 3d transition metals (V–Zn) are used for the first time as donors of excess electrons to develop a series of earthides, i.e., M⁺(3⁶adz)Ca⁻ (M⁺ = V–Zn), using 3⁶adz as the complexant. Density functional theory (DFT) calculations were carried out using the ωB97X-D functional along with the 6-31 G+(d,p) basis set to investigate their electronic and NLO properties. All the complexes exhibit high thermal stability compared with previously reported earthides, with interaction energies ranging from −12.10 to −117.7 kcal mol⁻¹. Natural bond orbital and frontier molecular orbital analyses show negative charge and HOMO density over the Ca metal, validating their earthide nature. The studied complexes show exceptional NLO response with enhanced first hyperpolarizability (β_o) values up to 3.17 × 10⁶ a.u. for Zn⁺(3⁶adz)Ca⁻. The high β_o values of the complexes are attributed to the position of the excess electrons in the p-orbital of the Ca metal, which is confirmed through the partial density of state spectra. The β_o values of the complexes are further rationalized using two-level model analysis. The earthides possess small transition energies ranging from 0.67 to 2.28 eV along with reduced energy gaps. Moreover, the application of an external electric field (EEF) further increases their β_o values. Notably, the β_o value of Zn⁺(3⁶adz)Ca⁻ increases from 3.17 × 10⁶ to 1.25 × 10⁷ a.u. under an EEF strength of 0.001 a.u. This work introduces a new strategy for designing alkaline earthides using transition metals as a donor of excess electrons and will encourage experimental efforts toward the synthesis of stable earthides.