Superalkali nature of the Si9M5 (M = Li, Na, and K) Zintl clusters: a theoretical study on electronic structure and dynamic nonlinear optical properties

Abstract

Zintl clusters have attracted widespread attention because of their intriguing bonding and unusual physical properties. We explore the Si₉ and Si₉M₅ (where M = Li, Na, and K) Zintl clusters using the density functional theory combined with other methods. The exothermic nature of the Si₉M₅ cluster formation is disclosed, and the interactions of alkali metals with pristine Si₉ are shown to be noncovalent. The reduced density gradient analysis is performed, in which increased van der Waals interactions are observed with the enlargement of the size of alkali metals. The influence of the implicit solvent model is considered, where the hyperpolarizability (β_o) in the solvent is found to be about 83 times larger than that in the gas phase for Si₉K₅. The frequency-dependent nonlinear optical (NLO) response for the dc-Kerr effect is observed up to 1.3 × 10¹¹ au, indicating an excellent change in refractive index by an externally applied electric field. In addition, natural bonding orbitals obtained from the second-order perturbation analysis show the charge transfer with the donor–acceptor orbitals. Electron localization function and localized orbital locator analyses are also performed to better understand the bonding electrons in designed clusters. The studied Zintl clusters demonstrate the superalkali character in addition to their remarkable optical and nonlinear optical properties.